Econ 385 Problem Set 2
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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 firm 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 firm 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 affect the optimal
location of the two distributers? (use only your intuition to answer
this question).
2. Consider the model of competition with differentiated 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, D1, given the price fixed by seller
2.
(b) Compute the price elasticity of the demand. (hint: elasticity ε is
(c) How does the elasticity change as a function of the transport cost?
Justify economically.
3. Consider a market in which two firms compete in prices, and they offer
a vertically differentiated product (i.e. differentiated by quality) vi(i =
1, 2). In particular assume v1= 1 and v2= 2 and call ui(x) = V + xvi−pi
the utility of consumer x ∈ [0, 1] if he/she buys variety viat price pi.
(a) Offer a graphical representation of the above setting when V = 10
and p1= 0.25 and p2= 0.5.
(b) Assuming zero production costs, derive the equilibrium prices and
demands.
(c) Compute the equilibrium profits at b. and c. Discuss how the profits
depend on the quality difference.
10 years ago
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