Problem 2 (14 points)

Consider the following two production functions:

A) q = L B) q = +

a. Which technology exhibits increasing returns to scale? Which decreasing returns to scale? Justify your answer.

Now suppose a firm can produce its output using technology B). The firm can hire workers at a unit wage of w = 1 and rent equipment at

a unit rental cost of r = 2.

The firm is negotiating a contract with a customer. The customer wishes to receive 30 units each period.

b. Show that if the firm wishes to produce the 30 units at the lowest cost possible it should hire 400 workers and rent 100 pieces of

equipment.

c. In an isoquant/iso-cost diagram illustrate the firm's cost minimizing technique. Label the graph and in the graph indicate the slope of

the iso-cost lines.

The firm and its customer sign the contract and the firm hires 400 workers and rents 100 pieces of equipment. Workers are unionized

and, in the short run, the firm cannot let them go.

The industry signs a new collective contract and the industry wide unit wage raises to w' = 2.

d. In the short run, by how much does the average cost of producing 30 units increase?