Suppose a "town" comprises people uniformly distributed along a line 30 miles long, with 100 people per mile. Travel costs are 1 dollar per person per mile. There is one bowling alley located at mile 10 and another located at mile 20. All customers are willing to pay up to 15 dollars for a night of bowling. The mile-10 bowling alley is a little newer - the marginal cost of caring for a customer while at that bowling alley is 2 dollars. The marginal cost of caring for a customer at the mile-20 bowling alley is 4. Ignore the fixed costs of each bowling alley set them equal to zero.

(a) Assume customers pay their own transport costs to the bowling alley and each bowling alley acts to maximize its profits. Calculate total consumers' surplus and the total profits of the two bowling alleys.

(b) Now assume the bowling alleys pay transport costs for their customers, and again, each bowling alley acts to maximize its profits. As carefully as you can, draw: (i) a 1 graph of price against location; (ii) a graph of profit against location; and (iii) a graph of consumer's surplus against location.

(c) What does "price discrimination" mean in this context?