A private garage owner has identified two distinct market segments: short-term parkers and all-day commuters. Their respective demand functions are Ps = 4 − s 200 PC = 2 – C 200 Here, Ps, Pc are the average hourly rates and Qs, Qc are the number of cars parked at these prices. There is no cost of parking cars. a. For now, suppose that there is unlimited capacity in the garage. If the garage owner cannot determine whether a customer is a short-term parker or an all-day commuter, and can only set one price, what is the profit maximizing price they should set? How many cars will park in the garage? b Now suppose that there is still unlimited capacity, but the garage owner can price discriminate by charging each group of consumers a separate price. What are the optimal prices Ps, Pc and number of cars Qs, Qc? c. Suppose that there is limited capacity in the garage, and there are only 400 parking spots. The owner can still price discriminate by type of consumer. What are the optimal prices Ps, Pc and number of cars Qs, Qc after accounting for the capacity constraint?