NPTEL- History of Modern Economic Thought

Module 3
Lecture 17
Topics
3.2 The Marginalist Revolution II

3.2.1 Product Exhaustion Theorem

3.2 The Marginalist Revolution II

The emergence of marginal theory made the use of mathematics possible which
opened doors to new analytical tools.

The second generation marginalists expanded the scope of mathematics for

economics. Economists from both sides of Atlantic contributed in the process.

The flagship of the second generation marginalists was the use of marginalists
theory for production. Ricardo can be seen as a early pre-cursor who assumed
diminishing return to land.

It took 75 more years to extend the theory for other factors of production. Major
contributions in this field came from Wieser (1851-1926), Bohn Bawerk (1851-
1914) (both from Austria), J.B.Clark (1847-1938; U.S.),Knut Wicksell (1851-1926;
Sweden), Wicksted (1844-1927) and Edgeworth (1845-1926) (both from
England)

The second generation marginalist theories culminated into the neoclassical

doctrines which was proposed by Alfred Marshall in 1890. We will have a
separate lecture on Marshall.

The principle of diminishing return tells us that if one factor is increased keeping
other factors constant output first increases at an increasing rate and then
increases at a decreasing rate and then it decreases. This is also known as the
law of variable proportion. The following table represents this law:

Dept. of Humanities and Social Sciences, Indian Institute Of Technology, Kanpur

NPTEL- History of Modern Economic Thought

Labour TP AP MP

1 10 10 10
2 21 10.5 11
3 33 11 12
4 46 11.5 13
5 58 11.6 12
6 68 11.3 10
7 75 10.7 7
8 80 10 5
9 83 9.2 3
10 83 8.3 0
11 80 7.3 -3

Table 1: Law of Variable Proportion

In the table TP represents total product, AP represents average product and MP

represents marginal product.

Average product is defined as and marginal product is defined as

From the production it can be readily deduced that a factor is employed to the
level such that

(1)

Let us now elaborate this condition. The left hand side of the equation gives the
amount of money the entrepreneur needs to spend to hire one extra unit of labor.
In equilibrium, this should be equal to the value of the extra product it produces.

This equation shows that wage (or any factor price) must be equal to the value of
the marginal product. For a production with n factors of production this can be
extended to

(2)

Dept. of Humanities and Social Sciences, Indian Institute Of Technology, Kanpur

NPTEL- History of Modern Economic Thought

Where represents the marginal product of factor and represents the

price of factor .

The term represents the marginal physical product from spending the last
rupee on factor 1. In equilibrium this must be same for all inputs. If not, i.e. say if
then the firm owner should reallocate the resources by spending one
less rupee on factor , and spend that one rupee on factor as the resultant
increase in output is greater than the resultant decrease.

3.2.1 Product Exhaustion Theorem

The product exhaustion theorem implies that paying each factor its marginal
product should exhaust the total product.

J.B Clark stated the same but did not offer any formal proof. Mathematically, this
should look like this
(3)

Wicksteed mentioned the same point and tried to offer a formal proof. He failed
to prove the result but maintained that there must be competition for this result to
hold.

We know that an easy proof exists that uses Euler theorem. However, Euler
theorem states the result is only true if the production function is homogeneous
of degree one. But if the production function is homogeneous of degree one that
means that it must show constant returns to scale.

A production function is said to show constant returns to scale if output increases

by in response to rise in all inputs. The function shows to decreasing
return to scale if output rises by mess than and increasing return to scale if it
rises by more than .

If the production function shows decreasing returns to scale then factor payment
is less than total output, and in case of increasing return to scale total factor
payment is more than the total output.
Hence, product exhaustion theorem is only consistent with constant returns to
scale production function.

Dept. of Humanities and Social Sciences, Indian Institute Of Technology, Kanpur

NPTEL- History of Modern Economic Thought

Wicksell argued that each firm goes through all three returns to scale. He
developed the concept of inverted U shaped long run cost curve. In Wicksel's
solution the production function need not be showing only constant return to
scale. In the long run the firm must operate at the minimum point of the average
cost curve implying zero profit. Technically we can say that at the minimum point
CRS operates.

Wicksel argued that perfectly competitive market would produce the zero profit
result and product exhaustion result would hold true.

Product exhaustion theorem was not just any other mathematical result. It bears
some important ethical implication.

This result shows that total product is distributed among all the factors according
to their contribution (measured by marginal productivity) to the production.

The ethical point was first raised by John Bates Clark who sitting in America
independently developed the idea of marginal productivity and utility.

The ethical implication of production exhaustion theorem drew attention of the

scholarly people. Because in a way this provides argument against the Marxian
exploitation theory.

However, the ethical arguments also drew many criticisms. One obvious criticism
is whether marginal product or average product is a factor's true contribution to
the society. Note that in product exhaustion theorem each factor is paid its
marginal product.

Moreover, even if a factor earns its marginal product that does not mean the
individuals get a just income. If the factors are distributed unjustly, individuals will
not get the just share of income. This argument can be extended to raise the
question why the productivity of a machine should be the just earning of the
owner.

Dept. of Humanities and Social Sciences, Indian Institute Of Technology, Kanpur