The document discusses the neoclassical theory of distribution and the concept of factor payments. It addresses the "adding up" problem of whether total factor payments will equal total product. Wicksteed showed that under constant returns to scale and factors paid their marginal products, total revenue will equal total costs through Euler's theorem. However, this assumes a linear homogeneous production function. Later economists like Samuelson and Hicks found the condition is only met at the minimum point of the long-run average cost curve, where a firm has constant returns to scale.

1. Prof. Prabha Panth,
Osmania University,
Hyderabad

2.  The Neo-classical theory of distribution is based
on Functional distribution of Income.
 The distribution of income shows how total
output in the market, is divided among owners of
factors of production.
 E.g. workers own labour, capitalists own capital, rentiers own
land.
 Total Product or Output has to be completely
distributed to all factors.
 No residues after all factors are paid.
 So what should be the basis to achieve such factor
payments?
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3. Assumptions:
1. Derived Demand for factors, i.e. Factor D based on
demand of what they produce,
2. Law of Variable Proportions applies.
3. Perfect competition in both product and factor markets.
4. Factors are independent of each other.
1. All factors are homogenous, and divisible.
2. All factors are natural factors, including capital. Capital is not
manmade capital, (this gave rise to many debates on how
realistic this assumption is).
5. Technology is given.
6. Ceteris paribus.
7. MP of factor = Factor price, is given by individual factor
markets. (e.g. w = MPL determined in the labour
market, r = MPK, determined in the capital market). D
and S of factors determines factor price.
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4. Demand for factors by firms:
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Taking a factor input, say labour, as
more L is employed:
1) Total cost increases, as more wages
are to be paid.
2) Output increases.
In the figure, assuming ceteris
paribus, as L increases, TP
increases, because MP is still
positive. TC also increases.
Multiplying MP with price of
x gives VMPL.
VMPL = MPL × Px
The firm will employ L up to
the point where VMPL = MC
i.e. w. Point A.
Same applies to capital.
VMPL
w
0
MPL
A
Qx
Labour
MC
Q
Figure 1

5. Firm’s Equilibrium
5
For a firm, the Supply curve of L is perfectly
elastic. Also factor price is given.
VMPL
w
0
A
Qx
Labour
w
Figure 2
B
L2L1
Profit
Conditions for Firm’s Equilibrium
1. First order condition or
Necessary Condition:
VMPL = PL (i.e. VMPL = w)
2. Second order condition or
Sufficient Condition: VMPL
should be declining.
So equilibrium of the firm is at
B, and the firm employs 0L2
of labour.
It earns abnormal profits of
AB. Same applies to capital.

6.  The downward sloping part
of the VMPL is the firm’s
demand curve for the factor
(labour).
 If the factor price (w) falls,
the demand for the factor
increases, up to the point
where the VMPL = Price of
the product.
 If w falls to w2 from w1, due
to external reasons, then the
firm increases employment
of labour, from 0L1 to 0L2.
 This applies to all factors of
production.
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VMPL
w2
0
A
Qx
Labour
w1
Figure 3
B
L2L1

7. The Adding up Problem or Product
Exhaustion theorem
 As assumed, if each factor is paid individually, would
the sum of total factor payments be equal to the
total product?
 In other words, would the value of total product (TR)
be equal to total factor payments?
 or will there be excess remaining, (surplus then who gets
it?)
 or will there be insufficient funds to pay the total factor cost
(i.e. deficit, then how to pay the factors?)
 Wicksteed applied Euler’s theorem to show Product
Exhaustion. According to him:
 If each factor is paid up to the point were its
VMP=Pf, then TR will be equal to TC, where TC =
VMP of all factors in long run perfect competition.
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8. 8
MPPL
w
0
Qx
Labour
Total
profit
Figure 4a
B
L
Total
wages
A
MPPK
r
0
Qx
Capital
Total
Wages
Figure 4b
B
K
Total
profits
A
In Fig. 4a, w = MPP of L, and total wages paid to Labour = 0wBL. The
surplus wAB is paid to capital = total profit,
In Fig 4b, r = MPP of K, and total profits = 0rBK. The residue rAB is
paid to labour = total wages.
The question is will owBL of fig. 4a = rAB of fig 4b? (total wages)
Similarly will wAB of fig 4a = 0rBK of fig 4b? (total profits), since both
factor prices are determined independently.

