the “production functions” for the average and marginal productivity of land and labour in...

Jozlrnal of Agricultural Economics. 117

THE “PRODUCTION FUNCTIONS” FOR THE AVERAGE AND MARGINAL PRODUCTIVITY OF LAND AND LABOUR

IN ENGLISH AGRICULTURE.

By COLIN CLARK and J. 0. JONES.

“ There is evidence of diminishing returns, as the size of the business increases . . . are the difficulties of organising and supervising labour on these large farms greater than the manager of average ability can successfully surmount ? I am afraid the inference cannot at present be denied.”

The speaker was Dr. C. S. Orwin, and the date 1935. The occasion of this comment was a paper by Dr. Carslaw and Mr. P. E. Graves of Cambridge, delivered to the Royal Statistical Society in that year, entitled “ The Labour Bill and Output on Arable Farms.” The authors had made a thorough analysis of the carefully compiled accounts, beginning in 1931, of about a thousand farms in the eastern counties. Work on this scale, which is common- place now, was a great innovation at that time, when most of the analysis of farm accounts was on a much smaller scale.

“ There is nothing which contributes more to the success or to the failure of the agricultural business than the organization of labour, and we know very little about it, excepting for Dr. Carslaw’s work ”-again it is Dr. Orwin who is speaking. Since 1935 little analysis of the productivity of labour on different sizes of farms has been undertaken, and certainly no work on Dr. Carslaw’s scale. Apart from the routine tabulations of Farm Management Survey and Milk Cost Investigation material and A. J. Wynne’s paper’ which was based on the F.M.S. tabulations, only two specific studies of this problem appear to have been published. The first, by Sturrock,’ in which the effect of size of farm on labour productivity, as measured by work units per man, was analysed for a sample of farms in the eastern counties for 1947 and 1948. The second by Maunder,S in which the effect of size of farm on the average productivity, capacity and efficiency of various resources was analysed for a small sample of closely defined chalk arable farms for 1910-3 and 1947-9.

In addition, these two workers have also been responsible for analyses of labour productivity within the dairy enterprise.‘

The most interesting of the Carslaw-Graves conclusions was presented in a diagram published on p. 618 of the Journal of the Royal Statistical Society, 1935, on “ Relation between Size of Farms as measured by Value of Gross Output, and Gross Output per Unit of Labour.”

Wynne, A. J., “Large and Small Scale Farming in England an3 Wales today.” Journal of Agricultural Economics. Vol X I . No. I . 1954.

Sturrock, F. G., ‘‘ The Productivity of Labour in Agriculture.” Jour. PYOC. Ag. Econ. Soc., Vol. IX, No. 1, 1950.

Maunder, A. H., Size and Efficiency in Farming. h.E.R.1.. Oxford, 1952. Labour Organization i n Milk Production, University of Cambridge, Department of

Maunder, A. H.. “ Labour in Milk Production. 11.” Farm Econontisl, Vol. VII, No. 3. Agriculture. 1949.

A.E.R.I.. Oxford, 1952.

118 Journal of Agricultural Economics.

This diagram showed that as gross output rose, gross output per ;G’s worth of labour, or per man year, rose fairly rapidly. But this trend was cut off sharply once aggregate gross output had risen to ;G1,750 (at prices of the early 1930’s; the analogous figure now would be L5,810). Once total gross output had passed that point, gross output per unit of labour appears not to increase any further, with increasing size of farm. (Messrs. Carslaw and Graves draw their curve actually turning downwards for the largest farms; but this cannot be defended on the evidence available; this misconception may have arisen out of a mistaken attempt to fit a parabola to the data, when a hyperbola would have been more satisfactory.)

Many of the present audience will have no direct recollection, or an inadequate one, on the period of which Messrs. Carslaw and Graves were writing. I t is rather difficult for us now to reconstruct the anxiety of the farmer of that day, facing a fall in prices more rapid and drastic than had ever been known, with a wage level strictly fixed by law, and many of his other costs also rigidly fixed. To say that these conditions made him concentrate his attention on the productivity of farm labour would be an understatement. It would be nearer the mark to say that it was not until the anxiety of those years had driven him almost frantic that he was willing to abandon so many time-honoured practices, and to explore every possibility of labour economy. Certainly the available evidence on the trend of labour productivity, which Messrs. Carslaw and Graves began to publish for East Anglia in 1937, shows that, from the early 1930’s) it began to rise at a rate which had never been heard of before. This rise, of course, is still continuing.

Since 1940, farmers have been interested in labour productivity for quite a different reason. In the war years, money was abundant, but labour extremely hard to get and farmers therefore sought to economise labour for a different reason.

General concern with this problem is again awakening, consequent upon the abandonment of a method of price k i n g which automatically com- pensated for rises in factor prices. I t therefore seems opportune at the present time to re-open the question, and perhaps to carry a little further the sort of investigation which Messrs. Carslaw and Graves began.

The source of all material for this paper was the original returns of the Farm Management Survey of 1951-2, excluding specialized poultry and horticultural holdings only. This gives a sample of 2,354 farms of almost all types and conditions. Criticisms of the results of this survey are, of course, legion. We use it because there is at present no better material upon which to base such an enquiry. Acting on the principle that there is safety in numbers. we hope to have eliminated the effects of minor variations in methods of compiling returns, etc.

The whole body of farm returns has been analysed, without any attempt whatever to subdivide into ‘‘ types of farm ” (other than the exclusion of those entirely concerned with poultry and horticulture as mentioned above). Some may criticise this drastic departure from established convention. The authors believe that the present classification into ‘‘ types of farm,” which was probably very valuable in the pioneering stages of farm management surveying in the 1930’s) has now outlived its usefulness. The methods which have to be adopted are indeed arbitrary (some examples were criticised at the Harrogate Conference) and may actually hinder rather than help a more thorough economic analysis. Putting it another way, the authors believe that it may be possible to obtain a description of farm “ types ” valid for economic analysis, based on precise numerical definitions of certam variables, particularly land, labour and fodder input. The authors certainly do not claim to have

Journal of Agricultural Economics. 119

established such a classification. They hope, however, that they will succeed in starting a discussion which will eventually lead to its establishment.

A great deal of labour has been expended on the analysis of the data. Many attempts at classification and analysis, as is always the case in such work, proved abortive. The first result which the reader might like to have submitted to him is a simple tabulation of the gross product per man on farms of increasing total gross product, in the form of a diagram comparable with that submitted by Carslaw and Graves.

I , I 1

0 2 4 S 8 to tz I4 16 18 I

Gross Output ( f * O o O ) p r r Form. (IPS2 wlmr)

Cross Outputper ClOO Labour 1951 - z

I 0

1 20 Journal of Agricultural Economics.

For the purpose of this diagram, gross output was defined in precisely the same manner as at the earlier date (later in this paper it wil l be defined differently); and 1931-2 prices were restated in 1951-2 terms by means of a coefficient of 332.

The similarity between the present day curve and that of the 1930’s is curious, (For that matter, very similarly shaped curves can be drawn for most of the farm regions of U.S.A. in 1939, though their general level of product per man was higher.) At first one is tempted to conclude that the 1935 conclusion, about the difficulties of organising larger farms, was true then, and remains true now.

The principal conclusions of this paper are, however, that, while diminishing returns to labour do prevail in large farm enterprises, they do so to a much less striking extent than is suggested by the Carslaw-Graves diagram. We also present the more novel conclusion that exceptionally high (though not increasing) marginal returns are obtainable on those farms which at present employ a small labour force on a fairly large acreage. We also set out to analyse the marginal return to land, when acreage varies with a given labour force. I t is indeed another way of stating our previous conclusion, to say that with a given labour force the marginal productivity of land is high over a certain range of acreage, but beyond that an additional acre of land has small or even zero marginal value.

A simple diagram of the Carslaw-Graves type fails to show these more complex relationships. A larger body of data, analysed by the Carslaw-Graves methods, and taking gross product, land, and labour as separate variables, would still, in the authors’ opinion, fail to give reliable results. An analysis carried out in this manner may be gravely distorted by an equally important variable, namely fodder input.

The authors’ aim, then, is to show how output varies between certain limits, consequent upon variation in particular factors, paying particular attention to variable fodder inputs, both outputs and inputs being measured in monetary terms.

In principle, the simplest means of obtaining the desired functional relations would be to measure increase in output consequent upon the application of increments of a particular factor, holding all else constant. This might sometimes be possible in very simple cases, such as the estimation of the effect of progressive application of fertiliser on plots of land which are otherwise identical; but in general farming it is clearly impracticable. It is hardly ever possible in the case of the ordinary farm to find a single factor which can be varied independently of all other factors.

A second method, which might be expected to prove more fruitful, would be to collect a very large mass of material from a very considerable number of farms; and, having defined one’s factors, or variables, to sort out the materials for various values of the respective factors. Thus, classes of farms might be obtained, within each of which class all the factors but one would be constant. Within each class, a true production function could then be obtained, showing the relation between a particular variable and gross output. The practical difficulty of applying this method results from the fact that, with a fair number of variables, a truly enormous sample would be required if it is not to be exhausted before the end point of the progressive sub-classification is reached

We are thus left with the method of approach which will be adopted in this enquiry-to discount, by statistical methods, the effect upon gross output of the variables other than the variable with which we are concerned at a

Journal of Agricultiirnl Economics. I21

particular moment. Thus a large sample of farms is used throughout the investigation, gross output being progressively adjusted in order to offset the effects of variation in various factors. The validity of the conclusions will thus largely depend upon the effectiveness of the various methods of adjustment which are described in detail in the footnotes and appendices.

“ I am not quite happy ” (again Dr. Orwin is speaking at the Royal Statistical Society meeting in 1935) “ about the method of calculating the gross output for the purposes for which it is used in this study. To take a case: before the wheat subsidy was given to farmers there were many wheat- growers who fed most of the wheat grown to their livestock. The farmer with a gross output of 53,000 under these conditions would show a gross output very much larger when the subsidy was introduced, when he decided to take it, cash his wheat crop and buy other foodstuffs in substitution. The increase would not in any way be reflected in the demands upon his capacity as an organiser or employer of a large number of men.”

To avoid this difficulty, Gross Output is therefore defined to imlude such fodder as is produced and consumed on the farm, and to which we can apply a realistic valuation. In practice, this includes almost all home-produced fodders but grass. I t has been assumed therefore that the value of the grazing, minus the value of labour and fertiliser which has been applied to it, is a product of land, and that its price is included in rent. This is somewhat unrealistic where the farmer concentrates upon intensive grass cultivation, the grass to be grazed directly, or conserved in the form of silage; but since intensive ley farming is not widely represented in the sample, the margin of error introduced here is small.

