Homework 2 Answer Key Econ 342 Spring 2024

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Pennsylvania State University *

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342

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Economics

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Feb 20, 2024

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Econ 342 Homework #2 McLeod Due on Canvas by 11:59 pm, Sunday, February 11 th , 2024. LATE HOMEWORK WILL NOT BE ACCEPTED. Name ______________________________________________________ ID # ________________________________________________________ Instructions: Please Read Carefully Please download and print out this form. After you have written your answers, scan it and upload it to Canvas. There are 50 possible points on this homework assignment.
1. (8 total points) Complete the following table: q FC VC TC AFC AVC ATC MC 0 24 0 24 ----- ----- ----- ----- 1 24 8 32 24 8 32 8 2 24 12 36 12 6 18 4 3 24 18 42 8 6 14 6 4 24 28 52 6 7 13 10 5 24 46 70 4.8 9.2 14 18 -1 point for each 4 incorrect responses: # wrong Point deduction 1-4 -1 5-8 -2 9-12 -3 13-16 -4 17-20 -5 21-24 -6 25-28 -7 29-31 -8
2. (26 total points) Suppose there are 3 firms in an industry. The Market Demand Curve is given by P = 128 – 4Q. Each firm has MC = 8 and FC = 0. Suppose the firms form a Cartel and agree to maximize the joint profits, split the profit-maximizing output equally and split the profits equally. A) (4 points) How much output will each firm produce? q i = 5 i = 1,3 B) (4 points) How much profit will each firm make? i = 300 i = 1,3 C) (4 points) Now suppose that Firm 1 decides to cheat on the agreement. Assuming the other 2 firms each produce the quantity given in A), write the equation for the residual demand that faces Firm 1. q R = 22 – (1/4)P or 22 - .25P D) (4 points) If Firm 1 expects each of the other firms to produce the amount of output in A), how much output should Firm 1 produce to maximize their profit? q 1 = 10 E) (4 points) If Firm 1 cheats on the agreement and produces the quantity in D), what will the market price be? P = 48
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F) (6 points) Given your answer to D) how much profit will each firm make? 1 = 400 2 = 200 3 = 200
3. (16 points) Suppose that two players are playing the following game. Player A can either choose Top or Bottom, and Player B can either choose Left or Right. The payoffs are given in the following table: Player B Player A Left Right Top 7 6 12 5 Bottom 6 2 8 4 where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B. Assume the players choose their strategies simultaneously. A) (2 points) Does Player A have a dominant strategy, and if so what is it? YES-TOP B) (2 points) Does Player B have a dominant strategy, and if so what is it? NO C) (4 points) For each of the following strategy combinations, write “TRUE” if the strategy combination is a Nash Equilibrium, and “FALSE” if it is not a Nash Equilibrium: i) Top/Left TRUE ii) Top/Right FALSE iii) Bottom/Left FALSE iv) Bottom/Right FALSE D) (4 points) For each of the following strategy combinations, write “TRUE” if the strategy combination is Pareto Efficient, and “FALSE” if it is not Pareto Efficient: i) Top/Left TRUE ii) Top/Right TRUE iii) Bottom/Left FALSE iv) Bottom/Right FALSE E) (2 points) What is Player B’s Maximin Strategy? RIGHT
F) (2 points) Suppose the players play this game where Player A chooses their strategy first. Player B observes Player A’s choice, and then chooses their strategy. Using the backward induction method that we discussed in class, what will be the outcome of this game? (Circle the correct answer.) Top/Left Top/Right Bottom/Left Bottom/Right
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