Question

Problem 5. You own a private parking lot near Stony Brook University with a capacity of 600 cars. The demand at this lot is estimated to be q 1000-2p where q is the number of costumers with monthly parking for parking passes and p is the monthly parking fee per car (a) Derive your Marginal Revenue schedule. (b) What price generates the greatest revenues? (c) Your fixed costs of operating the parking lot, such as the nmonthly lease paid to the landlord and the cost of hiring an attendant, are $25,000 per month. In addition, your insurance company charges you $20 per car per month for liability coverage, and the city of Brookhaven charges you $30 per car per month as part of its ice? policy to discourage the use of private automobiles. What is your profit-mavi

Answer 1

5)a) Q=1000-2P

P=500-0.5Q

TR=P*Q=500Q-0.5Q²

Marginal revenue=dTR/dQ=500-Q

b) Total revenue is maixmised when marginal revenue is zero

thus When Price=250 and Quantity=500, revenue is maximised

c) marginal cost=20+30=50

Thus profit is maixmised when MR=MC

Thus 500-Q=50

Q=450 and price=500-0.5(450)=275

Profit=225(450)-25000=101250-25000=76250