In the relationship between fodder and gross output as defined, the value of fodder, other than grazing and silage, produced and consumed on the farm is included both in factor input and in gross output. This, of course, tends to exaggerate any basic functional interdependence between fodder input and gross output, as both fodder and gross output contain a common factor. There is no harm in this provided that the fact is borne in mind.

For each f m , other than specialised poultry and horticultural holdings, an extraction card has been prepared containing the relevant data. The definition of the variables is given in Appendix I. It is assumed that readers wdl be so familiar with the form of the primary return for the Farm Manage- ment Survey that it is not necessary to reproduce or comment upon it at this stage. The only point which may require explanation is that weights (representing the approximate money value in per acre per year) have to be attached to those fodder crops which are recorded by acreage only, without any tonnage or money returns.

ADJUSTMENT OF THE DATA.

The sample contains a large number of dairy herds of varying sizes. As it has already been established independently of the enquiry that labour productivity in dairying varies with size of herd, it was considered desirable to offset the effects of varying herd size throughout thesample, before attempting to extract the labour production function.

While there are a few large dairy herds enjoying optimally low costs, they are regrettably rare. Most of the dairy output is produced from herds of a size in the neighbourhood of 20 cows only, and it was decided to “standardise ”

122 Journal of Agricerltwral Ecolzomics.

t o this level. In other words, the analyses which follow do not give full credit t o the labour economies which a farmer may get (but which so few in fact do get) by running a herd over 20 cows. The process of standardisation is described in footnote 1. On a farm with a herd of 19 cows, for instance, one “ hypothetical” cow would be added yielding a further 600 gallons per year to output, but also using up appropriate amounts of labour and fodder.

This method however becomes less satisfactory when we have to adjust a very small herd, or no herd at all, upwards to the figure of 20 cows. Where the herd is less than 10 cows-typical on predominantly arable farms where one or two cows are kept to supply the house and to eat up the roughagei t was decided that “ statistical elimination ” of such herds would be a more satisfactory procedure. Their output was therefore dedzccted from the total gross output and adjustment also made for the fodder and labour presumed to be devoted to them.

It is now possible to cross-classify the farms according to acreage and labour, so that a table can be prepared, showing roughly the relations between gross output and labour for each acreage group; and between gross output and land for each labour group. Important variables still remain, however, the effects of which have to be discounted.

The most important of the remaining variables is fodder input. In other words, some farmers spend much more on fodder, and some much less, than the average of farmers with similarly sized farms and similar labour forces. Actually, such farmers obtain a good deal more (or less) gross output than their counterparts; and these discrepancies make the statistical results harder to interpret. It is clearly desirable to eliminate this source of distortion and we have data by which it can be fairly satisfactorily done. A graph has therefore been prepared from the original data showing the relation between

Footnote 1. Methods of adjustment of labour, fodder, and gross output

(a) for elimination of herds <I0 cows. (b) for standardisation of other herds to 20 cows, by the addition or subtraction

LABOUR ADJUSTMENT.-The relation between labour used per cow and herd size was obtained from a study by A. H. Maunder (Farm Economist, Vol. VII, No. 3). The relationship is given by the equation Log Y=2.4459-0.2288 Log X, X being the size of herd and Y labour hours per cow. One man year equivalent has been taken as 2,500 hours.

FODDER ADJUSTMENT has been obtained by a two-stage calculation. For this purpose value of grazing has been included. It is assumed that grazing alone will provide Main- tenance Rations (MR)+Production Rations for 250 gallons of milk/cow (PR.1). This amount of fodder would be obtained from 5 tons of very good quality hay, and its value has been taken as equal to that of the hay, minus the value of the labour involved in haymaking. A t 1951 prices, the value of the grazing per cow might therefore be estimated at u12 10s. (price of their hay)+:! 10s. (labour cost of haymaking/ton)] x 5 per cow=k50pe7

It is now assumed that the remainder of the production ration (PR.2) will be provided by concentrates a t BO/ton, one ton of concentrate forming the production ration for 560 gallons of milk. This figure was obtained from a curve derived by A. H. Maunder from data supplied by M. B. Jawetz (Agricultttre, Vol. 60), showing the relationship between yield in gallons per cow per day, and fodder input measures in terms of S.E. (Y=l.9411--2585X+2.3603XJ, where X is S.E. per cow per day in lb., and Y is the yield per cow per day in gallons). It is assumed that 1 ton of dairy cake contains 1,400 Ib. S.E.

GROSS OUTPUT ADJUSTMENT is the relevant value of the increase or decrease in the total milk production due to the increase or decrease in herd size. (In the case of the elimination of small herds, this is, of course, the total volume of milk produced, which is given in the original data.)

of hypothetical cows yielding 600 gallons/year.

cow.

Jozcrnal of Agricultwal Economics. 123

Gross Output (adjusted for acreage) and fodder input (footnote 2) and this chart has been used to adjust gross output to a standard fodder input for each acreage and labour group-the standardized fodder input for each group being roughly the average fodder input of the farms within that group.

From the figures thus obtained, the following sets of diagrams have been constructed, the first set (pages 125-130 inclusive) showing how gross product vanes with varying labour force and the second set (pages 131-134 inclusive) showing how gross product varies with varying acreage, the other main variables being held constant. These relationships are represented by the upper curves in the diagrams.

The effect of other minor variables has yet to be eliminated, however, before the net marginal products of land and labour can be deduced. The lower curves have thus been prepared from the upper curves by deducting for each increment of the variable factor, the values of the corresponding

A- rnoakte B . 2 0 . . c - 3 0 - - 0 - 4 0 * . c - S D . .

---- -1w L

Footnote 2. METHOD OF STANDARDISATION FOR FODDER Imurs.-Individual curves were prepared

showing the relation between Gross Output and Fodder Input for each acreage group (50 acre intervals). From there it appeared that gross output increased by about k20 per acre when fodder was held constant. A general curve was therefore prepared showing the relationship between Fodder Input and (Gross Output-LPO per acre). This curve has been used to standardise the Gross Output of individual farms to that corresponding to the average Fodder Input of the acreage group to which it belongs. It was, of course, necessary to project the fodder standardization curve backwards into negative fodder-input quadrant, in order to obtain a standardization factor for such small dairy farms as now show a negative fodder input. This oddity, which is statistically unimportant, arises because the value of the dairy cows’ grazing has been deducted from an original fodder- input estimate which did not include it. The only relevant factor, for the purpose of standardisation, is the slope of the curve corresponding to the given fodder-input figures.

For comparison a set of curves derived from the Jawetz-Maunder curve has been included, showing the relationship between fodder inputs and gross output for dairy herds.


increments of machinery services, fertiliser inputs, and minor expenses (footnote 3). To be strictly accurate the increments of gross product attributable to the increments of these minor factors, rather than the values of the factors themselves, should have been deducted. However, the amount of statistical work involved in obtaining such figures would have been considerable, and the difference is not expected to be very great in relation to the major production functions, upon which we are concentrating at present.

The lower curves in the first set of diagrams therefore represent roughly the production functions of labour for various combinations of the other factors .

The curves, in fact, show broadly the product jointly of land (including buildings), labour, fodder, seed and livestock, as currently organised in England and Wales, with land, fodder and dairy herds held constant at the stated levels, and labour force varying. The slope of the curve at any point therefore gives the net marginal product of labour at that point in relation to the given combination of the other factors-which combination is roughly the average corresponding to the mean labour force represented on each chart.

Similarly, the lower curves in the second set of diagrams show the product jointly of land (including buildings), labour, fodder, seed and livestock, with labour, fodder and dairy herds held constant, and land varying. The slopes of the curves in this case give net marginal products of land in relation to the stated combination of the other factors.

In both cases, it is assumed that variations, in livestock other than dairying stock, and in seeds, will have a negligible effect upon the principal production function. Footnote 3.

that fertiliser inputs were roughly 5 per cent. of gross output over the whole range of farms where gross output exceeded €500/year. From a cross tabulation of Minor Expenses in relation to labour and adjusted acreage, it appeared that these expenses would be resolved into a sum of L50 per farmS.15~. per acre+an amount which varies with labour input; the marginal increments of minor expenses corresponding to increments of labour being given by the following table:-

0-1 man ... f65 . 3-4 men ... €150 6-7men ... €125 1-2 men ... f80 4-5 . . . . . L120 7-8 . . . . . €120

ADJUSTMENT FOR FERTILISERS, MINOR EXPENSES AND EQUIPMENT.-It W a s found

2-3 . . . . . f125 5-6 . . . . . dl20 8-9 . . . . . €120 . In the case of machinery and eguipmcnt, from a cross tabulation it was found possible

to resolve the average total value (Closing Inventory) into a sum of roughly €120 per man+an amount which varies with land input according to the following table:-

Size of labour force. Increment of Machine y per acre. 1 man . . . . . . . . . f l per acre

3 men . . . . . . . . . f4/acre up to 200 acres

4 men . . . . . . . . . f;4.6/acre up to 200 acres

5 men . . . . . . . . . f5.5/acre up to 200 acres

2 men . . . . . . . . . €1 -6 per acre

L24/acre over 200 acres

&26/acre over 200 acres

&2.5/acre over 200 acres 6 men and over . . . . . . Aslacre up to 250 acres

Aslacre over 250 acres The annual cost of the machinery services has been taken as 40 per cent. of total

value in each case, being composed of:- (a) Depreciation 15% (b) Services and

(d) ,An allowance of 10% to allow for the fact that much of the older equipment was entered m the returns at a value based on its original cod rather than on its present- day re$lacement value.

repairs 10% (c) Interest 5 Yo

The cost of fuel has been included in minor expenses.

Journal of Agriczlltural Economics. 125.

Gross M.P. 4 5 0 450 Net M.P. 2 97.5 ZS2.S

1 I I I

Cross marginal product - L3SO Not moryinol product -c203

I I I I

I 2 3 4 /obour

(man-yoar opuivafents)

20-29 Acres Fodder t66J

126 Journal of Agriczlltural Economics.

5000

4000

2000

2oca

1000

0

9'02s output I 30 - 49 Acres Fodder C 663

I x

; r o s s W 4 5 0 4 5 0 450

Vet MJ? 2 9 8 253 228

0 f 2 3 4 5 6

50001

CmssMP 500 so0 so0 so0 Net M.R 345 24s 220 250

I 1 I 1 I 1 I

2 3 4 5 6 7 0

labour f


Eooot

Fodder C99O p s s ourput

100 -149 Acres 9000

7000 - so00 -

labour

150-199 Acres Fodder Cll46 9000-

7000-

Iqbo W


5000.

