Question

A firm produces output according to the production function: Q = F(K,L) = 2K + 2L.

a. How much output is produced when K = 2 and L = 3?

b. If the wage rate is $65 per hour and the rental rate on capital is $35 per hour, what is the cost-minimizing input mix for producing 4 units of output?

Capital:

Labor:

Answer 1

a. Q=2K+2L

K=2 & L=3

Q=2*2+2*3= 4+6=10

Q=10

Answer= OUTPUT=10

b. w=$65

r=$35

Q=2K+2L

These are substitute goods, firms can only produce using either K or L.

Output needed=4

4/2=2K and 4/2=2L

cost for producing Q=4, when only K is used= 2*35= $70

cost for producing Q=4, when only L is used=2*65=$130

So, it is cheaper to produce 4 units of output using only capital and zero labor.

Answer=

Capital=2

Labor=0