=========================preview======================
(ECON200)Fall2007_Final.pdf
Back to ECON200 Login to download
======================================================
Microeconomic Theory II C ECON 200
Fall 2007
HKUST
Final Exam
December 12, 2007
8:30 am C 11:30 pm


Problem 1 (Total 15 points)
Suppose a monopolist sells to two different markets A and B and she can third-degree price discriminate. The inverse demand functions she faces in the two markets are PA = 10 C QA and PB = 10 C 2QB respectively. If she produces Q units in total, her total cost is Q2/6. What will be the equilibrium prices PA and PB and the total quantity produced Q?

Problem 2 (Total 20 points)
Suppose consumers are uniformly distributed on a Hotelling line of length 1 where a consumers location is given by l [0, 1]. Two firms A and B are located at l = a and l = b respectively with a<.5 and b>.5. Suppose consumers have transportation cost of c per unit of distance, and the firms A and B charge prices pA and pB respectively.
(a) Draw a diagram of the locational choice as done in class. Find the location of the consumer who will be indifferent between firms A and B. (You can assume that c and pA and pB are such that the indifferent consumer will be located between a and b.)

(b) Find the optimal pA and pB and the profits of the two firms assuming that a and b are fixed.

(c) Now suppose a is fixed and firm B can choose any b .5. What b will firm B choose to maximize its profit?



Problem 3 (Total 20 points)
Suppose in a Cournot game (quantity competition) with two firms, the inverse market demand is given by P = 100 C 2(q1 + q2) where qi is the quantity produced by firm i.
(a) If both firms have constant marginal cost of 10, find the market price, quantities produced by each firm and each firms profit.

(b) Now suppose if firm 1 expends a cost of F to acquire a new technology, it can produce any quantity at the marginal cost of zero. Firm 2 does not have this option. How much will firm 1 be willing to spend for this technology? How much will firm 2 be willing to pay as a bribe to legislate a bill to bar firm 1 from acquiring this technology? Show all your steps.



Problem 4 (Total 17 points)
An entrepreneur purchases two firms to produce widgets. Each firm produces identical products, and each has a production function given by q = (kili).. In the short run, k1 = 25 and k2 = 100. Rental rates for l and k are given by w = 4 and v =1 respectively.
(a) How should output be allocated between the two firms to minimize the short-run total cost of widget production?

(b) Given that output is optimally allocated between the two firms, calculate the entrepreneurs short-run total, average and marginal cost functions.

(c) How should the entrepreneur allocate widget production between the two firms in the long run? Calculate the entrepreneurs long-run total, average and marginal cost functions.



Problem 5 (Total 18 points)
(a) Consider the following 2-player simultaneous game.



Player IIs Pure Strategies

L
C
R



Player I