Consider a Hotelling linear city where four firms simultaneously decide their own locations 0 ≤ θi ≤ 1 (i = 1, 2, 3, 4) to sell their products. Suppose that one-fifth of consumers lives at a location x = 0, one-tenth of consumers lives at a location x = 1, and the remaining 7/10 of consumers live uniformly between x = 0 and x = 1.
Required:
(1) In the Nash equilibrium, where is the location of the firm from which consumers who live at a location x = 0 will buy a product?

a) x = 3/16.
b) x = 1/16.
c) x = 3/13.
d) x = 1/4.
e) x = 1/13.

(2) In the Nash equilibrium, where is the location of the firm from which consumers who live at a location x = 1 will buy a product?

a) x = 7/8.
b) x = 15/16.
c) x = 13/16.
d) x = 11/13.
e) x = 12/13.

(3) In the Nash equilibrium, what is the maximum distance for which consumers must travel to buy a product from the closest firm?

a) 4/13.
b) 5/16.
c) 3/16.
d) 3/13.
e) 1/8.