estimating the seasonal marginal products of labour in agriculture

ESTIMATING THE SEASONAL MARGINAL PRODUCTS OF LABOUR IN AGRICULTURE1

By S. K. NATH

Introduction THERE have been a number of studies to determine whether the marginal product of labour in agriculture in a country like India is positive. Some of the more recent and better known of these have been by Desai and Mazumdar [4], Raj Krishna [9], and Wellisz et al. [19]. The last two found the estimated coefficient of a man-year of labour to be positive, while the first found it to be not significantly different from zero in the sub-sample of farms which did not hire any labour. Of course, these studies analysed data for different parts of India, and from different years. In our opinion, these and other such empirical investigations of the marginal product of labour ignore a characteristic of backward agriculture which is of funda- mental importance: it is that in such agriculture the response of agricultural output to inputs is quite dissimilar in different parts of the year. This is because in crop production firstly, it is vital to do the right thing at the right time-and the right times for various operations come and go rather quickly; and secondly, only during a certain proportion of the total number of days in a year is the response of output to labour, and certain other inputs, keen. A great deal of work needs to be put in on such days. Such days, which are not all necessarily consecutive, constitute the busy season. Then there are the rest of the days of the year when the response of output to labour is sluggish; these constitute the slack season.

Indeed the seasonal variation in agricultural activity has been frequently noted. Thus Mazumdar [13] uses it to explain why input of labour and output per acre may be higher on the smaller farms. In his article on surplus labour, Sen [16]-having shown that according to his model more labour hours per acre will be used on the peasant farm resulting in a higher product per acre than on the capitalist farm-discusses how recognizing seasonality does not spoil that result. Similarly, a number of other authors-such as Clark and Haswell [3], Hansen and El Tomy [7], Mabro [1 1], Nakajima [14], Robinson [15], and Wellisz [18]-have noted and analysed one or other implication of seasonality in agriculture. But when it comes to estimating the marginal product of labour, it has invariably been the practice to ignore the seasonal differences. Similarly in discussing the uses to which these

1 I am indebted to the Ministry of Food and Agriculture, Government of India, for making available the data on which this study is based. Part of the research expenses were financed by Nuffield College, Oxford. I am grateful to Ian Little, Maurice Scott, Farouk Elsheikh, and members of a seminar at Warwick University for useful comments. Earlier stages of research were assisted by Jeremy Corbett.

376 ESTIMATING SEASONAL MARGINAL PRODUCTS

estimates are put, e.g. calculating a shadow wage rate, the implications of the seasonal variation are never noticed.

It is argued in this paper that in production function studies of crop production in the less developed countries in particular, the busy-season and the slack-season labour inputs need to be included as separate, independent inputs-each having a different marginal product. For, while for most industrial processes (and perhaps also for total farm production of the highly mechanized, mixed farms of the advanced countries) it is reasonable to assume that the response of output to variation in inputs in general -and in the labour input in particular-is the same in different parts of the year, such an assumption is unwarranted regarding an agricultural sector which is characterized by low intensity of cropping, little or no mixed farming, and labour-intensive techniques. Even in such agriculture there are some inputs which are used only in the busy or the slack weeks of the year, so that the annual amount used of such an input at a farm represents the amount used in one or the other season. Regarding such inputs, then, no special difficulty is raised by the usual specification of the production function to be fitted to annual data in a cross-section or time series study.

Labour hours are used in the two seasons in varying proportions on different farms. The slack-season and the busy-season labour inputs are substitutes for each other to some extent. Now if Y represents the value of the annual total crop yield, Lb the labour hours used in the busy season, and L8 the labour used in the slack season, then our arguments imply that the seasonal labour inputs need to enter the production function as separate inputs thus: Y = Y(Lb, Ls....).

If the production function is so conceived then though the marginal product of the busy-season labour (9YI@Lb) and the marginal product of the slack- season labour (&Y/&Ls) are both defined, the marginal product of the annual (total) labour is not directly defined because annual labour is not an argument of the production function.

