1. Consider the case of two gas stations that are located at two ends of a small town. The population is uniformly distributed from these two gas stations. The cost of traveling from one gas station to the other is 50 cents. The gas stations can buy a gallon of gasoline in the wholesale market at $1. 25 per gallon a. How does firm 1 set prices given the price p2 of the other firm?
That is, what is the reaction function of firm 1. b. What prices will the firms set in equilibrium?
2. Show that when the marginal cost of the two firms is different in the Hotelling model, then
a. The equilibrium prices are given by p ⋆ 1 = 2 3 c1 + 1 3 c2 +
t and p ⋆ 2 = 1 3 c1 + 2 3 c2 + t where c1 is the marginal cost of
firm 1 and c2 is the marginal cost of firm 2.
b. What would happen in this case if there is no product differentiation, that is we have the Bertrand price-setting model?
Answer for question a.a. How does firm 1 set prices given the price p2 of the other firm?
In Wholesale market the market cost is determined by Supply and Demand which sets the Equilibrium Price and Equilibrium Quantity.
Where as in case of Individual firm , the firm is not large enough to influence the price of the goods because there are so many firms in the market competing. So the firm set prices based on the MARKET PRICE.
Individual firm cannot set price above the market price because there are other firms which sets price at lower cost and the demand will be less.
Individual firm cannot set price below the market price because it will face loss.
Hence firm sets price basis the Market Price.
Market Price is determined by the price of the Whole Sale Market.
Answer for question 2a:
Question:Show that when the marginal cost of the two firms is different in the Hotelling model, then
a. The equilibrium prices are given by p ⋆ 1 = 2 3 c1 + 1 3 c2 + t and p ⋆ 2 = 1 3 c1 + 2 3 c2 + t where c1 is the marginal cost of firm 1 and c2 is the marginal cost of firm 2.
Answer : The Consumer will focus on the overall cost. They not only consider Price factor but also the distance which the firm is situated. So even the transportation cost is important for consumer.
Consumer will buy where the cost of the product is cheap also considering the transport cost.
Answer for question 2b:
What would happen in this case if there is no product differentiation, that is we have the Bertrand price-setting model?
In case there is no price differentiation and the price is regulated then the firms may split the market share 50-50.
Also in the absence of price competition the firms will go where the demand is.
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