The Cobb-Douglas production function is a statistical model that relates the quantity of output to inputs of labor and capital. It is based on an empirical study by Paul Douglas and Charles Cobb of the American manufacturing industry in the 1920s. Their study found that labor contributed about 3/4 and capital about 1/4 to increases in manufacturing production. The Cobb-Douglas production function has several key properties including constant, increasing, or decreasing returns to scale depending on the sum of exponents and that average and marginal products depend on the factor ratio rather than absolute quantities.

1. COBB DOUGLAS
PRODUCTION
FUNCTION
Swetha Shree R
Assistant Professor
Department of Economics
Ethiraj College for Women

2. The Cobb-Douglas production function,
named after Paul H. Douglas and C.W.
Cobb, is a famous statistical production
function.
The Cobb-Douglas production function is based on
the empirical study of the American manufacturing
industry made by Paul H. Douglas and C.W. Cobb.
INTRODUCTION

3. It is a linear homogeneous
production function of degree one
which takes into account two inputs,
labour and capital, for the entire
output of the manufacturing
industry.
This study led to the
conclusion that labour
contributes about
3/4th and capital about
1/4th of the increase in
manufacturing
production.

4. PROPERTIES OF COBB DOUGLAS PRODUCTION FUNCTION
The sum of the exponents of
factors in Cobb-Douglas
Production Function that is a+b
measures the Returns to Scale.
If a+b = 1; the Production Function
has Constant Returns to Scale
If a+b > 1; the Production Function
has Increasing Returns to Scale
If a+b < 1; the Production Function
has Decreasing Returns to Scale
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5. In a linear homogenous Cobb-
Douglas Production Function,
Q = A La K1-a , the Average
and the Marginal Products of
a factor depend on the ratio
of factors used in production.
PROPERTIES OF COBB DOUGLAS PRODUCTION FUNCTION2

6. PROPERTIES OF COBB DOUGLAS PRODUCTION FUNCTION
Average Product of Labour can
be obtained from dividing the
production function by the
amount of Labour, L
= A La K1-a / L
= A K1-a / L1-a
= A ( K / L)1-a
Average Product of Labour
Average Product of Capital
= A La K1-a / K
= A La / K1-1+a
= A La / Ka
= A ( L / K)a
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The Average Products of
Labour and Capital
depend on the ratio of
the factors and not on
their absolute quantities.

7. The Marginal Product of
Labour is the first derivative
of the production function
with respect to labour
Q = A La K1-a
MPL = dQ/dL = A a La-1 K1-a
= A a La K1-a / L
= A a K1-a / L1-a
= A a (K/ L)1-a

8. The Marginal Product of Capital
is the first derivative of the
production function with respect
to capital
Q = A La K1-a
MPK = dQ/dK = A La (1-a) K1-a-1
= A La (1-a) K-a
= (1-a) A La / Ka
= (1-a) A (L/ K)a

9. The exponents of Labour &
Capital in Cobb-Douglas
production function measures
output elasticities of Labour &
Capital respectively
PROPERTIES OF COBB DOUGLAS PRODUCTION FUNCTION
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10. The Cobb-Douglas production function
can be extended to include more than
two factors. For example: Agricultural
Production.
Q = A La Kb1 Db2 Gb3 Fb4
Where D – land,
G – Irrigation,
F – Fertilizers
b2, b3, b4, are exponents of
land, irrigation and fertilizers
respectively
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11. When the sum of the exponents (a+b) in the
two factor CDPF is equal to 1, it would show
Constant Returns to Scale.
Q = A La K1-a
If the inputs L & K are increased by a constant
‘g’ , then the quantity of output will be
increased to
A (gL)a (gK)1-a = ga g1-a A La K1-a
= g A La K1-a
= g Q [ga g1-a = g]
thus, when inputs are increased by a constant
‘g’, the output also increases by ‘g’ times.
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12. THANK
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