Of course, the suggested specification requires data on the hours of busy- season labour and the slack-season labour used in a year. We are lucky in having data from which, on some reasonable assumptions, the seasonal labour inputs can be derived. However, regarding some other inputs (e.g. bullock labour) which are used in both seasons, our data do not allow us similarly to derive the seasonal amounts. For these inputs we are forced to follow the usual practice of using their annual totals in our regressions.

Data, specification, and results Our data come from the first year, 1967-8, of the three-year study in the

Economics of Farm Management in the Ferozepur district of the Punjab.

S. K. NATH 377

This study is directed by Professor A. S. Kahlon of the Punjab Agricultural University, Ludhiana. The data are collected through the cost-accounting method for 150 holdings-10 each from a sample of 15 villages. The average size of a holding is 12*5 hectares, with a standard deviation of 8-4. The holdings are divided into five size groups, below 6, 6-9, 9-14, 14-24, and 24 and above, hectares. The 150 holdings covered about 11 per cent of the total cultivated area of the villages.

Of the total cropped area in the district, 32-3 per cent was under wheat, and 50*6 per cent under cereals as a group (including wheat). The other major crop of the area is cotton. The percentage for American cotton was 10*3; and for Desi cotton, 4*5. Fodders accounted for 15 per cent. Ferozepur contributed 21*4 per cent of the total wheat production of the Punjab and 15*6 per cent of the state's cotton production. Punjab in its turn is a major growing area in India for these two crops. The percentage of net irrigated area to area sown was 62 in the district in 1967-8. Most of the irrigation was by canal water, but this was an uncertain source of supply compared to old-style wells and tube wells.

In 1967-8, 89*7 per cent of the cultivated area of the 150 holdings was self-cultivated, 2*7 per cent cash rented, 05 per cent was fixed-kind rented, and 7*1 per cent was share rented. There was a marked similarity in the tenurial system in the different size-classes of farms. Of the total cultivated area, 98-3 per cent was sown area, and only 1 5 per cent currently fallow. The average intensity of cropping for all holdings together was 130 per cent. There was some but not a strong tendency for the larger farms to have lower intensity.

Our dependent variable in each regression equation is the money value of all crops which include Mexican wheat, Desi (or traditional) wheat, paddy, sugar-cane, cotton, fodder and by-products, etc.

Turning to the independent variables, we consider first area sown. This equals total area under cultivation minuLs current fallow land. We have tried to make this variable homogeneous over the different farms. Data provide figures for actual rent paid and imputed rent for each farm. We consider rent per hectare to be perhaps the best single measure of the quality of land that the data provide. In order to make units of area homogeneous between farms, we worked out district-level rent per hectare, and individual farm rent per hectare: by dividing the latter figure for each farm by the district-level rent per hectare we obtained a set of weights for all farms. These weights were then used to adjust the figures for area sown.

Every holding in this sample has some irrigation. Irrigation may be by old-style wells, tube wells, or canals. Separate information is not available about the amount of each different kind of irrigation used by a farm. But we are provided with figures for irrigation expenses which include irrigation


charges (actually paid or imputed) and depreciation on irrigation equip- ment. Like irrigation expenses, the figures for other inputs, except labour, are in terms of money value.

We now consider the data about labour. We are provided with hours and money value per year for family labour, permanently hired labour, and casually hired labour. Money value of family labour was apparently imputed on the basis of the market wage rate for like labour. Permanently hired labour and family labour are available for work throughout the year. Casual labour is hired on a day-to-day basis as there is need to supplement the permanently available workers. Of the 150 farms, 49 did not use any permanently hired labour, but each of the 150 farms used some casual labour. The mean value, for the sample, of the ratio of the casual labour to total labour hours was 0*26, with a standard deviation of 0 13.

