Question

A firm produces output according to the production function: 

Q= F(K, L) = 4K + 8L. 

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

b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 32 units of output? 

c. If the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour, what is the cost-minimizing input mix for producing 32 units of output? 

Answer 1

Answer 2

Answer
a)
Q=4*2+8*3=
the output is

b)
the production function is the form of substitute inputs so the firm will hire only the input with the higher marginal product per dollar

MPL=dQ/dL=8
MPK=dQ/dK=4
MP per dollar =MP/price of input
MPL per dollar =8/60=2/15
MPK per dollar =4/20=2/10

the MPK per dollar is higher so the firm should use only capital and no labor
then
Q=32, L=0, K=?
32=4K+8*0
4K=32
K=8
the firm should hire 8 capital and 0 labor
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c)
now the MP per dollar is
MPL per dollar =8/20=2/5
MPK per dollar =4/20=1/5
now the firm will hire only labor
32=K*0+8L
8L=32
L=4
now
Capital =0
Labor =4