# ECON 102 Homework 5

1. (42 total points) Suppose that a monopolistically competitive firm must build a production facility in order to produce a product. The fixed cost of this facility is FC = $24. Also, the firm has constant marginal cost, MC = $3. Demand for the product that the firm produces is given by P = 27-3Q. a) (27 points) Fill in the table below. If any of your values have decimals, you may round to only one numeral after the decimal (nearest 10th of a dollar). Quantity of OutputPriceTotal CostAverage Total CostTotal RevenueProfits123456789b) (10 points) How much output will this firm produce if it maximizes profit?c) (5 points) What price should this firm charge if it wants to maximize profit?2. (12 points) Carefully explain what will happen as we move from the short run to a long run equilibrium in a monopolistically competitive industry if firms are making a positive profit in the short run. Your explanation should clearly state what will happen to the demand curve facing an individual firm and the reason why this happens.3. (34 total points) Suppose that two players are playing the following game. Player A can choose either Top or Bottom, and Player B can choose either Left or Right. The payoffs are given in the following table, where the number on the left is the payoff to Player A, and the number on the right is the payoff to Player B:Player BPlayer ALeftRightTop2 51 4Bottom0 13 8A) (4 points) Does player A have a dominant strategy, and if so what is it?B) (4 points) Does player B have a dominant strategy and if so what is it?C) (16 points) For each of the following say True if the strategy combination is a Nash equilibrium, and False if it is not a Nash equilibrium:i) Player A plays Top and Player B plays Left ii) Player A plays Bottom and Player B plays Left iii) Player A plays Top and Player B plays Rightiv) Player A plays Bottom and Player B plays RightD) (4 points) If each player plays her maximin strategy what will be the outcome of the game? (Give your answer in terms of the strategies each player choosesfor example, Player A plays Bottom and Player B plays RightÂ)E) (6 points) Now suppose the same game is played with the exception that Player A moves first and Player B moves second. Draw the game tree associated with this situation. Using the backward induction method discussed in the online class notes, what will be the outcome of the game? 4. (12 total points) Suppose there are 12 firms in an industry. The percentage of total sales is given in the following table:FirmPercentage of total sales11621431241251068768695104114123A) (6 points) Calculate the HHI for this industry.B) (6 points) If firms 6 and 7 decide to merge, would this merger be challenged by the FTC? Why or why not?