The quality of labour in each of these categories may vary from farm to farm. In order to make the hours of labour more homogeneous within these categories, we weighted the hours of each kind of labour on a farm with the ratio of the estimated wage rate on that farm of a certain kind of labour to the estimated district-level wage rate. We assume that these adjusted hours of each of the three categories of labour are homogeneous over the three categories, i.e. that the personal efficiency of the typical family worker is the same as the personal efficiency of the typical permanently hired worker or that of the typical casually hired worker. This assumption seems justified because the estimated district-level wage rates for the three kinds of labour are almost identical.

We assume that casual labour is used only during the busy season. This seems a reasonable assumption for two reasons. First, this is what the farmers themselves say. Secondly it seems reasonable to expect that on a typical slack day the marginal real cost of applying labour of permanent workers comes into equilibrium with their marginal product at a level lower than the slack-season reserve price of the labourers who might be casually hired. A casual worker is unlikely to accept a wage lower than a living wage for work even on a slack day-not least because he usually has some work, albeit low-productivity work, of his own to do during the slack weeks. That work might be making music at weddings and other such celebrations, tending his own small plot, and so on.

We have added together the hours of family workers and permanently hired workers because both family workers and permanently hired workers are available for work throughout the year. We refer to this amalgamated input as permanent labour. Of the annual total of permanent labour hours that the data thus provide us with, some were utilized in the busy season and some in the slack season. The data do not give us any guidance on how to divide this total into the parts utilized in the two different seasons.

S. K. NATH 379

However, if we are willing to assume that the proportion (say A) of the total permanent labour utilized in the busy season is the same on all farms, and further, make an informed guess as to what this proportion is, then we can for each farm apportion a part of the annual total of permanent labour hours to the busy season, and another part to the slack season. We have tried three values of P in our calculations: 0-25, 0 5, and 0 75. As we shall see, the estimated coefficients for the seasonal inputs of labour are not very sensitive to a fairly big change in the value of Pi.

Once we have estimated the number of hours of permanent labour which are utilized in the busy season, we add them to the casual labour hours for each farm to arrive at the labour input for the busy season. This assumes that casual and permanent labour hours are perfect substitutes in the busy season. Since only permanent labour is utilized in the slack season, the labour input for the slack season is given by whatever is left of the annual total hours of permanent labour once those hours which are assumed to be utilized in the busy season are subtracted.

Since we shall be using a single equation estimation procedure, we are assuming that there is no joint determination of inputs and outputs; i.e. the factor amounts used are assumed to be exogenous. We also assume that the factors used and the outputs produced by different members of the sample are homogeneous and that they all have access to the same technical knowledge.' We tried linear, Cobb-Douglas, and transcendental specifications of the production function. It will be noticed (see Tables I and II) that in the odd-numbered regressions, labour hours used in the slack season and labour hours used in the busy season are included as separate independent variables; but for the sake of comparison in the even-numbered regressions we have followed the usual practice of adding together all labour hours used during the year, and including them as one independent variable which is described as undifferentiated total labour hours for the year.

We first tried some simple linear regressions (which are not reported here). We found that area sown (A) is fairly highly correlated with a number of other variables; the residuals of these regressions also indicated that the variance of the disturbance was roughly proportional to area sown. There- fore, we normalized all the variables for area sown in all regressions. Once we had obtained the regression coefficients for the linear equations, we multiplied each side of the regression equations by A, so that the regression coefficient of 1/A became the estimated constant, and the constant became the estimated coefficient of A. The results included in Table I for the linear regressions were obtained in this way. In the double-log equations,

1 These are the standard assumptions of the estimation procedure we shall use. It is not our purpose to review these assumptions here. For excellent discussions see Griliches [5] and Heady and Dillon [8].


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the specification chosen implies that we have restricted the sum of the elasticities with respect to all inputs (including area sown) to be equal to one. This procedure seemed justified because we first estimated two regression equations in double logs without normalizing any variable for area sown. In the first of them P was assumed to be equal to 0-25; and, in the second, 05. The sums of input elasticities worked out as 1H1 in each case; in neither case was the sum significantly different from 1.

