Price Discrimination Sample Homework

Question: Kayla lives in southeastern Michigan right near the Ohio border. She owns two gas stations, one located in Ohio and one located in Michigan. She recently hired an economist to estimate the demand for gas by her customers in the two locations. He has provided her with the following estimates.

In Michigan, QM= 55 – 25PM; Thus, inverse demand is P = 55/25 – (Q/25)

In Ohio, QO = 65 – 25PO. Thus, inverse demand is P = 65/25 – (Q/25).

a) The two gas stations are 40 miles apart, so she knows that she can charge different prices at the two locations without having to worry about one group of customers driving to the lowest priced store just to get the low price - that is, she is certain that all of her Michigan customers will buy from her station in Michigan and that all of her Ohio customers will buy from her station in Ohio. Her marginal and average cost of providing one gallon of gas is $1 in both locations. What is the profit maximizing price per gallon to charge in each location? How many gallons will a typical customer purchase in each location?

b) Suppose that federal law requires that the price be the same in both locations. What price will Kayla charge now? How many gallons will be purchased? And what happens to her profit?