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5. (30 points) Consider a Hotelling line city model, where two firms are located at the...
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...
Consider a Hotelling line of length 1. A grocery store is located at each endpoint. The...
Consider a Hotelling line of length 1. A grocery store is located at each endpoint. The grocery store at the west end point is owned and operated by Jack Donaghy and offers customers the use of a personal “grocery concierge”, free of charge, who assists the customer in shopping. The grocery store at the east endpoint is owned and operated by Milton Greene and does not offer its customers a grocery concierge. The utility of a consumer at location x...
9) In Hotelling's linear city (address model where consumers are uniformly distributed over a line of...
9) In Hotelling's linear city (address model where consumers are uniformly distributed over a line of size 1), suppose there are two firms located at the two opposite ends with constant marginal cost c. Consumers utility is given by V- tx2-p, where is per unit transportation cost, x is consumer's distance to a firm, V is the value of consuming the good and p is the price of the good. If firms compete by choosing prices, what is the Nash...
Question5 up to Question8 Due Date: Tuesaay, January zy at tne start or tne lecture Model...
Question5 up to Question8
Due Date: Tuesaay, January zy at tne start or tne lecture Model Setup Let's model an economy that produces and consumes only two goods, croissants (C) and espresso (E), between two cities, Toronto (T) and Paris (P). In Paris, each unit of labour produces 5 croissants or 2 shots of espresso. In Toronto, unit of labour produces 4 croissants or 10 shots of espresso. There are 200 units of labour in Toronto and 400 units of...
Suppose that there two goods X and Y, available in arbitrary non- negative quantities (so the...
Suppose that there two goods X and Y, available in arbitrary non- negative quantities (so the the consumption set is R2). The consumer has preferences over consumption bundles that are strongly monotone, strictly convex, and represented by the following (differentiable) utility function: u(x, y)-y+2aVT, where z is the quantity of good X, and y is the quantity of good Y, and a 20 is a utility parameter The consumer has strictly positive wealth w > 0. The price of good...
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 consumer with a utility function u(x1, x2) = min{21, 222}. Suppose the prices of...
Consider a consumer with a utility function u(x1, x2) = min{21, 222}. Suppose the prices of good 1 and good 2 are p1 = P2 = 4. The consumer's income is m = 120. (a) Find the consumer's preferred bundle. (b) Draw the consumer's budget line. (c) On the same graph, indicate the consumer's preferred bundle and draw the indifference curve through it. (d) Now suppose that the consumer gets a discount on good 1: each unit beyond the 4th...
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...
2. Suppose there are two consumers in a country: consumer 1 and consumer 2. The two...
2. Suppose there are two consumers in a country: consumer 1 and consumer 2. The two consumers have the following Cobb-Douglas utility function defined over consumption of goods X and Y: where 0 < β < 1. Each consumer has a different income, consumer 1 has income 1, while consumer 2 has income 12. For now, we will treat the income of each consumer as given. Denote aggregate income as I 12. (a) (10 points) Derive each consumer's individual Marshallian...
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...
9) In Hotelling's linear city (address model where consumers are uniformly distributed over a line of size 1), suppose there are two firms located at the two opposite ends with constant marginal cost c. Consumers utility is given by V- tx2-p, where is per unit transportation cost, x is consumer's distance to a firm, V is the value of consuming the good and p is the price of the good. If firms compete by choosing prices, what is the Nash...
Question5 up to Question8
Due Date: Tuesaay, January zy at tne start or tne lecture Model Setup Let's model an economy that produces and consumes only two goods, croissants (C) and espresso (E), between two cities, Toronto (T) and Paris (P). In Paris, each unit of labour produces 5 croissants or 2 shots of espresso. In Toronto, unit of labour produces 4 croissants or 10 shots of espresso. There are 200 units of labour in Toronto and 400 units of...
Suppose that there two goods X and Y, available in arbitrary non- negative quantities (so the the consumption set is R2). The consumer has preferences over consumption bundles that are strongly monotone, strictly convex, and represented by the following (differentiable) utility function: u(x, y)-y+2aVT, where z is the quantity of good X, and y is the quantity of good Y, and a 20 is a utility parameter The consumer has strictly positive wealth w > 0. The price of good...
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 consumer with a utility function u(x1, x2) = min{21, 222}. Suppose the prices of good 1 and good 2 are p1 = P2 = 4. The consumer's income is m = 120. (a) Find the consumer's preferred bundle. (b) Draw the consumer's budget line. (c) On the same graph, indicate the consumer's preferred bundle and draw the indifference curve through it. (d) Now suppose that the consumer gets a discount on good 1: each unit beyond the 4th...
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. Suppose there are two consumers in a country: consumer 1 and consumer 2. The two consumers have the following Cobb-Douglas utility function defined over consumption of goods X and Y: where 0 < β < 1. Each consumer has a different income, consumer 1 has income 1, while consumer 2 has income 12. For now, we will treat the income of each consumer as given. Denote aggregate income as I 12. (a) (10 points) Derive each consumer's individual Marshallian...
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