Equations (5a), (5b), (5c), and (6) are the transcendental production function-a generalization of the Cobb-Douglas function suggested by Halter et al. [6]. Though it too, like the Cobb-Douglas, restricts the elasticity of substitution between any two inputs to be equal to one, it does, unlike the former, permit the elasticity of output with respect to an input to vary. Thus it permits the marginal product of an input to increase, decrease, and be constant over different stages of production; whereas according to the Cobb-Douglas, marginal product of an input increases, decreases, or stays constant in all stages of production. This property of the transcendental production function is obviously greatly desirable for our purposes. In regressions (5a), (5b), (5c), and (6) all inputs and outputs have again been normalized for area sown. In these equations we grouped inputs other than labour and area sown, into two categories: those used mainly or only in the busy season, and those used in both the busy and slack seasons. The two groups were: 'Seeds, etc.', which includes seeds, manure, fertilizer, and insecticides and pesticides; and 'Total Capital

Notes to TABLE I

1. i = proportion of total annual hours of permanently available labour which is assumed to be used in the busy season.

2. The numbers in parentheses are the calculated standard errors of the respective coefficients. An asterisk indicates that the estimated coefficient is significant at least at the five per cent level.

3. Regressions (la), (lb), (ic), and (2) are linear; the other four regressions are in double logs. 4. All the variables have been normalized for the size of the area sown. 5. The dependent variable, total crops, is measured in money value.

Notation to TABLE I C = constant L' = hours of labour used in the slack season Lb = hours of labour used in the busy season Lt = annual total of hours of labour used A = area sown in hectares B = value of bullock labour used in a year S = value of seeds used in a year

M = value of manure used in a year F = value of fertilizer used in a year I = value of insecticides and pesticides used in a year

Kw = interest on working capital for a year Kf = interest on fixed capital for a year D = depreciation on buildings for a year R = irrigation expenses for a year E = miscellaneous expenses for a year


TABLE II

Regression results for total crops: Ferozepur district, Punjab, 1967-8 (transcendental specifications)

(5a) (5b) (5c) (6) ==0.25 3=0.5 3=0.75

a 6.20* 6-20* 6.18* 6.49* (0.196) (0.20) (0.021) (0.13)

Log L, -0-014 -0-016 -0-017 (0.012) (0.012) (0-013)

Ls -0-0002 -0-0008 -0-0026 (0.00034) (0 00065) (0-0016)

Log Lb 0.089 0.086 0-084 (0.047) (0.047) (0.047)

Lb 0.00077 0-00083 0.00087 (0.00048) (0.00047) (0 00046)

Log Lt 0 0035 (0.0088)

Lt 0-000013 (0 0000070)

Log S* 00022 0-0022 0.0022 0-0026 (0-0021) (0.0021) (0.0021) (0.0022)

S* 0.0018* 0.0018* 0.0018* 0.0018* (0.00036) (0*00036) (0 00036) (0 00038)

Log K* 0.027 0-027 0-027 0.030 (0 0082) (0 0082) (0 0082) (0 0084)

K* 0-000056 0 000053 0.000051 0-00022 (0.00016) (0 00016) (000016) (0-00016)

F test 30-36 30-28 30-22 33-61 R2 0.61 0.61 0-61 0-57

Notes to TABLE II 1. /3 = proportion of total annual hours of permanently available labour which is

assumed to be used in the busy season. 2. The numbers in parentheses are the calculated standard errors of the respective

coefficients. An asterisk indicates that the estimated coefficient is significant at least at the five per cent level.

3. All the variables have been normalized for the size of the area sown. 4. The dependent variable in these regressions is the logarithm of the money value

of the total crops.

