Suppose that the mta goal's is to maximize profit. Right now they are considering charging different prices for riding the subway, depending on whether it is rush hour or not. this is an example of price discrimination, charging different prices in different markets for the same good. They think they can do this because demand is higher during rush hour. Assume that the quantity demanded of subway rides during rush hour is r and during non-rush time is n. The demand functions are: Pr = 402 - 6r
Pn = 62 - 2n
You can assume that the cost of providing subway rides is the same no matter the time of day so that:
TC = 20 + 6(r+n)
a) Write out the equation for total revenue, TR, earned by the MTA when they charge different prices in each market. That is, when they price discriminate.
b) Write out the equation for total profit, II, when they price discriminate
c) Find the quantity rides they should sell in each market in order to maximize total profit. And find the resulting prices of each type of ride. Show that you've found a maximum. What is the total profit made by the MTA if they price discriminate in this way?
d) Now suppose that the MTA decides not to price discriminate. That is, they charge the same price in each market. Write out the demand function that the MTA faces in this combined market.
e) Write out the equations for total revenue, TR, and total profit, 7, if they do not price discriminate.
f) Now how many rides will they sell? At what price? What will be their profit? Show all of your work, including verification that you have found a maximum.
g) Should the MTA price discriminate? Why or why not?