900 850 700 400 400 400 4 0 0 :OO Cross MI! , 72s 1 as3 , 46s , 400 , 400 I 400 I 400 1 00 nMtM.A 0 I J 4 S 4 7 8 9 10

labour


y r o m output

1 4 0 0 r -S49 AcrE Ddder/ I200 X


&%SOW BOO ?SO 190 7W 6.70 bx) &Sod00 #x) 64) Jx) UD UO J o o x x ) y x I 4 S O Crora MP 677 495.U7.44? .*r7.400.400.4Q). UZ.Ju.JS2. JOS. JQS.JOS.25?. Nml M P

Journal of Agricultwal Economics. 13f

4.0 s o 30 Net MI? per ocrv

I

2 Men L 700 Fodder g r o t s output

2500

zoo0

/500

/ooo

roo I S 0 zoo 250 300 0 50 ucrcs

132 Journal of Agricdtural Economics.

6000

g r o s s output 3 Men LlOOOFoddrr

- 4_Mm L I Z 0 0 F o d d y

4000 -

J S O O -

-3000 -

2500

2000 - Net M P per a c r e

3.8 5.7 4.0 2.3 -0.3 t I

0 SO /00 /50 200 250 JOO JSO U C r Q S

Net M P per a c r e 3.8 5.7 4.0 2.3 -0.3

t I

0 SO /00 /50 200 250 JOO JSO U C r Q S

N i t M P per acre 5.5 5.7 J.2 $1 J.5 1.8 -0.J

0 SO 100 I S 0 200 250 JOO JJO 400 4JO

acres


6000 -

3000 -

Fodder LIJSO

42 6J 7.5 6 J J . 0 0-6 -04 Nrt M R p r m r

0 ) ocrew 0 SO 100 IS0 Kx) 250 300 JSO 400 450

K)O

6 0 C

5OC

401

134

Po00

0000

7000

Journal of Agricultural Economics. -

/

Net M.R p r acre

I S.9 6.3 4.1 3.5 1.9 , 1.2 , Q.2 , -1.0 0 50 I00 IS0 200 250 300 350 400 450 51

oerrr

0

4

0

a- J.J 37 W 7.0 4 6 4 7 2.J 0 9 Nw MR pur mri

0 50 I00 60 ZOO 250 JOO JSO 400 4SO 500


INTERPRETATION. These latter curves thus give a broad picture of agricultural land and

labour productivity over England and Wales during the period 1951-2. It will be seen that on very small farms (as distinct from specialised

poultry, and horticultural, holdings) the return to labour is in general rather less than the agricultural minimum wage rates; and at least 50 acres appears to be necessary economically to justify the employment of a second full-time worker. The net productivity of labour increases rapidly with size of farm, however, so that on an average 370 acre farm (for example) the net product of the seventh man is well over L500, his employment thus giving a net return to the farmer of about L240. On this size farm (356-399 acres) the average net product of labour appears to be in the region of L500, as opposed to L270 in the 20-29 acre group.

It might be suggested that the increasing return to labour with increasing size of farm is mainly due to more efficient management or, in other words, that there is a correlation between size of farm and a further variable, managerial efficiency. However, there does not appear to be any independent evidence that larger farms are generally more efficiently managed than the smaller farms. Certainly further research would be needed to establish such a hypothesis.

Rather, it appears that the larger farms are, on the whole, understaffed from the economic point of view-for when we consider the land productivity diagrams, the productivity of land on the larger farms seems to be very closely related to the amount of labour employed. The marginal returns to land dwindle rapidly as an average of 50 acres per man is progressively exceeded, and on an appreciable number of the large farms, where adjusted acreage is considerably in excess of 50 xnumber of men, an appreciable proportion of the land appears to be virtually wasted. Up to this point, however, the average net productivity of land lies roughly between L5 and l 6 per acre on the medium/large farms.

Over a very wide range, where the factors of production are combined in reasonable proportions, it appears that the net products of land and labour are, from the point of view of the farmer, very comfortably above the current rent and wage rates.

The figures presented are, of course, average figures which disclose nothing about the very considerable scatter in the originals from which they have been calculated. The aim of the paper has been restricted to the presentation of a broad picture. It should certainly not be inferred that the given productivity figures are the optimum obtainable.

By selecting the more productive farms from the original sample, a much more favourable picture could be constructed, which, in conjunction with the o v e d outline, could furnish further indications of the lines along which increasing productivity of farm land and labour might be sought. But that would be another story.

136 J w d of Agricultural Economics.

MARGINAL PRODUCTS. First figure in each box-Number of farms in sample. Second figure in each box--Marginal product of labour, A per man p a year. Third figure in each box-Marginal product of land, L per acre per year.

GROSSLY UNDERHANNED (M.P. of land, 0)

450 450 UNDERHANNED 1.7 I 1.0 I 5l I 45E 1 (Low Returns to Land)

3.0 2.2

OFTINAL CONDITIONS

M.P. of labour > L400 M . R of land > 3.5 'r 375 350

m R Y A N N H D

(M.P. of labour below minimum wage rate)

0.5 1.5 2.5 3.5 4.5 5.5, 6.5 7.5 8-5 9.5 LABOUR adjusted for herd size


SUMMARY OF ABOVE TABLE. ....

GROSSLY UNDER- OPTIMAL MAXIMUM OVER- UNDER- MANNED CONDITIONS RETURNS MANNED TOTAL MANNED TO LAND (M.P. of (M.P. of (M.P. of (M.P. of Land. 0) Land, <3.5 Land, >3.5 Labour <269)

Labour >400)

No. of farms 76 211 323 1,279 206 2,095 % of farms 3 -6 10.1 15.4 61 -1 9.8 100

Acres of land 22,150 47.025 72,575 123,913 7,326 272,989 yo of land 8.1 17.2 26.6 45-4 2.7 100

~

No. of men 234 765 1,621 4,278 530 7,428 % of labour 3 -2 10.3 21.8 57.6 7-1 100

_____ -. -- .- - -

A P P E N D I X I .

GUIDE FOR COMPLETING EXTRACTION CARDS. -

General .Voles: Do not record farms which specialise in poultry or horticulture. Doubly underlined letters and numbers refer to those on extraction card,

and other letters and numbers refer to those on the Farm Management Primary Return.

A. MAN-YEAR EQUIVALENTS

These are calculated by deducting the value shown in section Labour (E), row 11 from row 24, and dividing the difference by ,6269.

row 24-row 11 - -man-year equivalents. viz’. 269 For milk producer-retailers deduct 4 man-year from the figure obtained.

B. (i) PURCHASED FEED

Section Other Expenditure (C) row 7 plus Milk fed to Livestock (Dairy Products BB row 10) valued a t 2/- per gallon.

€3. (ii) Homa GROWN FODDER EQUIVALENT Stet3 1. Acreaees eiven section CroDs (A) to be weighted as follows:- ” - . , , -

Items 1-11 and Linseed, Rye, Flax ... t o be weighted by 15 Item 12 (sugar beet) . . . . . . . . . ,, ,. ,, 6

13 (potatoes) . . . . . . . . . I , 3 . I * 4 15 (mangolds and fodder beet) ,, ,. ,, 40 16 (turnips and swedes) 8 , n t 27 17 (kale) . . . . . . . . . . . . ,, ,, 27

Items 30 & 35 (hay) . . . . . . . . . . . . 8 , #, ., 7 Item 40 (hay equivalent R.G.s) ... , I . I , I ‘7

Cabbage ... . . . . . . ,, ., ,, 30 Rape and Must&d ,, ,, 8 Vetches and Tares ,. ,. I . 15 Rape and Kale ,. I , I , 12 Cabbage and Swedes ,. ,, ,. 27 Dried Grass I , I . I , 20

... . . . . . .

. . . . . .

. . . . . . . . . . . . . . .

. . . . . . . . . . . . . . .


Step 2.-Deductions to be made for crops sold and procedure to be followed. Of the crops sold ignore at this stage sugar beet, potatoes, cultivated orchard crops, small fruits, peas green and canning. For the remainder of the crops sold (if all the quantities and yields are not given) :-*

Take the value of the individual crop sold, add or subtract the valuation difference and apply the conversion facton given below to discover the fodder potential sold off the farm.

Feed value per unit Sale value per unit (Conversion factor=

Wheat ... Barley ... Oats ... Mixed Corn Dredge Corn Hay ... Flax ... Seed Corn Dried Grass

... ... ... ... ... ... ... ...

...

... 0.50 ... 0.33 ... 0.40

... 0.40

... 0.40

... 0.50

... 0.40 ... 0.33

... 1.00

Rye . . . . . . Linseed . . . . . . Peas ... Mangolds’ . . . . . Turnips and Swedes Kale . . . . . . Grazing . . . . . . Straw . . . . . .

... ...

...

...

... ...

... ...

1-00 0.33 1.00 1.00 1.00 1-00 1 *00 1 *00

Sfcp 3.-Deduct figure obtained in Step 2 from figure obtained in Step 1.

B. (5) TOTAL FODDER B (i)+B (ii). -- --

C. TOTAL ADJUSTED AREA

Total Arable+Total Permanent Grass+Rough Grazings equivalent. (If no Rough Grazing equivalent given, assume 6 acres rough grazing= 1 acre pasture.)

D. SIZE OF HERD

Sedtion (B) row 6+row 8. Cows, Milk or breeding+Heifers in Calf (Average of opening and closing numbers).

E. M n x Gallonage of milk including milk fed to livestock, used in household, made into cheese, etc. Section (BB) row 11.

El. VALUB OF MILK

F. CROP SALES

Total value of crops sold. Section (A) row 47. Sales fvaluation difference in case of crops sold.

C. LIVESTOCK SALES

Livestock sales-purchases fvaluation change.

H. GROSS CROP OUTPUT

Home feed equivalent B(ii)+ Crops - J. GROSS OUTPUT=E+G+H

Sales

* Where physical data is complete for crops sold the steps outlined need not be followed. Instead take:-(Opening quantity + production)-(Sales + closing quantity) = feed potential.