Notation to TABLE II C = constant Ls = hours of labour used in the slack season Lb = hours of labour used in the busy season Lt = annual total of hours of labour used S* = the sum of the values of seeds, manure, fertilizer, and insecticides and pesti-

cides used in a year. Log S* equals the sum of the logarithms of the foregoing inputs

K* = the sum of the annual values of bullock labour, interest on working and fixed capital, irrigation expenses, depreciation on buildings, and miscellaneous expenses. Log K* equals the sum of the logarithms of the foregoing inputs

S. K. NATH 383

Services', which includes value of bullock labour, interest on working capital, interest on fixed capital, irrigation expenses, depreciation on buildings, and miscellaneous expenses. Where these inputs enter the equations in their logarithms, their logarithms were added together to form the groups.

Table I gives the regression results for the linear and the double-log specifications; and Table II for those of the transcendental specifications. The odd-numbered regressions include the labour inputs for the busy and the slack seasons as separate inputs. The proportion of the annual total of permanent labour hours which is assumed to be used in the busy season, i.e. A, is equal to 0*25, 0.5, and 0 75 respectively in equations marked a, b, and c.

It will be noticed that the estimated coefficient of the busy-season labour input is positive and highly significant each time. Moreover, it is not affected by the different values given to /P. We expect positive marginal product in the busy season because at that time of the year all the farms in our sample hire some casual workers; there would be little economic sense in hiring them if the marginal product of labour in the busy season was not positive. On the other hand, the estimated coefficient of slack-season labour is always negative and mostly not significantly different from zero. But in regression (1c) it is both negative and significant. This casts doubt on either the realism of assuming Pi = 0.75 or the suitability of the linear specification of the production function, or both. But we are not surprised when the estimated coefficient of slack-season labour turns out to be not significantly different from zero. Though it has commonly been assumed that on a farm where some casual labour is hired, the marginal product of labour cannot be zero, that reasoning in fact applies only to the busy- season marginal product: there is no reason why even on such farms the marginal product of labour in the slack season may not be zero. For, on a typical day in the slack season, if at the point where the marginal product of labour becomes zero, the marginal disutility of effort by the permanent workers of the farm is also zero (or perhaps negative), then application of labour hours during the slack season may well be carried up to the point where its marginal product is zero.'

The other coefficients which are significant in all or nearly all regressions are those for bullock labour, seeds, fertilizer, insecticides and pesticides, interest on working capital, and irrigation charges. It is interesting to note that in the double regressions the inputs with the highest estimated elasticities are seeds, irrigation, busy-season labour hours, and working capital.

In regressions (2), (4), and (6), we ignored the seasonal variation in

1 For further development of this point, see Uppal [17], who, however, does not distin- guish between the two seasons.

4520.3 C c


activity, and included the annual sum of labour hours as one of the inputs. Its estimated coefficient is positive and significant, but rather small, in regression (2); while in the others it is positive though not significantly different from zero. If we had tried regressions of only this kind-with annual labour hours added together as one input-we might well have inferred from the results that in our sample the marginal product of labour was either very small or not significantly different from zero. But, as we have argued above, the results of regressions where slack-season and busy- season labour inputs enter as separate variables are more meaningful. They suggest that the marginal product of labour in the slack season was zero in our sample, but that of labour in the busy season was positive.

Results of the transcendental specification are reported in Table II. They are broadly similar to the previous results. Each coefficient of slack- season labour is negative; and none is significantly different from zero. All the coefficients of the busy-season labour are positive, though it is only the coefficient of the logarithm of an input which needs to be positive in the transcendental production function for the marginal product of that input to be positive. However, only one of the four coefficients estimated in connection with the busy-season labour in regression (5a), (5b), and (5c) is significantly different from zero at the 5 per cent level; the others just fail to be so. Few other coefficients are significant in Table II. This suggests that the transcendental specification does not fit the data so well.

