Question

Hotelling. Two firms, labeled 1 and 2, are located at the ends of a Hotelling line of length 1. L customers are uniformly distributed along the line. Each customers wants to buy one unit of the product and the product is worth V to each customer. A customer located distance d from a given firm incurs travel cost td to purchase the product from that firm. Firms produce at constant marginal cost c < V, and they engage in Bertrand price competition.

The products of firms 1 and 2 are substitutes at the equilibrium prices if the demand for each firm's product increases with a small increase in the other firm's price, starting from the equilibrium price. If each firm's demand does not change with a small increase in the other firm's price starting from the equilibrium prices, ther independent in demand at the equilibrium prices. Which of the following statements is true?
a. The products are substitutes at the equilibrium prices regardless of the values of V, 1, and c.
b. The products are substitutes at the equilibrium prices If V is sufficiently large relative to t and c.
c. The products are independent in demand (and not substitutes) if iftis sufficiently large relative to V.
d. (a) and (b) are true
e. (b) and (c) are true

Answer 1

(e) (b) and (c) are true

The products will surely act as substitutes if the consumer's valuation is larger than c and t at equilibrium prices. They would also act as substitutes when the values of distance and price are taken into account. Then if V is too small in comparison to t, the consumer may not demand either and they would not act as substitutes as the demand would now be independent just as stated in c