Assume a “Hotelling” line of a distance l = 1. There are two companies A and B, both of them being located at a longer distance. Company A is placed closer to the end of the line, while company B is placed further away. The distance from the beginning of the line to company A is a (a > l) and to B is b (b > a > l). Assume also that an indifferent consumer is located close to the beginning and the distances to A and B are, x and y respectively, where y = x + b – a. Assume quadratic transportation costs, i.e. cx2 and cy2, and prices PAand PB. Find the equilibrium prices and the condition under which both firms will have positive sales. (Hint: Assume that the quantity demanded of firm A is qA = a – x).
Assume a “Hotelling” line of a distance l = 1. There are two companies A and...
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...
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...
Find the distance of a point (1, 2, 3) to the line L: x = 3 + 4t, y = -2 + 2t, z = 2t. Give your answer correct to two decimal places.
1. Two cell phone companies A and V are located at the extremes of a line of length one and transportation cost t = 4.. Consider an initial situation where both firms offer a generic phone that consumers value the same (except obviously for the transportation cost.) Marginal cost is zero. (this problem was answered in class.) (a) Find the Bertrand equilibrium. Letting N = 800 denote the total population, show that profits for each firm will be 1600. (b)...
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...
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,...
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...
(1) (a) Find the equation of the line, Li, which passes through the points A : (4,y,z) = (0, -5, -3) and B : (x, y, z)=(3, 1,0). (b) Find the equation of the line, Ly, which passes through the points C:(x, y, z)=(-1, -3,2) and D: (x,y,z) = (4,3,6). (c) Show that L and Ly are not parallel lines. (d) Write the parametric equations for L, and L2, and then show that the lines Li and L2 do not...
1. A point charge +Q is located at the origin, and a point
charge -Q is located at (x,y) = (0,L).
(a) Find the electric field at point P, which is a distance L
away from both +Q and -Q, as shown in the diagram. Express your
answer in unit vector notation using the coordinate system
given.
(b) A point charge -2Q is placed at point P. Find the Coulomb
force on the charge -2Q due to the other two...
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(a) A solenoid is of length L and has n turns. i.Write the expression for the magnetic flux density B within the solenoid ii. State, in terms of B, the magnetic flux density at the ends of the solenoid. when the current in the solenoid is 2 marks] Two long straight wires are separated by a distance R. Both wires carry the same current / but in opposite direction. Point P is located midway...