Of the three specifications, the Cobb-Douglas production function then seems to fit the data best. We have used the results of this specification to estimate the seasonal marginal products of labour. However, since none of the estimated coefficients of the slack-season labour in the Cobb-Douglas specification is significantly different from zero, we have not used them to derive any estimates of the marginal product of the slack-season labour. The estimates of an hour of the busy-season labour obtained from regressions (3a), (3b), and (3c) are, respectively: Rs 1-5, Rs 1X3, and Rs 0O8. Each of these estimates is based on a different value of 3, the proportion of annual permanent labour that is assumed to be used in the busy season. In the absence of any firm basis on which to choose among the different values of 3, it is difficult to decide which of the three estimates is the most accurate.

Some policy implications An estimate of the marginal product of labour, for the year as a whole,

is meant to tell us the impact on the annual output if a unit of labour (say an hour or a man-year) is withdrawn for the year as a whole, everything else remaining the same. Our arguments imply that for a traditional agriculture marked by a strong seasonal variation in activity, the annual marginal product of a unit of labour is best estimated indirectly by first estimating

S. K. NATH 385

the seasonal marginal products of labour. Once we have these seasonal estimates, we can sum them to obtain the composite marginal product' for the year as a whole; but we cannot obtain an estimate of this annual (composite) marginal product directly from the production function, because when the production function is specified to take note of the seasonal nature of agriculture, annual labour input does not figure as an argument of the production function.

The results of our analysis are also relevant to the controversies about the existence of surplus labour and to the problem of estimating the shadow wage rate of labour. Regarding the concept of surplus labour, Sen [16] has convincingly argued that the criterion for its existence should be whether total agricultural output declines or not when one worker is withdrawn and compensating adjustments in work supply by those who are left behind are permitted. In other words, examining just the marginal product of labour by itself is not enough. With the help of a model in which family welfare depends on income as well as leisure and in which equal sharing of work and income is assumed, he shows that even with positive marginal product of labour, if the withdrawal of some labour takes place from a family farm, total output will be maintained at the same level if for those who remain on the farm marginal rate of substitution between income and work (or what he calls the 'real cost of labour') is constant over the relevant range. Our analysis suggests that at the time of the year (i.e. the slack season) when such adjustments by the remaining members of family are possible, there may be little or no need to increase the amount of effort supplied when some labour is withdrawn (for that season) because the marginal product of labour for that season is low or nearly zero anyway: and that at the time of the year (i.e. the busy season) when the marginal product of labour is positive and high, people on the farm are likely to be working rather near their physical maximum on a typical day (that being the reason why in some regions even the smallest farmers hire some casual labour on busy days)-so that the marginal 'real cost of labour' is not likely to be constant.

The theoretical issues involved in making estimates of a shadow wage rate have been recently surveyed by Lal [10]. He mentions many problems which must be taken into account in estimating a shadow wage rate. Seasonality of agricultural activity is another such problem. Indeed, if the marginal products of labour are as strikingly different in the different seasons as our findings suggest, then for such regions there may well be a

1 As far as I can ascertain, Mazumdar [13] is the first author to have used the term 'composite marginal product'. However, he did not develop the argument to the stage of pointing out that it cannot be directly estimated by including total annual input of labour in the production function to be estimated. Indeed in his later joint article [4], there is no mention of the concept.


need to estimate different shadow wage rates for different parts of the year. Our analysis suggests that the disguised unemployment in agriculture may be mainly seasonal. Thus there may be significant social advantage in encouraging certain kinds of mixed farming, cropping schemes, and cottage industries which would help provide more employment in the hitherto slack weeks. It is worth recalling that according to Mahatma Gandhi this was one of the strongest arguments for protecting and encouraging cottage industries in India. The findings also support arguments for providing seasonal employment in nearby towns for agricultural migrants during the slack season.' In an agricultural sector which is similar to our sample, if some labour does move out for the whole year (including the busy season) then our analysis shows that agricultural output is bound to suffer unless labour substituting methods and machinery are simultaneously introduced for the busy season. It is possible that some of the current technological developments in Indian agriculture-e.g. improved seeds, more regular supply of water, and fertilizers-will tend to increase the number of crops that can be grown in a year, and would thus increase the number of busy days in the year.2 On the other hand, if such developments did not increase the number of days on which ploughing, sowing, watering, weeding, spread- ing fertilizer, harvesting and threshing, etc., need to be done because of more crops per hectare per year, and other reasons, but, instead only raised the marginal product of labour on a typical busy day without increasing the number of such days, they would make the contrast between the busy season and the slack season even more striking without reducing the relative duration of the slack season.

