Kip’s Auto Detailing has locations in two distant neighborhoods, Uptown and Downtown. Uptown customers’ demand is given by QUT = 1,000 – 10P, where Q is the number of cars detailed per month; Downtown customers’ demand is QDT = 1,600 – 20P.. The marginal and average cost of detailing a car is constant at $20.

a. Determine the price that maximizes Kip’s profit if he prices uniformly in both markets. How many customers will he serve at each location? What will his profits be?

b. Suppose Kip decides to charge different prices at each location. What price should he establish in each location? What will his profits be? 

c. How big are the gains to Kip’s differential pricing scheme?