Suppose that the potential customers for hair braiding in a city consider hair braiding to be identical and that the market is perfectly competitive. Hair braiding requires special skills so the supply of workers in this industry is upward-sloping, and the wages earned by hair braiders increase as the industry output increases. Firms in this market face the following total cost:
TC = Q3 - 8Q2 + 20Q + W
where Q is the number of hair braidings and W is the daily wage paid to workers. The wage, which depends on total industry output, equals W = 0.1NQ, where N is the number of firms. Market demand is QD = 500 - 20P.
a. How does average total cost for the firm change as industry output increases? What does this relationship imply for industry's long-run supply curve?
b. Find the long-run equilibrium output for each firm.
c. How does the long-run equilibrium price change as the number of firms increases?
d. Find the long-run equilibrium number of firms and total industry output.
e. Find the long-run equilibrium price.
f. Suppose that demand increases to QD = 1,000 - 10P. Find the new long-run competitive equilibrium. Does this match your prediction about the long-run supply curve from part (a)?