Our analysis also highlights the need to gather and publish agricultural data differentiated according to the agricultural seasons. In a farm management survey in particular, daily records are kept of the inputs used, etc. It would be extremely useful if a weekly, or at least monthly, tabulation of them, which also indicated the kind of work done, was made available.

University of Warwick

1 It would seem that this already happens to some extent. See Agarwal and Varshney [1]. Some of the examples of seasonal industries they give are: production of sugar, coffee, and tobacco products; processing of cotton, jute, and wool; making bricks, tiles, and salt; and manufacturing ice, aerated and mineral water, and umbrellas.

2 There is evidence that this is already happening to some extent. See Billings and Singh [2].

REFERENCES 1. AGARWAL, B. L., and VARSHNEY, R. G., 'Seasonal variations in employment in

India', Economic and Political Weekly, Bombay, 29 November 1969, pp. 1845-9. 2. BIMLINGS, MARTIN H., and SINGH, AJAN, 'Labour and the green revolution-

the experience in Punjab', Economic and Political Weekly, Review of Agriculture, Bombay, December 1969, pp. A221-4.

S. K. NATH 387

3. CLARK, C., and HASWELL, M., The Economics of Subsistence Agriculture, ch. 6, 4th edn., London, 1970.

4. DESAI, M., and MAZUMDAR, D., 'A test of the hypothesis of disguised unemployment', Economica, 1970.

5. GRILICHES, Z., 'Specification bias in estimates of production functions', Journal of Farm Economics, 1957.

6. HALTER, A. N., CARTER, H. O., and HOCKING, J. G., 'A note on the transcendental production function', Journal of Farm Economics, 1957.

7. HANSEN, B., and EL TOMy, MONA, 'The seasonal employment profile in Egyptian agriculture', Journal of Development Studies, July 1965.

8. HEADY, E. O., and DILLON, J. L., Agricultural Production Functions, Iowa, 1961. 9. KRISHNA, R., 'Subsistence and family farms: some theoretical models of sub-

jective equilibrium', in C. R. Wharton, Jr. (ed.), Subsistence Agriculture and Economic Development, London, 1970.

10. LAL, D., 'Disutility of effort, migration, and the shadow wage-rate', Oxford Economic Papers, 1973.

11. MABRO, R., 'Employment and wages in dual agriculture', Oxford Economic Papers, 1971.

12. MATHUR, A., 'The anatomy disguised unemployment', Oxford Economic Papers, 1964.

13. MAZUMDAR, D., 'Size of farm and productivity: a problem of Indian peasant agriculture', Economica, 1965.

14. NAKAJIMA, C., 'Subsistence and family farms: some theoretical models of sub- jective equilibrium', in C. R. Wharton, Jr. (ed.), Subsistence Agriculture and Economic Development, London, 1970.

15. ROBINSON, W., 'Types of disguised rural unemployment and some policy implications', Oxford Economic Papers, 1969.

16. SEN, A. K., 'Peasants and dualism with or without surplus labour', Journal of Political Economy, 1966.

17. UPPAL, J., 'Work habits and disguised unemployment in underdeveloped countries: a theoretical analysis', Oxford Economic Papers, 1969.

18. WELLISZ, S., 'Dual economies, disguised unemployment and the unlimited supply of labour', Economica, 1968, esp. pp. 46-7.

19. WELLISZ, S., MUNK, B., and HUMMER, C., 'Resource allocation in traditional agriculture: a study of Andhra Pradesh', Journal of Political Economy, 1970.

estimating the seasonal marginal products of labour in agriculture

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