Question

You own a private parking lot near UC Berkley with a capacity of 600 cars. The demand for the parking lot is estimated to be Q = 1000 - 2p, where Q is the number of customers with monthly parking passes a p is the monthly parking fee per car.

1. (a) Derive your marginal revenue (per car per month) schedule.

2. (b) What price generates the greatest revenue.

Your fixed costs of operating the lot (such as monthly lease paid to landlord, cost of hiring an assistant, etc) are $25,000 per month. In addition the insurance company charges you $20 per car per month for liability coverage. Additionally, the City of Berkley charges you $30 per car per month as part of it’s ‘Clean Berkley’ campaign which includes discouraging the use of private automobiles.

3. (c) Derive your (monthly) total cost function and marginal cost (per car per month).

4. (d) What is your profit-maximizing price (monthly parking fee per car?

Answer 1

Ans. a) p = 500 - Q/2 , Now we will use the ' twice the slope ' formula for marginal revenue associated with linear demand curve , then MR = 500 - Q.

b) Revenue is maximized when MR is 0 , so 500 - Q = 0

Q = 500 and now putting the value of Q to find p.

p = 500 - 250

p = 250

c) The monthly Total Cost function is C = 25000 + 50Q and Marginal Cost = 50

d) We can find Profit Maximizing price , we have to make MR = MC . 500 - Q = 50 ie Q = 450

Putting the value of Q to find p

p = 500 - 450/2

p = 500 - 225

p = 275

Best of Luck !! !!