9.  Wicksteed assumed that:
1. The production function is linear, and homogeneous,
such as the Cobb-Douglas production function.
This denotes that there are constant returns to scale
throughout the production function,
2. Each factor price = VMP of that factor. VMPL = w,
VMPK = r, etc.
w = Q/L, r = Q/K, etc.
3. Applying Euler’s theorem, then the sum of the partial
derivatives, multiplied by the quantity = the original
amount.
Then TR = wL + rK + …+….
= (Q/L)L + (Q/K)K + …. + = VTP or TR
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10.  Assume a linear, homogeneous production
function, such as Cobb Douglas production
function.
Q = F(K,L)
= AKL
PK = r = MPK = Q/K = AK -1 L
Similarly,
PL = w = MPL = Q/L = AK L-1
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11. Applying Euler’s theorem:
(Q/K)K + (Q/L)L = Q
= (AK -1 L .K) + (AK L-1.L)
=  (AK L ) + (AK L)
= + (AK L)
Q = + (Q)
Value of output = value of inputs or factor prices
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12. If the above function exhibits:
1) Constant returns to scale: + = 1, so RHS = LHS, (TR =
TC), and value of output = sum of factor incomes.
2) Increasing returns to scale:  + > 1, then sum of factor
incomes will be greater than value of output. TC > TR, Q
<  + (Q). The TR earned will not be enough to pay
factor incomes, and there will be deficit.
3) Decreasing returns to scale:  + < 1, then sum of factor
incomes will be less than value of output, Q >  + (Q) or
TR. Thus there will be undistributed surplus after paying
the factor incomes.
Only if there are constant returns to scale, will the
entire product be exhausted, when output is
distributed to factors as per their marginal
productivity.
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13.  According to Wicksteed, LRAC is linear, i.e.
constant returns to scale.
 Otherwise TR TC, and there will be surplus or
deficits.
 But a linear LRAC cannot be used to achieve
equilibrium. So there is a conflict here.
 Walras and Wicksell tried to solve this in the
following way: “The condition required for
marginally determined rewards to exhaust the
total product, i.e. CRTS, is fulfilled only at one
point, i.e. the minimum point of the LRAC of a
perfectly competitive firm in long run equilibrium”
 That is at point C in figure 4.
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14.  If product exhaustion has to
take place, the production
function should exhibit
constant returns to scale
throughout.
 The LRAC should be a
horizontal straight line.
 Samuelson and Hicks stated
that if there is perfect
competition in the product
market, LRAC is U-shaped
curve, to fulfill conditions of
equilibrium. (i.e. MC = MR,
and MC).
 The U-shaped LRAC exhibits
all three types of returns –
increasing, constant and
decreasing.
 At C, in the figure, TR = TC
wL + rK) = 0PCQx
14
LRMC
LRAC
C, R
0
P
Q
AR=MR
C
Qx
Figure 5
Samuelson Hicks
solution

15. Assuming 2 factors of production, K and L:
TR = TC = P x Q = wL + rK
According to MP theory, w = VMPL= P. MPPL
r = VMPK = P.MPPK
Therefore, P x Q = L(P.MPPL) + K(P.MPPK)
Dividing both sides with P
Q = L(MPPL) + K(MPPK)
Thus, for a given price, if factors are paid according to
their MPPs, the total payments to K and L would be
equal to TR.
The entire product would be exhausted.
This is possible only at the lowest point of LRAC,
where the firm experiences CRTS.
At this point, product exhaustion is satisfied, and it is
not necessary to assume a linear, homogeneous
production function.
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16.  If there the product market is a monopoly or
other imperfect markets, there will be no product
exhaustion.
 Factors and consumers will be exploited.
 If the firm is not operating at constant costs, but
has increasing or decreasing returns, again there
is no product exhaustion.
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