Econ 385 Problem Set 2 1. Consider the following situation. The gas distributer Dot, is the only gas distributer in a certain town. This town is constituted by a road of 1 mile. The distributer is located exactly in the middle of the road. The consumers are uniformly distributed along the road and face a transportation cost t per unit of distance. The consumers have a valuation of V for buying gas. (a) Consider that the gas distributer is deciding how much to charge for gas. What price per gallon should he charge if he would like to sell to all the consumers? (b) If the ?rm considers opening a new gas distributer (and relocate his old one), where should he locate the distributers? How does the optimal price change when there are 2 distributers? (c) Consider that opening a new distributer has a cost of F = 1. If t = 20, how many gas distributers should the ?rm open? (d) Assume that some road work will be done in the middle of the road such that the left consumers cannot travel to the right and the right consumers cannot travel to the left. Would this a?ect the optimal location of the two distributers? (use only your intu
ition to answer this question). 2. Consider the model of competition with di?erentiated products à la Hotelling. A population of consumers is distributed uniformly in a line of length 1. A seller is placed at 0.25 of one end of the line and the other at 0.25 of the other end. Transportation cost of each consumer is t per unit of length traveled. (a) Determine the demand of seller 1, D , given the price ?xed by seller 2. (b) Compute the price elasticity of the demand. (hint: elasticity ? is (c) How does the elasticity change as a function of the transport cost? Justify economically. 3. Consider a market in which two ?rms compete in prices, and they o?er a vertically di?erentiated product (i.e. di?erentiated by quality) v (i = 1, 2). In particular assume v = 1 and v = 2 and call u (x) = V + xv ?p the utility of consumer x ? [0, 1] if he/she buys variety v at price p . (a) O?er a graphical representation of the above setting when V = 10 and p = 0.25 and p = 0.5. (b) Assuming zero production costs, derive the equilibrium prices and demands. (c) Compute the equilibrium pro?ts at b. and c. Discuss how the pro?ts depend on the quality di?erence.