Colin Clark:

Mr. Chairman, Ladies and Gentlemen. In these days of ever more complex research, the tendency is sometimes noticed for one participant to claim a large part of the credit of a paper where, in fact, most of the work and thought have been co-operative. In this particular case, and as thoroughly as I can, I want to draw attention not only to the work of Mr. J. 0. Jones, my co-signatory, but also to the very laborious work by Mr. Prickett, that very experienced officer in charge of the statistical records, and some contributions by others who are too modest to sign their names. I think that any expert reader will see how much we depended on some of Mr. Maunder’s reasoning and evidence, particularly the fine footnote which some of you wil l have by now digested, which makes very impressive reading; and also from Dr. Owen Price, who was a member of the Oxford Institute until last February and is now with Imperial Chemicals. Dr. Price made a lot of the e f f o e necessary to get the work set on foot. I think he would have been willing to sign his name with th is qualikation: ‘’ I think the methodology followed in this paper is very novel and the conclusions reached most interesting. I must, however, take exception to the assumptions in’Footnote 1. I am sure that the value of 550 per grazing per cow is much too high. I believe that the total feeding cost from all sources in the National Milk Cost investigation of 1951-2 was 547 lOs., L6 10s. representing grazing costs.” He then gives a table from the I.C.I. records of the land requirements of a dairy cow which are put in the neighbourhood of 2-34 acres per annum, of which :bout 1# is for her grazing, 0.64 for her hay, the rest for her feed crops. Dr. Price goes on: The same conclusion could be reached from another direction. Grass on the average farm probably provides maintenance requirements for a little under 200 days and a production ration for 250 gallons of milk. Taking into account an allowance for grazing activity, this should amount to about 19 cwts. of starch equivalent in total. Dairy cow pastures are known to yield about 14 cwts. of starch equivalent under average management conditions. Taking L8 per acre as a reasonable charge for grazing, this gives a total grazing cost per cow of somewhere about 510 to 511. If my assumptions are correct it would be worth while amending this footnote.”

Mr. Chairman. it is not only Footnote 1 which isprobably well deserving of amendment. We have in this paper set out on some very untrodden paths. What we are tempted to call our conclusions are interesting enough, but I think it would be much better to call them preliminary hypotheses which all require very careful re-examination and reworking. What I do look forward to from this conference is suggestions about how, when we come to go through the same work with a fresh set of evidence for the following agricultural year, we can improve both the methods and the results.

. I might add that Mr. A. G. Antill, the Lecturer in economic statistics in the Institute,

.has already managed to improve these statistical methods considerably over one sector .of the field. The trouble is that his results so f a r seem to be even more startling than those which Mr. Jones and I have obtained. You never know what will come next.

I should certainly point out, as every mathematician will, that the method which Mr. Jones and I have used is one of succeeding approximate eliminations and is not at all a satisfactory method in the eyes of the mathematician. It was, or it appeared to us. ,the only method which could be used in practice with the present state of OUT knowledge and with the information at present available to US. But, it is introduced, Mr. Chairman, only to be superseded at the hst possible momem.

When you read this paper, you may have thought that it was a highly condensed version of a very complex mass of statistics. Still. let US proceed to the bitter end. These highly coloured diagrams which we put before you are a condensation of a condensation. But they do set out the results in a very striking form. We have not gone out of our way to make it striking. It is the facts themselves which compel us to use that adjective. What t h e paper sets out to do, by a very involved technique, which I hope wil l be criticised, was to find the true net marginal productivity of both land and labour under varying conditions. The marginal productivity of fodder is a highly important factor, also the marginal product of one dairy cow more or less, but we decided to eliminate those in order to throw light on the true net marginal productivities of land and of labour. We are defining net marginal productivity in the most strictly orthodox text-book fashion. On the diagrams we have given the number of farms in each position. so that you can gauge ,their reliability. We must conclude that for the main run of the diagrams. except for the largest acreages or the largest labour forces, the data cluster quite well. After the paper had been printed we thought it worth while to set out all the data in a big diagram with labour on one co-ordinate and land on the other, making slight adjustments to labour for herd size. The moment that we had the data in that form, Mr. Chairman, we found that they were positively asking for this highly coloured treatment because they do split up into such highly coloured categories, to which we have applied adjectives which I do not

140 Journal of Agricultural Ecoma'cs.

think are in any way excessive. There is a category of over-manned fanzls-over-manned in the clearest Sense of the word-because the marginal product of labour is less than the national minimum wage. Those over-manned farms which are summarised here are about 10% of all the farms, only about 24% of all the land, but they carry about 7% of the labour force. Wales has its full share of them, where you get anything up to 3 or 4 men on 75 acres. Where you get less than 25 or 30 acres per man you are in a pretty clear condition of over-manning. Let me make it clear that we are excluding specialised horticulture and poultry holdings.

Now in the diagram there is a big central block to which we gave the somewhat non-committal title of " Maximum Returns to Land." The interesting point about this block is that in almost every box, the marginal productivity of land comes out at a very high figure. Our criterion is more than L3 10s. per acre, but some of them go up to k6 or Q per acre. This is the net marginal productivity of the land in the sense of what it would be worth to the farmer to pay in rent if he could get more land. I do not think I am exaggerating when I say there are a great many farmers ~$0, if they could get more land at that price, would be glad to take it. This category of Maximum returns to land " is fairly densely populated farm land, between 30 and 50 acres per man. Now the compara- tively small sector which we have described as optimum conditions, you get high returns both to labour and to land. That represents a slightly lower density. The typical farms under optimal conditions would be where you have 4 or 5 men working 200-250 acres. I d o not know whether that accords with qualitative evidence as indicating something like an optimal condition for all concerned. We get next the sector which is under-manned in the sense that land is now beginning to show low returns. That is a bit surprising, but. if you want to turn to the basic evidence you wiU see it in the individual diagrams in the paper, where the marginal product of land begins to flatten out once a certain acreage has been passed with a given labour force.

In other words, to put it in common-sense language, if your labour force is limited. extra land is very little use to you. You may, in fact, have almost a zero net producf: That is the last and the worst phase which we have had to call " Grossly under-manned because the marginal productivity of land has fallen practically t o zero. The '' Grossly under-manned " are only 3.6% of the farms, using or misusing 8% of the land, and the moderately under-manned are a further 10% of the farms and a further 17% of the land. But on the whole it is quite reassuring to see how much of the land and how much of the labour has put itself into the two central categories which we have called " Optimum Conditions " and " Maximum Returns to Land."

I must draw a few final conclusions. You might say that i t is surprising for us to cIaim that the marginal productivity of land and of labour are in fact very much higher, for most farms, than the current market prices of those factors. But, after all, the market is not in equilibrium. I think that a very large number of farms would be glad to get more land or more labour if they could get it at the current price or even considerably above the current price. We must ask ourselves finally how things got this way. Although we cannot give a single answer, I a m afraid the position we have got ourselves into hasbeen deliberately or indeed artificially brought about. The farmer in effect is suffering the nemesis of his own very remarkable influence on the course of policy which has been elterted during recent years. He has asked, directly or indirectly, to be provided with hi0 land and his labour as cheap as possible, and now, of course, he complains because the market is out of adjustment and he cannot get all that he wants.

If we go into the problem any further we inevitably bring in a certain amount of politics. (Those of you who are Civil Servants will have to appear not to listen and get on with some other task for the remaining few minutes.) I really do think that the Agriculture Act of 1947 was one of the worst Acts ever drafted. I can only conclude that it was drafted by men who were unaware of the simplest principles of economics. Not 90 much the Act itself dc j w c , but the developments which have since occurred dc facto. have meant in effect stabilising the tenure of every farmer good, bad and indifferent, at a rent far, far below the true net economic productivity of his land. I am surprised at the weakness of the Oxford and Cambridge Colleges, who ought by now to be the principal exponents of the right of the landowner, in failing to make any impression on public opinion on this matter. The very low rents which are being paid now quite apart from the question as t o whether they are just to the landowner, are doing very serious economic harm and leading to misuse of the land.

Journal of Agriculturai Economics.

DISCUSSION ON MXSSRS. CLARK AND JONES’ PAPER.

141

K . Rasnwssen: Mr. Chairman, Ladies and Gentlemen, I must say that Mr. Colin Clark and his

colleagues have given me a couple of very interesting days’ reading this paper. When I tirst saw the title I noticed the words “ production functions,” the study of which have been of especial interest to me. I just should like to ask Mr. Clark whether he would care to present one function for what he and his colleagues have been doing in this paper; it would certainly be a most complicated function.

Mr. Clark said at the beginning that he did not like the method of successive elimination. I do not like i t either. When you start successive eliminations one of the necessary steps is to go back to your k s t corrections after having made the later correction. This has not been done in this paper and in spite of the fact that the results come out more or less as text-book illustrations (worked out without any bias from actual experiments but more or less as we believe it is from deductive reasoning) I am not quite certain that the facts which have been analysed here do give substance to this latest presentation.

I should like to hear Mr. Clark explain why in trying to find the marginal productivity for land, or labour, in English Agriculture, he makes certain corrections in the internal accounts. W these corrections for fodder and for cows, correcting cow numbers to 20, or if he likes i t better down to zero, are rather arbitrary.

But is it not a normal function of the larger farm to carry more livestock? Isn’t that the natural way in which you produce more from more land especially in this country with grassland being of such very great importance? I do not see that any internal breakdown of the fodder input can exclude this complication.

I wonder if Mr. Clark in his further work might consider simplifying the concepts because, after all, as one of the persons who cosperated in working out the figures has already pointed out the corrections made to the data might be of such great importance that their influence could have changed the whole shape of the curves. As far as I can see, these corrections must have a tendency to alter the slope of the curves.

Why should it not be possible to find the net increase in value produced by the land, the capital, the labour, and may be by purchased inputs from outside (whether fodder or fertilizer, etc.), by making a simultaneous calculation of the different groups’ influence.

I do not mind the calculation of labour units made; I think it is a natural method, but could not the acreage have been used similarly, and may be as a third variable, total purchases from outside sources. I do not see any reason why purchased fodder and purchased fertilizers should be treated differently.

The corrections used by the authors in the material from these accounts will be of no importance to a typical arable farm, whereas they might change the whole picture for a typical dairy farm. I am personally very much in favour of taking only the external account into consideration in production functions.

This very arbitrary breakdown of food used for feeding the cows on the farms and of an assumed contribution from the cows to the product of the farms might cause great distortions of the original data. You have certain facts (that is if you trust the accounts) when analysing the accounts, e.g.. you have figures for what has been purchased from outside. In studies of National Income we have the contribution t o National Income from the factors working in the farming enterprise, that means the land, the capital, the labour workingon the farm (but notpurchasedfeedingstuffs, fertilizers, fuel, etc.). This agricultural contribution to National Income can then again be presented either inclusive or net of depreciation of machinery and buildings.

