Suppose that consumers have a linear demand function and are located uniformly from distance x = 0 to distance x = 1. The transportation cost to distance x is tx.
(i) Compute the optimal f.o.b. prices when discrimination is allowed.
(ii) Suppose that transportation is operated through a competitive sector at the same unit cost, t. Compute the optimal uniform (i.e. nondiscriminatory) f.o.b. price, assuming that the whole market is served. Can one say that in the no-discrimination case some consumers “cross-subsidize” others?
(iii) Which arrangement serves the largest market in general?