Question

4. Consider a production process where capital and labor are perfect complements – two units of capital are required for each unit of labor to produce four units of output.

1) Derive the production function for this production process.

2) If the wage rate is $5 per unit of labor and the rental rate of capital is $8 per unit of capital, how much capital and labor should the firm employ to minimize the cost of producing 100 units?

3) What will the total cost be to produce the 100 units using the quantities of capital and labor determined in part 2)?

Answer 1

4)a) The production function,

Y(L,K)=4min{L,0.5K}

B)The cost minimization condition;,

L=0.5K

100=4*L

L=25

L=0.5K

K=25/0.5=50

C) TC=w*L+r*k=5*25+8*50=125+400=525