I should like to ask Mr. Clark whether he considers that a simultaneous equation analysis of a production function is preferable to successive steps like this without the essential step for successive analysis of correcting back to the first correction. I wonder whether successive eliminations like this, in fact do not add to the work so that a simultaneous analysis (which can be made mechanically) is cheaper, and from the method point of view preferable.

It has been mentioned in the paper that the actual variations in gross output and net output have been considerable. I understand that in the sixth t o the tenth diagrams inclusive the numbers given at each point refer to the number of farms that have been averaged in obtaining these points. I should like to point out that in that case there is a rather daring extrapolation in certain of these curves and 1 think it is a little misleading when looking a t the curve for the net marginal product to see all the points marked on the line as all these points have been taken from the hand-drawn line above minus some smoothed-out figures for certain expenses. I and certain readers of this paper have been wondering where these exact points, all on the line, have come from.

142 Journal of Agriczcltural Economics.

With these remarks, I should like to say how much I have enjoyed this paper, mainly because of the problem it is tackling. But personally I should hesitate in drawing too serious political conclusions from these curves. I think that after a little more thought, Mr. Clark might not jump to too strong political criticism based on this analysis.

I should like to see the analysis being carried further, making certain minor--or. maybe better, major-improvements in the methods of calculation. That might bring most valuable results because the problem dealt with is no doubt one of the most important problenls for agricultural economists to analyse. Perhaps I ought to say for agricultural economists with a specific interest in statistics, because I believe there will be other very important tasks for agricultural economists who do not care much for statistics.

C . Antill: I do not think that the methods used will meet the main objections which are raised

against the classical regression I think, moreover, that the methods of t t e paper have a defect to which conventional regression analysis is not subject.

Granted that we are concerned with a single equation, that the independent variables are not affected by errors, and that we choose the right form of function for fitting, a straightforward multiple regression analysis will give us unbiased estimates of the required constants.

In the same circumstances the methods of the paper, though perhaps interesting as a preliminary exploratory technique, wi l l not give unbiased estimates if, as is obviously the case with this material, there exists a degree of correlation between different input factors.

To show the practical consequences of this, I have made an analysis of the whole of the data for the acreage group 100 to 149 acres by ordinary regression methods.

The results obtained are appreciably different from those of the paper. My object was to fit, by least squares, a function of the same general form as that of

the authors, and to show that the resulting marginal productivities are appreciably different from those of the paper.

For this purpose I have accepted certain variables as defined in the paper; they are:-

rocedures as an analytical tool in this field.

X, = Gross Output Adjusted for Herd Size. X, = Labour Adjusted for Herd Size. X, = Acreage. X, = Fodder Adjusted for Herd Size.

The authors do not indicate the general form of the production function which they envisage. I have, however, made certain inferences about the form of function which is implicit or established in that part of the argument which leads to #he estimate of grossmarginal productivity of labour for a partkular acreage group.

For the purpose which I have speci$ed the production function is assumed or shown by the authors to have the following characteristics:-

(a) that it is the sum of a number of functions, one function for each input factor considered;

(b) that it is linear in land; (c) that it is linear in labour. Thc function which I have fitted to the data was therefore of the general form

x i =I Ax, + Bx, + f(x4) all variables being measured from their means.

A quadratic term in X, was at first included ,in the fitted function to allow for the suspected curvilinearity of the fodder effect, but the departure from linearity in fodder was found to be well below the 5 per cent. level of significance. The function finally adopted was therefore linear in fodder and the regreession equation on this basis was:-

It should be noted that, even if the reality of a curvilinear fodder effect were admitted and allowed for, the coefficients of x, and x3 would be altered by only negligible amounts to 661.5 and 9.571 respectively.

The regression estimate is L663 with standard error L2S. The estimate given in the paper is &550 (see the ninth chart in the paper). The methods of estimation which were used appear then to have caused appreciable bias.

X~ = 6 6 3 . 5 ~ ~ + 9 . 5 2 5 ~ ~ + - 9 5 2 6 ~ ~

J O U Y H ~ of Agricultural Economics. 143

The regression estimate is 50-9526 with standard error LO-065, i.e. for each &1 of fodder input we get almost precisely €1 of output.

I am reluctant to interpret this last result because I have misgivings about the nature of fodder as it is defined for the paper and because I do not know to what extent the cited relationship is a mere reflection of the identity of the values of home-grown fodder which appear simultaneously in input and in output. A t present I do not feel able to make a judgment on these two points.

In conclusion, I should like to emphasise that I am not estimating the gross marginal productivity of labour in the 100 to 150 acres class as L663 rather than 5550, for straightforward regression methods are themselves inadequate to this task though they are free from the particular possibility of bias which I have indicated. One of the possible snags in this field is the possibility that through technical necessity or convention there may be pairs of input factors, say factors A and B, such that the volume of input of factor A determines the input of factor B, the observed deviations from perfect relationship being attributable to errors of measurement, recording, etc. In such circumstances, there may be no such thing as a marginal productivity of factor A in isolation from factor B, or, if there is potentially such a thing, the available statistics will give us no valid basis for estimating it. We may then, none the less, be led by an uncritical application of regression analysis to estimate a production function involving A and B, to differentiate it partially with respect to A and B, and to call the results, quite wrongly, the marginal productivities of factors A and B respectively.

In the mid-nineteen-thirties, Ragnar Frisch devised his method of coduence analysis as a tentative solution to the problems which arise when it is sought to estimate relationships within a set of variables which may in fact contain several subjects of variables each of which is governed by a distinct relationship.

I did, in fact, apply this method to data for farms largely engaged in milk production in Lancashire, Cheshire and Wales, using a conventionally defined gross output value and with wages bill, rent, and value of equipment as the principal inputs. By Frisch’s criteria, the estimated marginal productivities in thk material were all gravely suspect.

I believe that Koopman’s method of weighted regression, supplemented by more recent devices for estimating the number of linear relationships probably existing within a given set of variables, might offer a more hopeful approach than confluence analysis. But, to apply this method, we need estimates of the variances and convariances of the errors of observation, etc., affecting each of the variables. I do not believe that these can be estimated satisfactorily from the data. Is i t possible for those well acquainted with the technique of analysis of farm accounts to estimate roughly the relative frequencies with which errors of plus or minus varying proportions occur in the values of the main variables recorded on the annual record for the individual farm. and to guess at the sign and magnitude of any correlations which seem likely to exist between the errors affecting different variables?

Professor E. Nash: Mr. Chairman, I should like to associate myself with the welcome the previous speakers

have given to this paper and say that I have been most interested both in the paper itself and in Mr. Clark’s very bright and entertaining remarks in presenting it to us. I have also been very interested in his highly-coloured diagram or illustration displayed in front of us.

Might I begin with a question about that diagram. I take it that what is plotted on the diagram is the estimated marginal product of the two factors. Does the fact that the line bounding the orange-coloured zone tends to bend over mean that as a farm gets bigger you ought to have it more densely equipped with labour?

Colin Clark:

smaller acreages. The fact that it bends is not significant. . . you can take it as roughly linear for the

Professor E. Nash: I see. Well, I am sorry to have asked perhaps a stupid question which is simply due

to the fact that we did not have this diagram before us in the paper. But I have one or two further observations about the paper itself, though they are moreconcernedwith the method than the conclusions. The conclusions are full of meat and will repay long reflection, if we accept them, but before we do so I should like to ask a few questions about some of the methods.

144 Journal of Agricul twd Economics.

My observations will be much less technical than those to which you have just listened. First of all, I was rather surprised and puzzled over what I cannot help thinking is the curious definition which is given t o gross output in this analysis, and I was not at all convinced by the reason given in the quotation from Dr. Orwin. I can perfectly understand what Dr. Orwin meant when he made those remarks in 1935, only afew years after the wheat subsidy had been introduced, because the effect of that subsidy was then fresh in every- body’s mind. What the subsidy did was, of course, to introduce very suddenly a great disparity between the returns from wheat and other cereals and a great disparity also between the returns obtainable from wheat if you sold it, and the return you could get if you fed it on your own farm. If you had a set of records going back before the period of the wheat subsidy, the introduction of the subsidy would, of course, seriously distort the comparison between those farms which were benefited by this subsidy and other farms who could not, or for any reason did not, take advantage of it. But does MI. Clark think that anything of that sort applies today? Is there any comparable disparity in the returns now available from different cereals, or anything else which would have the same sort of effect in distorting the relative validity of the output figures in their ordinary sense from one farm to another? I should like to hear any further observations which he or his collaborators might have to make on that point.

I also wonder whether the treatment adopted did not, like some of the factors already mentioned by Mr. Rasmussen, possibly introduce some error into the results. What is done is to add back to the gross output the output of the home-grown crops used as fodder, but that is unfair to the man who uses purchased feed and also to the man who uses grass. I cannot say that I see any convincing reasons for doing this. I should have thought the treatment adopted likely to have a differential effect on farms of M e r e n t sizes for, after all, the small livestock farms wiU on the average be more dependent on purchased feed than the larger farms, and therefore their output wi l l suffer in comparison with that of the larger farms by this treatment.

The other point I should like further information about concerns some of the adjustments, particularly adjustment L F o d d e r Adjustment. I found the curve given in Footnote 2 a bit puzzling because as far as I could measure its slope with a ruler it seems to be well above unity throughout. This, of course, is not a marginal product curve, because the product is adjusted for acreage and herd size, but not for other things, so that what the slope of the curve represents, I take it, is the increment of product got from an increase of fodder, plus the other things that increase when you increase. fodder, keeping, however, your herd size and your acreage constant. But the slope seemed to be rather more above unity than I should have expected and moreover it struck me as odd that the slope should increase as the fodder input increases. Does that mean that there is an increasing return to the input of fodder?

It occurs to me in this connection that a much simpler method of dealing with t h i s problem would have been to use the net output instead of the gross output, that is merely to deduct the value of the fodder from the gross output. No doubt this method would have been imperfect, but would it not have been an alternative to this very complicated adjustment for fodder?

M. B. Jawctz: I believe Professor Nash wanted to make one further point, at least he discussed it

w i t h me. It concerns the adjustment of the herds to a “standard ” of 20 cows of 600 ut. Now, we know from milk costings and other sources that, generally, output

Ep::iust%ighest on the small farms, falling with increasing farm size and increasing again on large farms, say, over 400 acres. High yielding herds are associated with production functions different from those of low yielding herds. Holding the herds constant at an “average” level can only disclose production functions pertaining to that level. Those for lower and, particularly, for high yields may be vastly different.

