ricardian theory of value

The Ricardian Theory of

Value

Prof. Prabha Panth,Osmania University,

Hyderabad

▪ Ricardo analysed the Dynamic process of capital accumulation in a free enterprise economy.

▪ He integrated the theory of Value, Accumulation and Distribution in his analysis.

▪ What leads to the expansion of an economy?

▪ It is the accumulation of capital (K) stock.

▪ Increase in K stock leads to increase in productive capacity, and

▪ This leads to increase in output, leading to expansion of the economy,

24-07-2017Prabha Panth 2

RELATIONSHIP BETWEEN GROWTH, AND

DISTRIBUTION:

▪ Ricardo showed that the Theory of Growth (Accumulation) is linked with the Theory of Distribution.

▪ Capital Accumulation leads to Growth of Output,

▪ Output = Profits + Wages + Rent (Distribution)

▪ Profits are the source of Investment. Wages and rent are consumed,

▪ Investment leads to Capital Accumulation,

In other words, Profits → Investment → Growth of Capital → Growth of output.

This shows the relationship between Accumulation and Distribution of Income.


RELATIONSHIP BETWEEN GROWTH, DISTRIBUTION AND VALUE:

▪ Total Profits come from Total Surplus = Total Output – (wages + rent).

▪ There are a large number of heterogenous goods produced in the economy,

▪ So it is necessary to aggregate them, with the help of some measure of Value.

▪ To estimate the rate of surplus and the rate of profit, the various goods have to be valued, in order to aggregate them.

▪ For this a Theory of Value is required.

▪ This shows the relationship between Theory of Accumulation, Distribution, and Value.


RICARDO’S THEORY OF VALUE

▪ Ricardo rejects Adam Smith’s concept of “labour commanded” theory of value.

▪ For such values are also affected by changes in wage rate. (See lesson on Adam Smith’s theory of Value).

▪ According to Ricardo, labour embodied is the source, as well as the measure of value. Exchange values are governed by labour embodied in commodities.

▪ He states, “The amount of society’s labour allotted to the production of a commodity, is the true source of value, and the best (though imperfect) measure of value.”


LABOUR EMBODIED THEORY OF VALUE

▪ For a given technology, the Labour embodied in a commodity is constant.

▪ Then, based on labour embodied in production, it is possible to get relative prices, which are directly equal to labour values.

▪ For e.g. if A requires 10 hours of labour, B requires 5 hours, then PA: PB = 2:1 (relative prices)

▪ Thus, exchange value arises due to:

▪ Labour embodied in all economic goods,

▪ Scarcity (but only for rare objects).


Ricardo states,

▪ “If men employed no machinery in production but labour only, and were all the same length of time before they brought their commodities into the market, the exchangeable value of their goods would be precisely in proportion to the quantity of labour employed.”

▪ “If they employed fixed capital of the same value, and of the same durability, then too the value of the commodities produced would be the same, and they would vary with the greater of less quantity of labour employed in their production.”


OTHER FACTORS AFFECTING VALUE

▪ Ricardo was aware of other factors affecting value:

▪ Distributional changes,

▪ Differences in quality of labour (skilled vs. unskilled), but this can be shown in terms of differences in wage rates.

▪ Differences in capital input used. If X required more capital equipment than Y, then Px > Py.

▪ Not only direct labour and capital, but backward linked industries also affect relative values.

▪ Different time intervals for different goods. More time, more value

▪ Durability of different capital goods. More durable – less value added per period.


OTHER FACTORS AFFECTING VALUE

▪ Technical progress – especially labour saving, reduces exchangeable value.

▪ He states, “Economy in the use of labour never fails to reduce the relative value of a commodity, whether the saving be in the labour necessary to the manufacture of the commodity itself, or in that necessary to the formation of capital, by the aid by which it is produced.”

▪ Ricardo hence felt that Labour Embodied in production is the best measure of value.

▪ For, even if wages increased, and profits fell, the labour embodied in production will not change.

▪ Hence there will be no change in the relative prices.


ROLE OF FIXED CAPITAL

▪ Ricardo initially felt that only a small modification is required in the theory, in case capital goods are used in production along with labour,.

▪ Instead of direct labour embodied determining exchange values, the indirect labour needed to produce the tools and implements that labour uses, will also have to be computed to get labour values and exchange values.

