An Industry Can Be Characterized by the Following Production Function

Question

Examlex · Accepted Answer

The Answer is (a)

\mathrm { MP } _ { \mathrm { L } } = \frac { \partial \mathrm { Q } } { \partial \mathrm { L } }

\begin{aligned}& = .60 \left( 2.5 \mathrm {~L} ^ { 60 - 1 } \mathrm { C } ^ { A 0 } ight) \& = 1.50 \mathrm {~L} ^ { - .40 } \mathrm { C } ^ { .40 } \\mathrm { AP } _ { \mathrm { L } } & = \frac { \mathrm { Q } } { \mathrm { L } }\end{aligned}

(b)

\begin{array} { l } = \left( 2.5 \mathrm {~L} ^ { 6 } \mathrm { C } ^ { 4 } ight) / \mathrm { L } \= 2.5 \mathrm {~L} ^ { - 40 } \mathrm { C } ^ { 40 }\end{array}

(c) This production function is of the Cobb-Douglas form and the sum of the exponents of the labor and capital variables indicate the returns to scale. Since the sum of the exponents is

1.0 ( .60 + .40 )

, this production function exhibits constant returns to scale, i.e., a

\lambda

-factor increase in each of the inputs will yield exactly a

\lambda

-factor increase in output.

An Industry Can Be Characterized by the Following Production Function

Definitions: