Kelly and Sarah are directly opposite to each other at the extreme ends of a 5 km street. There are 100 people uniformly distributed over this street and they each buy a can of cola from either Kelly or Sarah. The transportation cost of these consumers is $1 per kilometer.

(i) Suppose Kelly charges a price of P_K and Sarah charges a price of P_S. What are their demand functions? Let the quantity sold be Q_K and Q_S.

(ii) Are the demand functions downward-sloping? Are the goods substitutes or complements?

(iii) Find the equilibrium prices set by Kelly and Sarah.

Go back to question 1 above. Suppose that a consumer located x kilometers away from Kelly gets a net payoff of U_K = A - 2x – P_K, when she buys from Kelly, where A > 0 and U_S = B - 2(5-x) – P_S, when she buys from Sarah, where B > 0.

(i) Find the demand functions for Kelly and Sarah.

(ii) If A > B, will Kelly and Sarah sell the same quantities when they charge the same prices?

(iii) Explain why Kelly sells more although they charge the same prices, A > B.