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
𝑀𝑁
x
100
Since w is constant, r varies directly with
MP. As long as profits >0, accumulation
takes place.
Rent
Profit
Wages
AP
MP
w
M
A
B = Rent = AP - MP
C1 = no surplus
C
R
M1
N N10 K,L
Output
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.
Rent
Profit
Wages
AP
MP
w
M
A
B = Rent = AP - MP
C1 = no surplus
C
R
M1
N N10 K,L
Output
T
Figure 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
Rent
b
a
N0
MP
w
Output
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
▪ =
𝑤𝐿1 1+𝑟 𝑡1
𝑤𝐿2
1+𝑟 𝑡2 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.
𝑃1
𝑃2
𝑃1
𝑃2
𝐿1
𝐿2

▪ 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 not
change 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

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