There is one point which I consider very important-the sub-classification into types of farming. Mr. Clark, rightly. points out that the Ministry’s classification defies its own purpose. It does not really represent the type of farming groups, but what are termed ‘ I type of farming areas.“ Nevertheless, type of farming groups can be analysed out from them quite precisely. Mr. Clark suggests working out a classitication according to certain arithmetical factors as a basis for economic analyses. But he makes no suggestion as to details. Well-defined “ farm types ” have quite distinct numerical characteristics which differ from those of other ‘ I farm types.”

I happen to work now on a different line from that presented in tonight’s paper, but there is a certain similarity. I investigate total inputs a t various levels of production in various type of farming groups. I have been lucky working in Wales where the definition of the types of farming is sharp. I find quite a striking difference in the slopes of the curves


depending on the type of farming as defined by the analysis. As total input curves usualiy run more or less parallel to labour input curves I believe that classification into types of farming would be very important in determining the production function of labour; and that one cannot lump all the British farms together, as, depending on type of farming, results may be vastly different.

There is one more point which I should like to stress: it,& this bringiy to a common denominator of the home-grown foods that are consumed by the acre and therefore not measured. This weighting is given in Appendix I under " B (ii) " Home Grown Fodder Equivalent.

I think this is throwing out a very important variable. We have here, purelynumerical paper inputs of fodder factors. The element of luck, as Mr. Rasmussen would undoubtedly remark, and the elements of skilful management and technical farming have been eliminated. The fact that a man had 8 acres of kale does not necessarily mean that he is more efficient or less efficient than someone else. We are bound to ask: what sort of kale did he have?

We are bound to ask what use he made of that kale. This, of course, would come out in the input-output relationship if you eliminated these fodders without doing away with their influence, as has been done in this paper. so that the result will make itself felt in each case. Bringing them to a common denominator did eliminate very important variables, be it the factor of management, or luck, or technical skill in agriculture.

D. K. Britton: I should like to take up the point which Mr. Rasmussen raised when he questioned

the use of the term " production functions " to describe the contents of this paper. I do not think this is a mere quibble about words; it goes to the root of some of the criticisms which we have already heard.

As I understand it, the calculation of a production function is an exercise designed t o show the effect on production when a factor of a number of factors together are varied. For example, if on any given farm all factors but labour were to remain constant and we studied the change in production when labour increased, we might call the result a production function; or if we kept all factors but land constant we could obtain a production function which would tell us whether there were diminishing returns to land.

Now it seems to me that in this exercise which we are discussing, after classifying the farms into size-groups of labour and of land respectively, the authors have made the assumption that the figures produced for successive size-groups are representative of what would take place if an individual farmer moved from one position to the next-shall we say from 6 men to 7, or from 200 to 300 acres.

In reality, each size-group of farms has its own production function. The authors of the paper, having represented each of these by a single point (evidently some kind of average) and then joined these points, suggest that the resulting cuwe is a general production function. I would have thought that this paper would have been more correctly described as a study of size and efficiency, or size and productivity-size being measured either by labour force or by area-than as a presentation of production functions.

Other research workers who have done a great deal of study of production by size of farm (area) or by size of business (output)-I think, for example, of Mr. Blagburn's work- have been rather careful not to use the phrase " marginal " to suggest that a comparison of one size-group with the next is an indication of what would happen on an individual farm if the farmer intensified in terms of one factor and kept the others constant. The whole apparatus of marginal analysis is concerned with what happens on an individual enterprise or group of enterprises when factor inputs are changed in that enterprise or those enterprises. It cannot draw upon evidence from two different groups operating a t different levels of factor input, without making the vast assumption that in all other respects except factor input the groups may be regarded as identical.

I think this is important, for the following reason. Let us take land. We have the data classified in terms of different size-groups of land, and we have been shown the apparent effect on production if you move up from one size-group to another. Now I would have thought that marginal analysis, and the production function with which it operates, had as a basic postulate that the successive increments that you add are homogeneous. However, data on land values and rents and so on would certainly not suggest that as you move from 200 acres to 300. or still more from 300 to 500, the land that yo; take in is of the same quality and of the same value per acre as the initial " increments of land which you were using. I should like to ask the authors of this paper whether they have taken that fact into account and set it aside as being of negligible importance, or whether they have gone ahead assuming that they are adding homogeneous increments of land when passing from one size to another?

146 Journal of Agricultural Ecmmics.

If we take labour, there may be little fault to find with the assumption that if you add one man to a labour force of 6 the “ commodity ” which you are buying will be very similar to the 6th man, the 5th man, and so on. But I think that if we look at the lower end of the labour size-distribution-at the farms with only one or two workers and where the family element is a big part of the total labour supply-we cannot even make that assumption. I take it that in the present paper labour input includes an allowance for the labour of the farmer and his wife and so on? Well now, let us suppose, as I believe is often the case with the Farm Management Survey records, that the farm family labour estimate is perhaps, shall I say, more nominal than real-at any rate, the farmer does not really count all the hours he works in the way that he counts the hours he pays for. Then the successive increments of labour which you are introducing in passing from one to two to three and 80 on up your labour size-groups are not homogeneous additions at all. Indeed, the farmer and his wife may be prepared to work for less than the marginal wage, and that may be the explanation of the findings of the study with regard to labour. So I should like to ask the authors to consider whether they are not too readily making the assumption that additional increments are homogeneous. Are they assuming that if you take sufficient numbers into account you are, in fact, eliminating this bias? It seems to me that you just cannot make that assumption.

In the h a 1 page of the paper, where we find the “interpretation.” there is the surprising suggestion that “there does not appear to be any independent evidence that larger farms are generally more efficiently managed than the smaller farms. Certainly further research will be needed to establish such a hypothesis.”

Well, Mr. Chairman, may I respectfully suggest that if all the effort which has obviously gone into this paper had been put first into the solution of this problem, to determine whether larger farms are generally more efficiently managed than smaller, the results of the present study might have been very different, because I believe that some kind of adjustment would have been made for the management factor. As far as I have been able to follow the paper, there are adjustments for cows and fodder and so on, but not for management, as size goes up. I think evidence could be produced-&. Rasmussen has some data for Denmark, for example-to show pretty strongly that efficiency of management does increase with size of farm, if only because of education and other assets which are found to be possessed in a much more marked degree by the farmers who have the larger farms than by the farmers who have the smaller farms. In any case, can we not accept as a rough and ready test of efficiency the net profit of the farm, and do not all our Farm Management Survey results strongly indicate that, on this basis, large farms are more efficiently managed than small?

J. H. Kirk:

The conclusion from Mr. Clark’s paper which I think has been so disconcerting to economists here, is that there appears to be a substantial number of farmers who are just being very silly because by taking on a few more men or a few more acres, which can often be done, they may substantially enlarge their profits. But is it really necessary to look t o the machinations of the N.F.U. or the vagaries of Cabinet Ministers to discover why farmers do not do that? Is there not some simpler explanation of the facts, if indeed they are facts?

I would imagine that the production function on any individual farm is bound by the nature of the case to be discontinuous. The 7th man might indeed produce a marginal profit of k600, but the 8th man might only produce about L200.

One sort of situation which could produce that result is the very obvious one in which the limiting factor on the whole farm is the buildings. A more generalized explanation would be that the farmer has approached the limit of his capital resources or of his borrowing powers.

It is. of course, not very difficult to find explanations of that sort so as to account for the facts, if indeed the facts are correct. I am bound to say that the previous contributions to this discussion have left me under a pretty considerable doubt as to what are the facts that we have to explain or explain away.

C. H. Blagburn:

As some of you may have ,noticed I am not a statistician and that may therefore be the reason that I am more inclined to admire the ingenuity of the authors’ attempt to solve this problem than I am to be appalled a t the statistical heresies which I daresay it contains. But there are just a couple of points which appeal to me as being slightly doubtful and I would like to put them to the authors of this paper rather in the form of questions.

Joerrnal of Agricultural Economics. 147

They tell us that with regard to what they call the other minor variables the effect of which has yet to be eliminated, that is to say, increments of machinery services, fertilizer input and so forth, while to be strictly accurate the increments of gross products attributable to the increments of these minor factors rather than the value of the factors themselves should have been deducted. What, in fact, they have done is to take the value of the factors themselves.

Colin Clark: We took what we thought were the increments.

C. H . Blagburn: But you say that you have deducted the values of the factors themselves rather than

the increments attributable to them. You say that the difference is not to be expected to be very great. Is that a fa i r conclusion? I would have thought that the increment to be expected from a given increase in fertilizer input, for example, might very materially affect the productivity of the labour employed and similarly with regard to increases in the use of machinery. I would have thought that the effect of those factors would have been just as important as the effects of increases in fodder input, for example, and I would have thought that to have adopted this method therefore-simply to deduct the value of the input rather than to try to attempt to arrive a t the increment due to it-would very much falsify the result.

The other point is one in which the authors may have been quite statistically orthodox and correct. I don’t know. But what I would like to know is whether the approach is realistic. We are told that what the curves show “ is broadly the product jointly of land, labour, fodder, seed and livestock, with land, fodder and dairy herds held constant a t the stated levels and labour force varying. The slope of the curve a t any point, therefore, gives the net marginal product of labour at that point in relation to the given combination of the other factors.” Well, no doubt that is statistically correct, but is it realistic? In other words, do farmers in fact take on an extra man and do nothing else? Don’t they, for example, in the case of the dairy farmer, take on an extra man in order to be able to keep more cows. In other words, you get an increase in the number of men and an increase in the number of livestock and an increase in the fodder input, and I cannot help thinking that any results which emerge from the kind of treatment where you assume that one factor only is varied and the others remain completely stationary is going to give unrealistic results. I would like to know whether that is 90 or whether th is is simply due to my non-statistical mind?

W . N. Beckett: There are similar dif6culties in crop forecasting, a type of work I was engaged on for

many years overseas. I would like to make one observation and ask one question. Criticisms have been made of the method of using successive elimination, and

suggestions that multiple regressions and that type of analysis might be more useful. It has been pointed out that you might refine the methods by regarding land not as homogeneous but qualifvlng it in some way. No doubt i t is possible to refme the methods, but it is well to remember that it is possible to over-refine one’s methods and to make them much more complex than is merited by the data. It is the same sort of thing as using a sledge hammer to crack a nut. or a laboratory balance to weigh the crop of an acre of land. If this type of work is done, its great merit, and to me its,great interest, is that it provides pointers. The question I would like to put forward is: Cannot you produce something much more crude than these methods, not much more comp!ex? ” I am thinking of what I would call, for want of a better word, the “score card. You are familiar with the additive method in photography for calculating your exposure. You use various factors, time of day, type of subject, light, etc.; you have a simple range for each factor from which you judge the number, add them up and get your exposure. It is possible to do that with a crop. I tested this additive method in the tropics for estimating the yield of cocoa, using various factors. The basis was more trial and error than statistical analysis, and it could not be expressed as a multiple regression, but it gave the results. What I would like you to do, using this data is to give us a simple additive formula that would give the individual farmer something that he could use. You could have as many factors as you like because at the end you have to deal with a few numbers only.

