EC1001 - Introduction to Economics - Economics Assignment Help

Assignment Task

1. Consider a (small) linear city L of total length of 100Km (L = [0, 100]). It has no restaurants so far and govt. has recently given permission to KFC to open its two franchises, F1 and F2. Note that each franchise is owned by a different firm i.e. Fi is operated by firm i, where i ∈ N = {1, 2}). According to KFC norms, both firms have to serve the same food item and charge the same price per unit of food, which is decided by the head office. Therefore, the only decision these firms need to make is where to locate their restaurants. Assume that customers are uniformly located over the entire city, which has a total mass of 100. Each customer needs to travel to buy food and thus spends traveling cost in addition to the price of food. Because price, quality and taste of food from each franchise is identical, a customer’s choice of franchise primarily depends on the traveling cost and she prefers to buy from the nearer franchise. And if a customer finds both the franchises at equal distance then she divides her demand equally. Formally, for any two points x, y ∈ [0, 100], d(x, y) denotes the distance between them i.e. d(x, y) = |x − y|. Suppose a customer stays at point x and restaurants F1 and F2 are located at l1 and l2 respectively, then her choice of restaurant is denoted by Cx(l1, l2) which is as follows:1 Cx(l1, l2) = F1 if d(x, l1) < d(x, l2)
F2 if d(x, l1) > d(x, l2) {F1, F2} otherwise

Assume that each firm has equal constant per unit cost of production. As prices and costs are fixed2, maximizing the profit is equivalent to maximizing the demand (which is obviously based on locations of both firms). This question has two parts, in each part preferences of customers and objectives of firms remain the same.

(a) For a location choice (l1, l2), where l1 ≤ l2, compute the demand for each firm i.

(b) In this setup, we define a location choice (l 1, l?2) as an equilibrium, if no firm wants to change its location, given the location choice of other firm i.e. given l?1 can not get higher profits by choosing some location other than l?1 . Similarly given l? Find such an equilibrium. Is it unique or could there be multiple such equilibria.

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