▪ However, Ricardo later found that it was much more complicated – for heterogeneity of inputs, durable capital goods, interdependence of processes, and changes in distribution – all have an impact on relative prices.


1. RICARDO’S ONE GOOD MODEL

1. Corn is the only commodity – both input, and also output.

2. Wages, rent, and profits are paid in terms of corn.

3. No fixed capital, only circulating capital – corn.

4. Rate of profit = Surplus corn/corn capital.

5. Wages are paid in advance of production,

6. Circulating capital is the wage fund.

7. No measure of value, as there is only one good.

8. Wage rate and rate of profit are inversely related. (w↑ r↓)

9. Rent is paid out of surplus, so has no impact on value.


▪ Assumptions:

1. Diminishing returns to agriculture. At the extensive margin, the marginal land is less productive. At the intensive margin, increased application of K,L does not lead to proportionate increase in output, MP↓. (Niggardliness of Nature)

2. Single good corn – both input and output, and also paid to factors.

3. Malthusian theory of population, as w ↑, population ↑.

4. Wage rate fixed at subsistence.

5. Land is fixed in quantity, and differs in quality. Heterogenous land.

6. Technology is given.

7. Three classes – a) workers receive subsistence wage, b) rentiers receive rent based on MP of land, and c) capitalists receive profits as a residue, after wages and rent are paid.

8. Capital is wage fund.


▪ In a one commodity world like corn, no need to estimate values, as all values are expressed in terms of corn.

▪ Only circulating capital, i.e. corn paid to workers in advance of production. Here capital is the Wage Fund.

▪ Investment or Accumulation is governed by the rate of profit, r = profits/wage fund.

▪ Rent is paid because land is heterogenous and there is competition among tenants. Landlords do not invest, but consume the rent, which is paid out of the surplus.▪ Wage rate is set at subsistence.

▪ Rent arises due to the niggardliness of Nature (that leads to diminishing returns due to the differing fertility of the soil).

▪ Profits are the residual payments, after rent and wages are paid.


In the figure, as K, L increase, AP falls, as also MP.

1) Given wage rate 0w, 0N labour can be employed. Output is 0RBN. Total wages = 0wMN

Wage fund is the capital accumulation of the previous period = 0wMN.

Rent is determined by the MP at A = CRBA. Residue wCAM = profits. Rate of profit r = Surplus/wage fund (capital)

= wCAM/0wMN = 𝐴𝑁 −𝑀𝑁

𝑀𝑁=

𝐴𝑁

𝑀𝑁- 1 =

𝐴𝑀

𝑀𝑁x

100

Since w is constant, r varies directly with MP. As long as profits >0, accumulation takes place.


Ren

tP

rofi

t

Wages

AP

MP

w

M

A

B = Rent = AP - MP

C1 = no surplusC

R

M1

N N10 K,L

Ou

tpu

t

T

Figure 1

2) When output increases, as per Malthus, population also increases, and demand for corn ↑.

So more land is cultivated, employment increases to 0N1. But marginal land is less fertile (extensive margin) or existing land more intensively cultivated.

Diminishing returns sets in, Total wages = 0wM1N1, and Rent = MP at M1, so total rent = wTM1N1.

Rent has taken out the entire surplus.

Total profits are zero at M1, and accumulations ceases.

The economy enters a Stationary State.


Ren

tP

rofi

t

Wages

AP

MP

w

M

A

B = Rent = AP - MP

C1 = no surplusC

R

M1

N N10 K,L

Ou

tpu

t

TFigure 1

▪ Ricardo pointed out that as the economy expands, increasing Rents and Wages squeeze out the Profits,

▪ When profits are zero, there is no investment, and no accumulation.

▪ The economy reaches a Stationary State.

▪ Conflict between the classes, as rents and wages are consumed not invested.

▪ Since rent is paid out of surplus, increase in rent does not affect values.

▪ But if price of corn increases, AP and MP shift upwards, and total rent increases.

▪ “High rent does not affect value, higher values affects rent” – Ricardo

▪ One good model, no need for valuation, as all are expressed in physical terms, in terms of – corn, r is a pure number, independent of value.


THE STATIONARY STATE

▪ As capital accumulation takes place, two effects follow:▪ There is increased demand for labour, leads to rise in w-rate. But as per

Malthusian theory, increase in wages leads to increase in population.

