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9) In Hotelling's linear city (address model where consumers are uniformly distributed over a line of...
1. Two firms compete in a linear city of length 1 unit. Consumers are uniformly located...
1. Two firms compete in a linear city of length 1 unit. Consumers are uniformly located along the city. Consumer i's utility derived from buying firm j's product is given by jj-(-x)2-Pj where j 1,2 indicate the two firms, t is the per unit cost of travelling along the city, is the location of consumer i, x is the location of firm j, and pj is the price of product j. Product one contains some intrinsically superior features and 22,...
2. Consider a version of the Hotelling model in which prices are endogenously determined. Two firms...
2. Consider a version of the Hotelling model in which prices are endogenously determined. Two firms sell horizontally differentiated products located at opposite ends of the one-dimensional product space. Firm O is located at 0. Firm 1 is located at 1. M consumers are uniformly distributed between 0 and 1, with each consumer's location giving his most preferred type of product. Each consumer places value v on one unit of his most preferred product, but incurs a transportation cost. AD...
5. (30 points) Consider a Hotelling line city model, where two firms are located at the...
5. (30 points) Consider a Hotelling line city model, where two firms are located at the two extreme points. The length of the city is 1, and the consumers are evenly distributed over the line. Transportation cost per unit is t. The utility of the good for each consumper is 2 and each consumer only consumes one unit of good. Consumer's utility is zero without purchase. Suppose price charged by fir i 1; 2) is pi a). (10 points) Determine...
Consumers live uniformly in a "linear-1-mile city". There are two firms, located at r-0 and r...
Consumers live uniformly in a "linear-1-mile city". There are two firms, located at r-0 and r - 1, which each produce the same physical good at marginal cost of c > 0. Consumers have transportation cost t per unit of distance. Firms are competing for customers by selecting their prices pı 2 0 and p2 2 0. It is assumed that each consumer will buy exactly one unit of the product. Firm 1 Consumer at r Firm 2 cost of...
Consider a main street, which is 1 mile long. There are N people uniformly distributed along...
Consider a main street, which is 1 mile long. There are N people uniformly distributed along the main street. Each customer either buys one unit of product from one of the two firms located at either end of the main street every day or buys nothing. If a customer buys no product, her utility will be zero. Each customer’s reservation utility of consuming this product is $V. Each customer’s there and back transportation cost is $t per mile. Suppose that...
2) Consider a location model of differentiated products where the set of possible products is the...
2) Consider a location model of differentiated products where the set of possible products is the line segment [0,11 and consumers are uniformly distributed along the line segment. Transportation costs in this model are equal to td, where d= |x- is the distance between the consumer's ideal variety and the variety she purchases. If a consumer with ideal variety x* purchases variety x at price p, then her utility is If the consumer does not purchase the good her utility...
Consider a market in which consumer type x is uniformly distributed on the unit interval. Consumers...
Consider a market in which consumer type x is uniformly distributed on the unit interval. Consumers demand 0 or 1 unit (they buy at most one unit overall in the market). Firm A is located at 0 and firm B at 1. Firms incur constant marginal costs of production c = 1/2. There is mass 1 of consumers. A consumer located at x ∈ [0;1] obtains utility ux = r−x−pA if she buys from firm A; ux = r−(1−x)−pB if...
Two firms compete in a market with demand given by D(p) = 100 − p, where...
Two firms compete in a market with demand given by D(p) = 100 − p, where p is denoted in cents (p=100 is 1 dollar). Firms can only charge prices in whole cents – i.e. p can only take integer values, and not values like 1.5. Marginal costs for each firm are given by MC=10. Firms compete by simultaneously choosing prices. When prices are equal, each firm gets one half of total demand. b. Find all the Nash equilibria of...
A question of game theory 2. Imagine that a large number of consumers are uniformly distributed...
A question of game theory
2. Imagine that a large number of consumers are uniformly distributed along a boardwalk that is 1 mile long. (Hint: "Uniformly distributed" is a mathematical expression which refers to the uniform distribution of a continuous random variable. In this exercise, it essentially describes a situation such that half of the consumers are located along the first half mile of the boardwalk, and the other half of the consumers are located along the second half of...
EC202-5-FY 10 9Answer both parts of this question. (a) Firm A and Firm B produce a homogenous good and are Cournot duopolists. The firms face an inverse market demand curve given by P 10-Q. where...
EC202-5-FY 10 9Answer both parts of this question. (a) Firm A and Firm B produce a homogenous good and are Cournot duopolists. The firms face an inverse market demand curve given by P 10-Q. where P is the market price and Q is the market quantity demanded. The marginal and average cost of each firm is 4 i. 10 marks] Show that if the firms compete as Cournot duopolists that the total in- dustry output is 4 and that if...
1. Two firms compete in a linear city of length 1 unit. Consumers are uniformly located along the city. Consumer i's utility derived from buying firm j's product is given by jj-(-x)2-Pj where j 1,2 indicate the two firms, t is the per unit cost of travelling along the city, is the location of consumer i, x is the location of firm j, and pj is the price of product j. Product one contains some intrinsically superior features and 22,...
2. Consider a version of the Hotelling model in which prices are endogenously determined. Two firms sell horizontally differentiated products located at opposite ends of the one-dimensional product space. Firm O is located at 0. Firm 1 is located at 1. M consumers are uniformly distributed between 0 and 1, with each consumer's location giving his most preferred type of product. Each consumer places value v on one unit of his most preferred product, but incurs a transportation cost. AD...
5. (30 points) Consider a Hotelling line city model, where two firms are located at the two extreme points. The length of the city is 1, and the consumers are evenly distributed over the line. Transportation cost per unit is t. The utility of the good for each consumper is 2 and each consumer only consumes one unit of good. Consumer's utility is zero without purchase. Suppose price charged by fir i 1; 2) is pi a). (10 points) Determine...
Consumers live uniformly in a "linear-1-mile city". There are two firms, located at r-0 and r - 1, which each produce the same physical good at marginal cost of c > 0. Consumers have transportation cost t per unit of distance. Firms are competing for customers by selecting their prices pı 2 0 and p2 2 0. It is assumed that each consumer will buy exactly one unit of the product. Firm 1 Consumer at r Firm 2 cost of...
2) Consider a location model of differentiated products where the set of possible products is the line segment [0,11 and consumers are uniformly distributed along the line segment. Transportation costs in this model are equal to td, where d= |x- is the distance between the consumer's ideal variety and the variety she purchases. If a consumer with ideal variety x* purchases variety x at price p, then her utility is If the consumer does not purchase the good her utility...
A question of game theory
2. Imagine that a large number of consumers are uniformly distributed along a boardwalk that is 1 mile long. (Hint: "Uniformly distributed" is a mathematical expression which refers to the uniform distribution of a continuous random variable. In this exercise, it essentially describes a situation such that half of the consumers are located along the first half mile of the boardwalk, and the other half of the consumers are located along the second half of...
EC202-5-FY 10 9Answer both parts of this question. (a) Firm A and Firm B produce a homogenous good and are Cournot duopolists. The firms face an inverse market demand curve given by P 10-Q. where P is the market price and Q is the market quantity demanded. The marginal and average cost of each firm is 4 i. 10 marks] Show that if the firms compete as Cournot duopolists that the total in- dustry output is 4 and that if...
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