Drumpf Country Club has the only golf course in Distopia. The (annual)demand to play a round of golf on its course is given byD (p) = 12000 10pwhere D (p) is the number of rounds demanded each year if Drumpf chargeda uniform price of p per round. The marginal cost of having someone playa round of golf is zero and the annual (fixed) cost of maintaining the golfcourse is 1000000.(a) (15 points) Determine the optimal uniform price for Drumpf tocharge for a round of golf. Compare the welfare of golfers and Drumpfin this situation compared to what would have been the case if the pricehad been set equal to the marginal cost (and the fixed cost had beencovered by a subsidy from the Distopian Government). What is thedeadweight loss that arises from Drumpf employing monopoly uniformpricing instead of having marginal-cost pricing
Question
Drumpf Country Club has the only golf course in Distopia. The (annual)demand to play a round of golf on its course is given byD (p) = 12000 10pwhere D (p) is the number of rounds demanded each year if Drumpf chargeda uniform price of p per round. The marginal cost of having someone playa round of golf is zero and the annual (fixed) cost of maintaining the golfcourse is 1000000.(a) (15 points) Determine the optimal uniform price for Drumpf tocharge for a round of golf. Compare the welfare of golfers and Drumpfin this situation compared to what would have been the case if the pricehad been set equal to the marginal cost (and the fixed cost had beencovered by a subsidy from the Distopian Government). What is thedeadweight loss that arises from Drumpf employing monopoly uniformpricing instead of having marginal-cost pricing
Solution
The optimal uniform price for Drumpf to charge for a round of golf can be determined by setting marginal revenue equal to marginal cost. Since the marginal cost is zero, we need to find the price that maximizes revenue.
The demand function is D(p) = 12000 - 10p. We can write the revenue function as R(p) = pD(p) = p(12000 - 10p) = 12000p - 10p^2.
To find the price that maximizes revenue, we take the derivative of the revenue function with respect to price and set it equal to zero:
R'(p) = 12000 - 20p = 0.
Solving for p gives p = 12000 / 20 = 600. So, the optimal uniform price for Drumpf to charge for a round of golf is $600.
If the price had been set equal to the marginal cost (zero), the welfare of golfers would have been higher because they could play for free. Drumpf, on the other hand, would not be able to cover the fixed cost of maintaining the golf course without a subsidy from the Distopian Government.
The deadweight loss that arises from Drumpf employing monopoly uniform pricing instead of having marginal-cost pricing is the difference in consumer surplus. Under monopoly pricing, consumer surplus is the area under the demand curve and above the price, from 0 to the quantity demanded at the monopoly price. Under marginal-cost pricing, consumer surplus is the area under the demand curve from 0 to the quantity demanded at a price of zero. The difference between these two areas is the deadweight loss.
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