▪ But increase in output < increase in population, due to diminishing returns.

▪ Increase in population → more demand for food → more land cultivated. ▪ But marginal lands are less fertile, so MP of land decreases (extensive margin).

▪ Or existing land is intensively cultivated (by applying more K, and L), leading to diminishing returns.

▪ Competition among farmers for the more productive land, leads to payment of rent. Rent is equal to the MP of land. More the margin expands, more the payment of rent from intra-marginal lands.

▪ So w-rate again falls to subsistence (Iron law of wages). But total wage bill increases as more labour is employed.

▪ Profits are sandwiched between Wages and Rent, gets reduced.

▪ As profits tends to zero, accumulation ceases. Stationary State.


THE TWO-SECTOR MODEL

▪ Malthus criticised Ricardo’s single good model. Workers cannot subsist on corn alone, will exchange it for other consumer goods like soap, or cloth, etc.

▪ Heterogenous goods in the economy, requires more sectors for their production.

▪ Different capital goods are used as inputs in different sectors.

▪ These different goods have to be aggregated. Hence a Theory of Value is needed.▪ In a single good model, Pr = Q – (W + Rent), where W is circulating capital

or wage fund. r = Pr/W in corn terms.

▪ But in a heterogenous model, it is not possible to estimate Profits in this way.

▪ Since there are different goods, all goods have to be valued to enable them to be aggregated.


▪ When more goods are produced in an economy, there will be more processes to produce them.

▪ K/L ratios may differ between processes.

▪ Different goods have to be valued to enable aggregation.

▪ In such a model also, Ricardo assumed that Labour embodied can be used as a measure of value.

▪ In (Figure 2), Rent is ignored, as it is an intra marginal payment. At a given point b, the rent of the marginal land is zero.

▪ At b only Pr + W = MP, i.e. only L and K are taken.

▪ MPP is the inverse of MC = W + Pr.


▪ If there are two processes, producing two goods, for the sake of simplicity, Ricardo assumes that K/L is same in both processes.

▪ Capital* is accumulated labour, in terms of wages that capitalists advance towards production. No fixed capital.

▪ Duration of these advances depends on the ratio of circulating to fixed capital, and durability of fixed capital.

▪ Therefore if a) ratio of current L to accumulated L is the same in all processes,

▪ And b) length of time is the same in all processes,

▪ Then: relative prices = labour embodied.


Profit

Wages

Rentb

a

N0

MP

w

Ou

tpu

t

Figure 2

*From M. Blaug: “Economic Theory in Retrospect,” CUP.

TWO SECTOR, TWO GOODS MODEL

▪ For the sake of simplicity, Ricardo assumed that:

▪ Rent is ignored, by taking MP = contribution of only K & L, since rent = AP – MP. So Q is produced only by K, L.

▪ Uniform proportion of K/L in all processes.

▪ All values are in terms of corn.

▪ Time frame is uniform over all processes.

▪ w, r are uniform over all processes.

In such a case, relative Prices = relative quantities of Labour embodied in them.

And, if w increases uniformly in all processes, r decreases correspondingly, and relative prices do not change.


▪ P1 = wL1(1+r)t1 P2 = wL2(1+r)t2

▪ = 𝑤𝐿

11+𝑟 𝑡1

𝑤𝐿2 1+𝑟𝑡2 cancelling w’s, we get

𝐿1

𝐿2(1+r)t1 – t2

▪ Or = only if t1 = t2,

▪ Rate of profit is uniform over all industries (competition). Assumes that if all prices are given in terms of corn, then it is possible to estimate rate of profit in physical terms.

▪ rc = req

▪ Wage rate is uniform: If Good A needs 10L, and B = 5L, then La: Lb = 2:1. If wage rate is 5 units of corn, then Pa:Pb = 50: 25 = 2: 1.

▪ Ratio of labour embodied (labour values) = relative prices.


𝑃1𝑃2

𝑃1𝑃2

𝐿1𝐿2

▪ Complications:

▪ If fixed capital is taken into account, not circulating capital, this ratio of relative prices to labour embodied may not hold.

▪ Rate of profit r, is not independent of prices.

▪ K/L is not uniform over all sectors, so that changes in distribution, w, r affects prices.

▪ Hence, increase in w will not affect all processes equally, since r will not fall proportionately in the different sectors.

