Suppose that in the model consumers have transportation cost t per squared unit length. (These are quadratic

transportation costs). Thus, if the location of shop one is at x=0 and the location of shop two is at x= 1, it costs a

consumer at point x, t(x)^2 to get to shop one and t(1-x)^2 to get to shop two.

(1)Find the demand function by finding the location xi of consumer I who is indifferent between shop 1 and

shop 2. What is the demand for consumer going to Shop 1 when p1=10, p2=15, t = 10, and N=1? What is

the demand for consumer going Shop 2 when p1=10, p2=15, t = 10, and N=1?

(2) Find competitive prices and profits per firm if the marginal cost of production is c, when c=10 and t=30

Assume symmetry, i.e. p1 = p2, and that N =1.

(3) Where is the optimal place (from a social welfare point of view) for the shop on the left to locate? Where is

the optimal place for the shop on the right to locate? (hint: the location minimizes transportation costs for the consumer).

(4) In this specific model is there too much or too little differentiation?