What a successful businessman, or successful economist for all that, does is to use whatever data he has. If he has a statistical office that can chum the stuff out he may even use electronic computors, but in practice he uses many more factors than are in fact dealt with statistically: his own brain subconsciously handles more complex data than the most elaborate type of electronic machinery yet built. Whether he gets the right answer is the only criterion of his success.

148 JourBal of Agricultural Economics.

R. Dudman: I should like to ask Mr. Clark how far he thinks he is entitled, statistically, to call his

paper “ Production functions for the average and marginal productivity of land and labour in English Agriculture? ”

In the first place, I question whether any valid function can be calculated except over a time series, since we all recognize the very narrow limits within which farms in this sample can be regarded as comparable units. In the second place, if you deduct the Welsh farms from this sample, you are lef), with a sample represen*g about 0.8 of 1 % of English farms. Mr. Clark has set aside certain minor defects in the F.M.S., but its non- representative nature is recognized as a major defect. Even if this were not so, I should be interested to know what standard error Mr. Clark would be prepared to tolerate from a sample as small as 0.8 of I % ?

Even if we ignore the fact that there is no logically justifiable connection between sample fact and population inference unless the sample is representative, these calculations deal, to some extent, with the question of farm size; the F.M.S. provides an even smaller sample of small farms-rather less than 0.6 of 1 % . If I am wrong in thinking that only calculations over a time series would give valid functions, I still believe that MI. Clark’s sample, even ignoring its non-representative nature, is far too small for the purposes to which he has put it.

Sir James Scott Watson: I was eavesdropping when Mr. Clark was speaking to others present, but I was very

interested in the remarks about rent that he made just a t the end of his talk. There is, I think, wide agreement that a large proportion of our farms are grossly under-rented, and it has often been said that this circumstance is affecting the efficiency of farming-by keeping in business a lot of people who would be better out of business. I think we would all agree about that. Of course, it has been long recognized that there is atime-lag between prices and rents during periods of inf la t ionthat prices rise first, wages second and rents last. Sir William Dampier put all that in mathematical terms which even I could understand. But it does seem that the present lag in rents is quite exceptionally long, f a r longer than one would have expected from the study of past inflations. Why should this be? I have been curious enough to ask quite a number of land agents and landowners why they do not put up rents. The answers vary, but some ofthem are quite simple. If you talk to a large landowner who is paying 19/6 in the A he will say that if he doubles the rents he will gain not ten thousand pounds but ten thousand sixpences and that this is just not worth all the unpleasantness that it would cause.

Then there is, in some cases, another way out: one can wait until one has a farm with vacant possession and sell with vacant possession, knowing that the break-up of the estate, in the long run, is inevitable. Another and different motive until quite recently has been patriotism. The landowner knew that it was important to increase the output of food from his land, that his tenants, by and large, were short of the capital that was needed for expansion, and rather than deprive the farmer of perhaps A200 a year by way of a reasonable rent increase, he made a gift to the tenant in order to help the production effort. I admit also, of course, that there is a great deal of sheer sentimentality in the outlook of the older landowners; they say: I ‘ Old John is not very bright; he is making a pretty middling job of his farm but, after all, his family have been with my family for four generations and I haven’t the heart.” Well, you see, that isn’t a thing that you can put in terms of simple economics.

The lag in rents has nothing to do with the Agriculture Act of 1947. Arrangements for going to arbitration about farm rents have been in operation far longer than that. Arbitration is still available; it is still open to either party to say that the rent is too high or too low and have somebody in to say what the rent should be.

I am bound to say that I think the ideas of many valuers have been too low; they have taken the view that current prices were unlikely to last and that it was well to be on the conservative side.

It is a complicated business. What is certain is that the adjustment of rents to the change in the value of money has been slower than in times past.

A . R. Bird: The chart before us presents a method of economic classification of British farms.

I wonder whether it would not be interesting and useful if we were to see, within each of those economic groups, a further classification based on the present physical ty-pes of farming. We could then see to what extent the varying frequency distribution of, say, dairy

Journal of Agriculturd Economics. 149

farms or arable farms is related to variations in the use of resources. It may be shown, for example, that the greatest under-employment of labour occurs in a particular group of small dairy farms. Possibly a detailed tabulation of findings of this type could be made.

R. H. Tuck: I have never calculated a production function myself or even partly calculated one;

nor is the task of calculating one a region upon which I frequently concentrate my thought and reading. Consequently, the questions I now have to ask might very well strike those who have, as a little naive. I hope, however, you will be tolerant if I ask a few innocent questions in a spirit of some humility, in the hope of benefiting more from what I have before me.

The first point I was going to raise I think was dealt with to my satisfaction, though possibly not to the authors’, by Mr. Rasmussen in opening the discussion. I was worried about the logic of, for example, standardizing fodder intake-a process which involves being able to isolate the effect of fodder variations upon output from the effect of variations in other inputs before you can carry out the standardization. I had better make that clear. In order to estimate how a change in fodder has influenced output (so as to be able to correct for it) you have first of all to know how much of any given variation in output observed on given farms is attributable to fodder changes and how much to changes in the other factors like land and labour, which are involved.

In short, to use the terminology of this paper, you have to know the marginal product of fodder, which requires correcting first for the other variables as. for example, land, in the same way as it was necessary to correct for fodder before you could arrive at an estimate of the marginal product of land. So, in order to get to the correction for fodder, you must first of all find the marginal product of land, in order to get which you first require to know the marginal product of fodder and so on. In short, there is a certain circularity about the process.

I gather that the answer to this is, that this process should indeed be carried on ina circle and that the circle would in fact turn out not to be a circle but a convergent spiral. But in the present case, the circle did not even go more than one time round.

A second point that I want to ask about is this: to what entities do these marginal products apply? I presume that these entities are in fact strictly defined, ideal farms, falling within certain size ranges, having on them certain numbers of cows (I gather it is either 30 or some number like that, 30 or nought), and being standardizedin other respects, notably in respect of their intake of fodder. Now, take one particular size group for which if we are to accept these estimates we know the marginal product of, say, labour, and suppose that th is applies to a farm falling in the 200-249 acre group having a certain number of cows upon it and making use of a certain labour and fodder intake. Is it to be assumed that the marginal product of labour on another farm in that same size and labour group but having more cows, is the same? In short, does the marginal product of labour, say, vary with the level of use of other factors in the same way, ‘as it is assumed to vary with changes in land use? I found in the contribution of Mr. Antill in his assumption of a straightforward linear function, the implication that it is presumed not to vary. If I under- stood him correctly and if the function he defined is in fact assumed, then the marginal product would be the same for a particular factor whatever happens to some of the other factors. However, my purpose in raising this point is to emphasise that unless the assumption is made that marginal products which apply to a farm of a certain stipulated size and type continue to apply unchanged when these definitions are relaxed, then it is not to the generality of farms in the country to which these marginal products apply, but, as i t seems to me, to certain limited types of farms, in fact rather conventional farms having the characteristics clearly defined in the paper.

My next point has also been raised (from a different point of view, I think) by other speakers though I would still like to ask it in my form.

How far is it valid in these proceedings, these ‘‘ production functions ” proceedings, in which I am now including not only those described in this paper, but also the other approaches which have been referred to-I am still worried as to how far it is legitimate to take one farm which has a certain gross output and to compare it with another farm which is identical in all respects except that a given factor, say labour, is present in greater quantity, measure the gross output on both of them and then to say that the difference between the two is attributable to the extra labour used.

For, even when I say identical in all respects, there is one respect in which they must differ, namely, they cannot have the same man upon them guiding their activities. Farm A and Farm B are identical, say, except in their use of labour. It might well be that the data available might prove that Farmer B could obtain off Farm A a certain amount more gross output given certain extra labour. It is by no means clear to me that the same data would prove that the original farmer, Farmer A. could do the same thing and achieve the same results.


In short, I want to know whether any estimates of marginal productivity could conceivably be made by any analysis however refined in its logical bases which would cater for anything other than an ideal availability of managerial skill. Can one, in fact, estimate the potentialities of adding labour here and labour there or this other factor here and there, given the actual human material which is available on these various units and which, after all, we have to use to exploit them and given the fact that these individuals are certainly diverse in kind, as they are in any collection of human beings.

I now have one final question to ask. Would these estimates, or the similar, more elaborate estimates, envisaged by various speakers and by the authors themselves, would they ever be thought of as superior to those reflected (in conditions of free competition) in the prices for the various factors paid by operating entrepreneurs, who presumably have to make precisely such estimates in gauging what sort of bargain they will strike.

If it is thought that these calculations could be developed to the pitch that they would be more precise in a comprehensive way, even in individual cases, I should be sorry. I have to admit that straight away, I should be sorry. But the implication would be that some serious amendment of the autonomy given to individual entrepreneurs ought to be contemplated. If, however, it is not felt that such precision is within our grasp, it might st i l l be urged that they might be more accurate over certain ranges, say, :f farm-type or farm-size. In that case, in situations in which, over limited fields, precedence of precision,” if I might put it that way, is given to estimates of marginal productivity obtained in this way, as opposed to estimates made by the individual practitioners themselves, can I record a plea that the subsequent action is, not to enter into the field of allocation of resources between different productive units but rather to concentrate one’s effort upon examining what defects in the institutions have led to any particular irregularity which might come to light.

MY. J . 0. Jones: Mr. Clark pointed out a t the beginning of this meeting that we were notpresenting

you with established conclusions which were cast iron and quite secure from the barbs and arrows of politicians, economists, farmers and statisticians. Rather we have presented you with some tentative conclusions, which have been reached after a certain amount of thought, in the hope that you would apply more thought to it and tell us how we might improve the analysis. I must say that we have been amply rewarded in that respect. We have had excellent suggestions and I believe that even many of the questions which were asked in supposed levity were very pointed and were directed at very real targets. I a m not going to try to answer all the points that have been raised, partly because hfr. Clark will come after me and he can pick up the so f a r unconsidered problems, if only because I do not remember all the points that have been raised. But the discussion, I think, has really separated itself into two parts: a general discussion of methodology and criticism of details. I do not say that one part is any more important than the other. But first, let us look at the methodology, and here I believe Mr. Antill and Mr. Rasmussen. in their respective ways, have put the main oints. Other speakers have also seized on some of those points and have amplijied them; owever, I will confine myself to Mr. Rasmussen and Mr. Antill’s remarks, or at least to some of those remarks, in the hope that in doing so I will also cover the surrounding issues.

