Consider a simple Hotelling city setup. There are two firms located at either end of a street of length one mile (so, Firm 1 is at 0 and Firm 2 is at 1). 100 consumers are uniformly located along the street. Consumers bear a transportation cost of $t per unit of distance. Each consumer will buy 1 and only 1 unit of the good. The firms can produce the good at zero marginal cost. Denote Firm 1’s price p1 and Firm 2’s price p2. a. Call x (where x must be between 0 and 1 inclusive), the location of the consumer who is indifferent between buying from Firm 1 and from Firm 2. Write down a formula for x. (Hint: it should have a p1 in it, a p2 in it, and a t in it!).
Consider a simple Hotelling city setup. There are two firms located at either end of a street of length
one mile (so, Firm 1 is at 0 and Firm 2 is at 1). 100 consumers are uniformly located along the
street. Consumers bear a transportation cost of $t per unit of distance. Each consumer will buy 1 and
only 1 unit of the good. The firms can produce the good at zero marginal cost. Denote Firm 1’s
and Firm 2’s price p2.
a. Call x (where x must be between 0 and 1 inclusive), the location of the consumer who is
indifferent between buying from Firm 1 and from Firm 2. Write down a formula for x. (Hint: it
should have a p1 in it, a p2 in it, and a t in it!).
This model was developed by Harold Hotelling in the year 1929. The model represents the concept of locational equilibrium a duopoly. There will be 2 firms and they have to choose their location while taking into account transportation costs and consumer’s distribution. It includes 2 approaches: Static model and Dynamic model. According to the game theory concept the firms must choose a location and then choose a selling price for their product. To maximize profit business must set in best location and three key variables must be evaluated:
Customer distribution
Transportation cost
Competitor's location.
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