14.7 Suppose that the demand for stilts is given by Q= 1,500-50P and that the long-run total operating costs of each stilt-making firm in a competitive industry are given by TC = 0.5q 2

- lOq.

Entrepreneurial talent for stilt making is scarce. The supply curve for entrepreneurs is given by Qs = 0.25a;, where w is the annual wage paid.

Suppose also that each stilt-making firm requires one (and only one) entrepreneur

(hence, the quantity of entrepreneurs hired is equal to the number of firms). Long-run total costs for each firm are hence given by TC = 0.5q 2

- lOq + w.

a. What is the long-run equilibrium quantity of stilts produced? How many stilts are pro duced by each firm? What is the long-run equilibrium price of stilts? How many firms will there be? How many entrepreneurs will be hired, and what is their wage?

b. Suppose that the demand for stilts shifts outward to Q= 2,428 - 50P.
Answer the questions posed in part (a).

c. Because stilt-making entrepreneurs are the cause of the upward sloping long-run supply curve in this problem, they will receive all rents generated as industry output expands.
Calculate the increase in rents between parts

(a) and (b). Show that this value is identi cal to the change in long-run producer surplus as measured along the stilt supply curve.