The Key West Parrot Shop has a monopoly on the sale of parrot souvenir caps in Key West. The inverse demand curve for caps is:
P = 30 - 0.4Q
where P is the price of a cap and Q is the number of caps sold per hour. Thus, the marginal revenue for the Parrot Shop is:
MR = 30 - 0.8Q.
The Parrot Shop is the only employer in town and faces an hourly supply of labor given by:
w = 0.9E + 5
where w is the hourly wage rate and E is the number of workers hired each hour. The marginal cost associated with hiring E workers, therefore, is:
MCE = 1.8E + 5.
Each worker produces two caps per hour. How many workers should the Parrot Shop hire each hour to maximize its profit? What wage will it pay? How much will it charge for each cap?