1.A widget manufacturer has the following production function: Q=2K+L. MPL=1, MPK=2

a.What is the RTS along the isoquants?

RTS________

b.If the wage rate is $10 and the rental rate on capital is $15, what is the cost minimizing combination of K and L the producer will choose to produce 10 units of output.

Capital (K)__________

Labor (L)___________

c.If the wage rate is $10 and the rental rate is $10, what is the cost minimizing combination of K and L will the producer choose to produce 10 units of output?

Capital (K)________

Labor (L)_________

1.Suppose that a firm's production function is: Q= 10LK

Its marginal product functions are:

MPL=10K

MPK=

The cost of an hour of labor, w=$20; the cost of a unit of capital, r=$80.

a.Initially the firm is producing the output of 80 and it has determined that the cost-minimizing quantities of labor and capital are 4 and 1. Suppose the firm needs to increase output to 160. If capital is fixed in the short run, how much labor will the firm require? Calculate the cost.

Labor________

Cost_________

b.Find the least-cost combination of capital and labor required to produce the output of 160. Calculate the cost.

Labor___________

Cost____________

=

b.Find the least-cost combination of capital and labor required to produce the output of 160. Calculate the cost.

Labor___________

Cost____________

1.Heavy Metal Company produces brass fittings.Heavy Metal's engineers estimate the production function represented below as relevant for their long-run capital-labor decisions.Q = 5KL,

where Q = annual output,

L = labor measured in person hours,

K = capital measured in machine hours.

The marginal products of labor and capital are:

MPL= 5K MPK= 5L

Heavy Metal's employees earn $25 per hour. The firm estimates a rental charge of $50 per hour on capital.Heavy Metal forecasts annual costs of $100,000 per year, measured in real dollars.

a.Determine the firm's optimal capital-labor ratio, given the information above.

b.How much capital and labor should the firm employ, given the $150,000 budget?

Capital (K)__________

Labor (L)__________

c.Calculate the firm's output.

Output (Q)_________

d.Suppose now the firm sets a target output of 8000. What would be the cost-minimizing allocation of capital and labor for the firm?