(econ522)[2008](s)mid~PPSpider^_10257.pdf

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Midterm Exam

Microeconomic Theory II, ECON 522

HKUST

March 31, 2008

2:00 pm C 5:30 pm

Problem 1 (Total 15 points)

In each of the following 2-player games, what strategies survive iterated elimination of strictly dominated strategies? Find all the Nash equilibria for each game.

a)

Player IIs Strategies

L

C

R

Player Is Strategies

T

(0, 2)

(4, 3)

(3, 1)

M

(1, 2)

(2, 0)

(2, 1)

B

(2, 4)

(3, 6)

(0, 3)

b)

Player IIs Strategies

L

C

R

Player Is Strategies

T

(1, 3)

(5, 4)

(4, 2)

M

(2, 2)

(3, 2)

(3, 1)

B

(3, 5)

(5, 3)

(1, 4)

Problem 2 (Total 12 points)

Suppose two players are trying to divide a pie of size 1 among themselves. First, player 1 divides the pie into two pieces of size y and 1 C y where y[0, 1]. Then player 2 chooses either of the two pieces. Player 1 receives the remaining piece. Assume that a players utility is strictly increasing in the size of the piece of the pie she gets.

a) Draw the game tree for this game. (5 points)

b) Find all the subgame perfect equilibria of this game. (7 points)

Problem 3 (Total 18 points)

Consider a dynamic version of the Hotelling model where the customers are uniformly distributed on the unit interval [0, 1]. Each customer has a unit demand for the good (the valuation v is sufficiently high) and is characterized by her location l[0, 1]. Firm 1 is located at location l1<0.5 and firm 2 is located at l2>0.5. A customer located at point l [0, 1] incurs a transportation cost of t |l C l1| if she purchases from firm 1 and a transportation cost of t |l C l2| if she purchases from firm 2, where t > 0. Except for the locations, the goods produced by the two firms are identical. Both firms have zero marginal and average production costs. In period 1, firm 1 announces a price of p1. In period 2 (and after observing p1), firm 2 announces a price of p2. Observing both prices, consumers decide which firm to buy the good from. Solve for the subgame perfect equilibrium of the dynamic Hotelling game, showing your work. What will be the profits of the two firms? If l1 + l2 = 1 then is there a first-mover or a second-mover advantage (over the static game) in the dynamic game?

Problem 4 (Total 25 points)

a) Suppose a firm produces 2 goods: good x and good y using 2 inputs: labor (l) and capital (k). The prices the firm receives for goods x and y are px and py respectively. Suppose the production function for x is f(kx,lx) and the production function for y is g(ky,ly). The functions f and g are increasing in both inputs. Moreover, the total endowments of capital and labor for the firm are K and L respectively. What is the equilibrium price ratio px / py? (6 points)

b) Now suppose f(k,l) = k2l and g(k,l) = kl2. What will be the ratio of the capital-labor ratios for good x and good y? Do you have enough informati