Question

a firm uses (K) and labor (L) and these are perfect substitutes. one unit of output can be produced using 1 unit of capital or 2 units of labor. What is the equation for the production function? show the isoquant map

Answer 1

Production function for perfectly substitute inputs:

Q= aL+bK General form

For Q=1, It requires either 1 unit of capital or 2 units of labor it implies

If K= 0, then

Q= aL+b(0)

Q= aL

1= a(2)

a= 1/2

If L=0, then

Q=bK

1=b(1)

b=1

Equation of Production function:

Q= 1/2 L + K

Equation of Isoquant:

K= Q-1/2 L

Slope of Isoquant: dK/dL= -1/2

Isoquants are parallel to each and straight line curve slopes downward from left to right.

There are three isoquants:

First one with intercepts (10,5) is for Q=5.

Second one with intercepts (20,10) is for Q=10

Third one with intercepts (40, 20) is for Q=20..