Econ hw in 45 mins

Econ 302 Homework #4 McLeod

Due in class Wednesday, November 5th.

Name ______________________________________________________

ID # ________________________________________________________

Instructions: Please Read Carefully

Please print out this form. The first sheet is intended only as a cover sheet. Do not write anything on the first sheet except your name and ID #.

Please answer each question on the page provided. If you need extra space, you may use the back of the sheet.

There are 50 possible points on this homework assignment. You may work together, but you MUST WRITE UP YOUR OWN WORK and TURN IT IN, IN PERSON, AT THE BEGINNING OF CLASS on Wednesday, November 5th. Late homework will not be accepted.

PLEASE STAPLE YOUR HOMEWORK!!

1. (28 points) Suppose a monopolist can purchase Labor at a price w = 1 and can purchase Capital at a price r = 9. The monopolist’s production function is given by Q = L1/2K1/2. The demand facing the monopolist is given by P = 78 – 6Q.

a) (12 points) What is the Monopolist’s total cost function?

TC = 6Q

Slope of Isoquant = Slope of Isocost (4 points)

L* = 3Q (2 points)

K* = 1/3Q (2 points)

TC = w*L +r*K (2 points)

TC = 6Q (2 points)

b) (2 points) What is the Monopolist’s Marginal Cost?

MC = 6

c) (14 points) Complete the following table. In the first column, find the values for the Monopolist. In the second column, find the values if the market were instead perfectly competitive.

(1 point each)

	Monopoly	Perfect Competition
Price	42	6
Quantity of Output	6	12
Quantity of Labor used (L*)	18	XXXXX
Quantity of Capital used (K*)	2	XXXXX
Consumer Surplus	108	432
Producer Surplus	216	0
Deadweight Loss	108	0
Lerner Index	6/7	0

2. (12 points) Suppose there are n identical firms in a market. Each firm’s cost function is given by C = 648 + 8q2, where q is the amount that an individual firm produces. This means that an individual firm’s marginal cost is given by MC = 16q. Also, the market demand is given by P = 306 – 3Q, where Q is the total amount of the good produced by all of the firms combined. Therefore, Q = n*q.

a) (4 points) How much output will each firm produce?

q = 9

b) (4 points) What will be the market price?

P = 144

c) (4 points) How many firms will there be in long run equilibrium?

n = 6

3. (10 points) Suppose that two players are playing the following game. Player 1 can choose either Top or Bottom, and Player 2 can choose either Left or Right. The payoffs are given in the following table:

		Player 2
Player 1		Left	Right
	Top	6 2	2 1
	Bottom	1 0	0 3

where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B.

A) (1 point) Does player 1 have a dominant strategy, and if so what is it? YES--TOP

B) (1 point) Does player 2 have a dominant strategy and if so what is it? NO

C) (1 point each) For each of the following strategy combinations, write TRUE if it is a Nash Equilibrium, and FALSE if it is not:

i) Top/Left True

ii) Top/Right False

iii) Bottom/Left False

iv) Bottom Right False

D) (1 point) What is Player 1’s maximin strategy? TOP

E) (1 point) What is player 2’s maximin strategy? RIGHT

F) (2 points) If the game were played with Player 1 moving first and player 2 moving second, using the backward induction method we went over in class, what strategy will each player choose?

TOP/LEFT or (6,2)