In the city of Crullaire, the demand curve for doughnuts is given by the equation P=39-Q/20, where Q is the number of doughnuts per day and P is the price of a doughnut. Each doughnut shop that is open has a fixed cost of $200 per day which must be paid so long as the shop is in business and regardless of the number of doughnuts it sells. There is also a variable cost of $4 for each doughnut sold. Each doughnut shop has a capacity of 40 doughnuts per day. Initially, 12 doughnut shops are open in Crullaire. A doughnut shop that is open cannot escape its fixed costs immediately; instead, the doughnut shop must give 6 months advance notice to its landlord that it will close. It also takes about 6 months to organize and open a new doughnut shop.
What are the short-run competitive equilibrium price P* and quantity Q* of doughnuts in Crullaire?
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