▪ Any change in distribution affect r differently in different processes, so that to keep r uniform over all processes, relative prices have to change.

▪ Even without change in technology or labour embodied.


RELATIONSHIP BETWEEN K/L AND RELATIVE PRICES

▪ Example 1: capital is circulating capital (in terms of corn)▪ K/L is uniform over all processes.▪ Two goods, A and B.▪ Perfect competition, same rate of profit in both processes.

In the example below, Labour embodied in the two goods: A = 10 hrs: B =5 hrs = 2:1, and Relative prices = 15:7.5 = 2:1.So relative prices = Labour embodied. This is possible only if K/L is uniform over all processes.


Good L (hrs) K

(corn)

K/L w

(corn)

r % PrC =

rK

Wc =

wL

TC =

W+Pr

Price

A 10 100 10/1 1 5% 5 10 10+5 = 15

B 5 50 10/1 1 5% 2.5 5 5+2.5 = 7.5

▪ Example 2: K/L is not uniform over processes, what happens?

▪ Labour embodied in the two goods X and Y,

▪ From the example below we see that K/L is not uniform over the two processes (X: 10/1, and Y:6/1). Other variables are all the same as Ex,1.

▪ But what happens to relative prices? It can be seen that as K/L is not the same in Y as compared to X, the relative prices now come out to be 15:6.5, whereas labour embodied = 2:1 (or 10:5),

▪ So now relative prices 15 : 6.5 2 : 1 (labour embodied)

▪ Therefore relative prices = labour embodied only if K/L is the same in all processes. If not then relative prices labour values.


Good Output

Kgs

L

(hrs)

K

(corn)

K/L w

(corn)

r % Prc =

rK

Wc =

wL

TC =

W+Pr

Price

X 200 10 100 10/1 1 5% 5 10 10+5 = 15

Y 100 5 30 6/1 1 5% 1.5 5 5+1.5 =6.5

EFFECT OF CHANGE IN DISTRIBUTION ON RELATIVE

PRICES▪ Not only if K/L is not uniform over processes, but also when

distribution changes, relative prices will also be affected.

▪ If L is more in the production of A than in B, then an increase in wage rate will increase total Wages more in A than B, and result in a greater fall in rate of profit in A than B.

▪ To keep rate of profit the same in both processes, relative prices have to change.

▪ P = W + Pr,

▪ Pr = P – W, or rK = P – wL ,

▪ or r = (P – wL)/K

▪ or K = (P-wL)/r.

▪ If increase in w → fall in r, then price of K will remain constant. But if w↑ r↓ then price of K will change.


▪ Example 3: Changes in distribution and effect on Relative Prices:


Good Output

Kgs

L

(hrs)

K

(corn)

K/L w

(corn)

r % Prc =

rK

Wc =

wL

TC =

W+Pr

Price Value of output

X’ 200 5 100 20/1 1 10% 10 5 10+5 = 15 200 x15=3000

Y’ 100 2.5 90 36/1 1 10% 9 2.5 9+2.5 =11.5 100x11.5=1150

Labour embodied relative prices National product = 4150

Example 4: If the wage rate increases to 2 units of corn:

Good Output

Kgs

L

(hrs)

K

(corn)

K/L w

(corn)

r % Prc =

rK

Wc =

wL

TC =

W+Pr

Price Value of output

X’ 200 5 100 20/1 2 5% 5 10 10 + 5 = 15 200 x15=3000

Y’ 100 2.5 90 36/1 2 5% 4.5 5 5 + 4.5 =9.5 100 x 9.5=950

In e.g. 4, when w increases from 1 to 2, the rate of profit r in the two processes will fall,

but not proportionately, at the old prices of 15:11.5 (as in e.g.3)National product = 3950

Rate of profit of X’, rx’ = (15-10)/100 = 5/100 = 5%. (Where r = rate of profit or surplus = surplus/capital)

Rate of profit of Y’, ry’ = (11.5- 2.5)/90 = 9/90 = 10%. So if relative prices do not change, then the rate of profit will differ over the

two processes.

If rx’ = ry’, it is necessary for the price of Y’ to fall, because the rate of profit of Y’ > rate of profit of X’ (10% > 5%). But in the

case of perfect competition, r has to be the same in all processes.

So in Example 4, if we take a uniform rate of profit of 5%, we find that the price of Y’ will fall from 11. 5 to 9.5. Therefore, when

K/L is not uniform over processes, a change in distribution, leads to change in relative prices.