Mr. Antill put forward the hypothesis that the conclusions were biased, and proceeded to verify his hypothesis by doing a multiple regression analysis. I think Mr. Clark and I would readily concede that there is bias. I can point to just the place where the bias arises and that is in the fodder standardisation curve. -4s Mr. Rasmussen and Professor Nash have pointed out, all that has been kept even approximately constant here is acreage and size of herd. Labour, machinery and everything else vary in every waypossible. Well, so let it be. As Mr. Rasmussen and Mr. Tuck have mentioned, if one decides to analyse problems in this manner, one has t o start off with a crudity somewhere-and this is the initial crudity we started off with. Of course, it does not mean that we have to stop there. We could take the first approximations to marginal productivity curves for land and labour, and use these to obtain a better fodder standardisation curve. Using that better fodder standardisation curve we could then get a more nearly accurate estimate of the marginal productivity of labour. I strongly suspect that the figure which we would get by doing this would not be very different from the one which Mr. Antill produced.

If you look at Mr. Antill‘s figure for the marginal productivity of land, you will find that it is, within statistically acceptable limits, the same as the result which Mr. Clark and I obtained. We might, I think, claim that it is so because we have adjusted for land. Well, we can do the same thing for labour. Therefore, although hIr. Ant9’s criticism can legitimately be directed against the figures we have offered, the objection could be avoided to some extent without abandoning the method. We did not get round to doing this adjustment certainly, and one of the reasons why we did not get round to doing it was

Joeernal of Agricultural Economics. 151

that up to a very short time ago we were getting these present figures. Had we tried to refine them any further we would not have had a paper of any sort to present to you. We felt that the figures which were arrived at, crude as they were, were at least worthy of putting forward for your consideration; and that is what we have done.

Mr. AntiIl, and I think Mr. Rasmussen also, would like to adopt the alternative course of attempting to solve the whole problem simultaneously; but I believe that while this is an approach which appeals to the mathematician, there are snags t o it. If you are going to attempt a conventional multiple regression analysis you have to decide upon the formof your function. Of course, the conventional analysis suited Mr. Antill‘s purpose because we had already shown the form of the function in this particular case to be linear. We had arrived at that conclusion, we had not anticipated it-and that is the strengthof the adopted method as opposed to the conventional regression method. With the regression method one has to assume that the function will be of a certain type. One has to hit upon the form of the function. This might be easy enough when we are dealing with material of a type which is familiar, and where the variables have been suitably defined, and are known to be independent. But in this case we have two sorts of decisions to make-we have to decide whether or not the overall form really is additive and we also have to decide upon the form of each of the functions themselves. Well, they might be linear-it would be very convenient if they were-but we cannot take i t for granted. They might be cyclical- as someone suggested with regard to labour. They might be linear in the logarithms-and so on; so that the attractiveness of the multiple regression analysis-at least from the point of view of the ordinary economist, who wants to get something reasonably workabl- the attractions of that method have their counter-balance in the mathematical problems which arise. Certainly there are statistical devices for the selection of the least inappropriate forms of function from the relatively small number of farms,yhich Iend themselves to this purpose; but it is possible that several different forms will fit ” given data equally well from a statistical point of view and would yet lead to very different interpretations. In other words, in selecting the form of the function we often beg the very questions we wish to answer. I would say that both methods should be combined at this stage in our progress. Mr. Antill and I have already had very useful conferences on the subject and I feel quite sure that no matter which side we approach from-and there is a lot of work to be done on this-we will find a common meeting ground in the middle. I should not be at all surprised if, when we reach that spot, we will h d Mr. Colin Clark already sitting on it!

With regard to the details, the first objection was raised by Dr. Price in relation to our fodder adjustments. Now, I think Dr. Price and we are slightly at cross purposes here. Dr. Price has concentrated upon the cost of grazing, whereas it was our intention to use. purely as a standardisation factor, the value of the grazing. This could not be anopen market value obviously, because grazing has no open market. It could only be a value to the particular farmer. We reasoned that the nearest we could get t o this was to take the market value of a quantity of hay which would have the same fodder potential. We reckoned that it would take about 5 tons of hay to give the average amount of fodder per cow which would have been provided by grazing on a normal farm in a normal year. It just happened that in this particular year hay was very expensive-it was L12 10s. a ton. Therefore, we deducted the labour costs of the hay and that lef t us with a figure of L50 per cow. This i s what a farmer would have had to pay to replace his grazing, and for the purpose in hand, it appeared more appropriate to take this estimate of the value of the grazing rather than the actual cost which the farmer had incurred in obtaining it.

Both Mr. Tuck and Mr. Britton stress the importance of management and imply that failure to take this vital factor into account is a grave defect in the present analysis.

I believe that there is a basic confusion here. Certainly differences in management lead to dserences in efficiency; but management is not a variable of the same type as land labour and fodder. It is the job of management to combine these basic variables so as to maximise their joint productivity. The efficiency or otherwise of management wil l therefore be revealed in an analysis of the productivity of the basic factors in combination- provided, of course, that these variables are suitably defined. We certainly do not claim to have reached adequate definitions and doubtless the difficulties of doing so will limit the usefulness of this sort of analysis; but even at the present crude level there is evidence, for example, that many larger farmers are grossly inefficient in their use of land. Thus, i t is not necessary to investigatc rnanagerial efficiency independently, or as a preliminary to this type of analysis--a- - ‘ Britton seems to suggest. In so far as our analysis of the productivity of the basic I J L L ~ A is successful, the degree of efficiency of management will come out in the wash.

Regarding Mr. Blagburn’s point about the unrealism of supposing a farmer to increase one factor alone, I think the difficulty is not basic, but anses from the practical necessity of having to present dynamic concepts-such as relative rates of change in inputs and outputs-in static terms. The combination of diagrams which we have presented do in fact allow one to anticipate to some extent the effect of simultaneous changes in land, labour


and fodder in varying proportions to each other. It is hoped that future effortswill facilitate the predictions of the effects of such simultaneous changes to a much greater cxtent.

I am not a t all sure myself that production functions can be evolved only from time series, as Mr. Dudman has suggested. Perhaps Mr. Clark will have something to add to that. Certainly a time series might give us a more homogeneous sample; but i t also introduces difficulties of its own. In time we hope to include this aspect.

Regarding the problem of the quality of land: certainly the quality of land does vary and it does not follow because a farmer takes on more land he takes on more land of equal quality; but again we were using the F.M.S. returns which gave us no means for assessing this. Therefore, if the work was worth doing at all we just had to take what we were given, making a rough adjustment for rough grazing and assuming that land is on the whole homogeneous otherwise. I know that from many points of view this is quite unsatisfactory, but when we are concerned only with the very broad picture we feel that possibly it was not too bad. We would, of course, like to have better materials and we would like to have better methods. We hope at least that the discussion which has arisen will stimulate the obtaining of both.

Colin Clark: I enjoyed Mr. Tuck’s contribution and I certainly do not claim that this sort of

laborious analysis can get a better result in most cases than the free judgment of the market. It is only because the free market in land has been so grossly interfered with that we had to make any statistical judgments of this nature a t all. With labour it is different; labour is an article which, in the opinion of the great majority of economists, cannot safely be left to the free market; that is to say, to individual bargaining, least of all the labour of rural workers, who are in a weak bargaining position. Therefore, some form of trade union bargaining, if not national intervention, is necessary where labour is concerned. The strength and skill with which trade union leaders press their case is rather a chancy matter. I think there is no a priori presumption that free negotiation by trade unions will get a socially optimum price for labour.

I think Mr. Jones met a point which I might restate in another way. When we are dealing with fertilizers, and the minor costs, we have in effect assumed that their marginal product was equal to and fully measured by their price. In so far as we are not justified in making that assumption, we have, as Professor Nash and Mr. Blagburn suggested, somewhat overstated the marginal productivity of land and labour. I am glad to think that it is that way, because we certainly got the results rather high. This method of successive eliminations is only a first stage of attack on the problem. I think we can claim that it has given us some interesting hypotheses to work on. There have been several criticisms of our methods, but nobody seems to disagree with the broad results. We have, I think, discovered some interesting and important non-linearities, which must be taken as a warning by the next orthodox statistician who makes an attempt at simultaneous solutions by Koopmans’s method, or whatever method is finally adopted.

The last and most awkward question, raised by Professor Nash particularly, is about fodder. Why could not we, Professor Nash asks, work on net products or debiting the price of fodder, or ignoring the fodder produced on the farms?

I think that in many ways Professor Nash’s method would be better. The reason why one hesitates to use a net product is because there you are, in effect, doing just as you are with fertilizers-you are assuming that the true marginal product of the fodder is measured by i ts market price. I think in a year like 1951-52, when many farmers still had difficulty in getting the quantities and qualities of the fodders they would have liked to have got, it is unsafe to make that assumption. Indeed, the evidence which we have been working on so far seems to show that there is a definite non-linearity in the returns to fodder. One questioner asked whether we were claiming that there were increasing returns in the use of fodder, which is contrary to the general expectation. I can only ask you to take one more look a t the third diagram. I am not implying there is any final answer. I t is a most perplesing diagram. Wh3t we have done is plot the Maunder-Jawetz results side by side with our own. For a given size of herd, as you see, there are fairly sharply decreasing returns to fodder, once you have passed a certain point. On the other hand, the farmer is always free to enlarge his herd or to buy. (Professor Nnsh: “ But you standardise the herd! ”) Y e s , we have tried to standardise the dairy herd but not the other stock, and some of the other stock, particularly pigs, yield a much flatter curve. If Mr. Antill’s results are true, and f l spent on fodder only adds ,/1 to the product, that is rather a startling conclusion, and carries the implication that many farmers may be spending too much on fodder. But I am not solving this question. I am only asking you to leave it open for a while. The returns to fodder may be less linear, and less in relation to its costs, than w e first supposed. Until we have answered that question, we cannot adopt the simple device of measuring net oritput by regression equations.

the “production functions” for the average and marginal productivity of land and labour in...

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