Question

A firm produces an output with the production function Q=K*L2, where Q is the number of units of output per hour when the firm uses K machines and hires L workers each hour. The marginal product for this production function are MPk =L2 and MPl = 2KL. The factor price of K is $1 and the factor price of L is $2 per hour.

a. Draw an isoquant curve for Q= 64, identify at least three points on this curve.

b. If the firm is currently using K = 1 units and enough L to produce 64 units of output, how many units of L is the firm using?

c. Under the conditions described in b. above, what are the total costs of production?

d. Draw the isocost curve and isoquant in part b.

e. Mathematically show that the above combination of K and L is not the cost minimizing combination of K and L to produce Q= 64. Should the firm hire more labor or more capital? Why?

f. What would be the cost minimizing combination? Show your work. Identify the cost minimization capital-labor combination on the graph.

g. How much would the firm save if it used the K and L combination obtained in part f. instead of the combination obtained in part b.?

h. Suppose that a new minimum wage is imposed at $4 while the price of K remains at $1. Use formulas to show that the optimal combination found in f. is no longer cost minimization. Should the firm hire more labor or more capital? Why?

i. If the firm wanted to continue producing Q= 64 what would be the optimal combination of K and L? Why does optimal combination of K and L change? Show your work and identify this new combination on a graph.

j. What are the new costs of production in part h?

Answer 1

graph

It's mandatory to solve first four parts