▪ In this example, K/L is not uniform over the two processes.

▪ So Lx’: Ly’ Px’:Py’, (2:1 15:11.5) when w = 1, r = 10%

▪ Secondly, when w increases to 2 units of corn, r falls from 10% to 5%, what happens to relative prices?

▪ Px’ is constant (corn is the numeraire, or the measure of value). But P’ falls from 11.5c to 9.5c. (this is called the Reverse Wicksell effect)

▪ Again Lx’: Ly’ Px’:Py’, (2:1 15:9.5) when w = 2, r = 5%

▪ Thus, changes in distribution lead to changes in relative prices, if K/L is not uniform over processes.


EXAMPLE 4 – IMPACT OF CHANGES IN DISTRIBUTION

Good Output

Kgs

L

(hrs

)

K

(corn)

K/L w

(corn)

r % Prc = rK Wc

= wL

TC =

W+Pr

Pric

e

Value of

output

X’ 200 5 100 20/1 2 5% 5 10 10 + 5 = 15 200 x15=3000

Y’ 100 2.5 90 36/1 2 5% 4.5 5 5 + 4.5 =9.5 100 x 9.5=950

National product = 3950


Labour embodied relative prices, also the relative prices have changed, due to change in

distribution (w and r).

Physical outputs and inputs are the same.

But the Value of total product of the economy has fallen from 4150 c to 3950 c.

Thus a change in relative prices, due to change in distribution, leads to change in the Value of total or

National output, even if physical output remains constant.

Since the total output in price terms has fallen, the actual distribution of W and Pr will also fall.

This is the Ricardian Puzzle.

w = 1 r = 10% Value of NP = 4150 c Physical output = 200 X’ and 100 Y’

w = 2 r = 5% Value of NP = 3950 c Physical output = 200 X’ and 100 Y’

THE RICARDIAN PUZZLE

▪ “A change in distribution, changes that which has to be distributed.” – Ricardo.

▪ As seen in e.g.4, when K/L is not uniform, changes in w and r (distribution) affects the relative prices.

▪ This results in change in the value of the National Product.

▪ Now a larger, or smaller NP is available to be distributed between wages and profit.

▪ Thus Valuation and Distribution are interdependent.


THE INVARIANT MEASURE OF VALUE

▪ If Y’ was the numeraire, the measure of value with which other goods are valued, then a change in distribution will affect its price.

▪ If the price of the numeraire itself changes, then it is not an efficient measure of value.

▪ So it becomes difficult to determine if a change in relative prices is because of changes in the cost of production, conditions of output, or because of changes in the value of the numeraire itself.

▪ So Ricardo felt that it is necessary to have a measure of value that does notchange with changes in distribution – An Invariant Measure of Value.

▪ Labour embodied cannot be taken as an invariant measure, because labour values relative prices, when K/L is not uniform over all processes.

▪ The cost of production approach to value differs from pure labour embodied values.


▪ Ricardo wanted to find out if there is any commodity whose value is unaffected by changes in distribution – the invariant measure of value – so that all commodities produced in an economy can be measured with that commodity.

▪ Such a commodity should be produced under “Average” conditions, and have the following features:

▪ K/L should be the same in all processes, so relative Ps = ratio of labour embodied, so changes in distribution will not affect prices.

▪ Average K/L should be taken, deviations would cancel out, so that relative P = relative L values.

▪ But Ricardo could not find any commodity that would satisfy these conditions.


▪ Ricardo’s analysis can be summarised as follows:


1. One good Model

No need for pricing. All values in terms of corn

Goods: Corn = wage, profit, input, output


2. Two goods Model

Pricing of goods needed for exchange

Value = labour embodied = wL

Prices = Cost of prod = wL + rK

Will ratio of V = ratio of P?

Two factor inputs = K, L


Depends on K/L in different sectors

If K/L is not uniform, then, ratio

of V ratio of Ps

If K/L is uniform then ratio of values V= ratio of prices P


3. If K/L is not uniform, change in w and r (distribution) affects prices differently

Ricardian Puzzle:

NY w, r

Changes in distribution,

may change Ps.

If P of numeraire changes, it cannot act as an Invariant

measure of Value

Relative prices change to keep r uniform over

processes.

ricardian theory of value

Education