Problems
The following problems will form the basis for the final. These problems are not to be handed in.
9/2 Problem: As a general rule, is it safe to assume that a change in the price of a good will always have its most significant impact on the quantity demanded of that good, rather than on the quantity demanded of other goods? Explain.
9/9 Problems
1. When a monopolist identifies its profit-maximizing quantity of output, how does it decide what price to charge? Show in a picture.
2. You have been asked to provide antitrust advice to AAA Widgets. AAA is considering purchasing a competitor and are trying to determine if the FTC will give them more trouble purchasing Best Widgets or City Widgets. You do a study of demand and find that the elasticity of demand for Best is 4 and the elasticity demand for City is 2. You also find that the diversion between AAA and Best is 20%, while the diversion between AAA and City is 15%. Which merger AAA/Best or AAA/City is likely to lead to a higher price increase? Explain.
9/16 Problems
1. Why wouldn’t Firm 1 choose a price less than c (Firm 1’s marginal cost)?
2. If Firm 1 is located at the 0 point (left most point) in the city and Firm 2 is looking to enter the city and compete in the market, would they be more likely to enter at 0.5 (half way along the line) or at 1 (right most point in the city). Explain
9/23 Problems
1. Consider the data table below and the assumption that each state chooses death penalty if and only if it reduces the state homicide rate. Given the data and assumption what can we say about the impact on homicide rates of implementing the death penalty.
Assumption:
E(HR | DP = 0, DP State = 0) > E(HR | DP = 1, DP State = 0)
E(HR | DP = 1, DP State = 1) > E(HR | DP = 0, DP State = 1)
2. You have been hired by Staples to assess the evidence presented by the FTC in the Staples case. What concerns would you raise about the evidence that the FTC presented on the effect of the merger on prices? What analysis would you suggest that Staples do to test the FTC’s results. In particular, discuss the assumptions made by the FTC in their analysis of competition on prices.
9/30 Problems
1. The merging parties claim that the merger will save $1 million dollars because they will be able to consolidate their head quarters and cut support and managerial staff. Do you think the FTC should consider these cost savings when weighing the costs and benefits of the merger? Explain your answer.
2. Consider the equation (p - c)/p = 1/e, where p = price, c = marginal cost and e = elasticity of demand. Say price is current p = 0.7, marginal cost is c = 0.5. After the merger the elasticity of demand will fall 20% and marginal cost will fall 20%. Using the equation explain what will happen to prices after the merger. NOTE THAT THERE WAS AN ERROR IN THIS QUESTION THAT WAS CORRECTED ON 11/8/14.
10/7 Problem
1. Consider Hotelling’s linear city model. Let t = 0.5, c = 0.1 and the monopoly price is 0.7. At the monopoly price 0.77 people in the linear city purchase from the monopoly (Firm 1) at position 0. Firm 2 is considering entering at position 1. The fixed cost of entry is 0.28. Will Firm 2 enter? Explain.
10/21 Problems
You have been hired by Al to help him with winning a game Rock-Paper-Scissors against Betty in the school yard tomorrow. The winner receives $1 from the loser.
1. Write down the game: players, strategies, payoffs.
2. Write down the payoff matrix (like we did in class)
3. For each of Betty's strategies, write down Al's optimal strategy.
4. Does Al have a dominant strategy? Explain.
5. What is the Nash equilibrium? Explain
10/28 Problems
Consider Al's problem from 10/21. But instead of both Al and Betty choosing simultaneously, you learn that both have agreed that Al gets to choose first. Once Al has chosen, Betty chooses her action.
1. Write down the game: players, strategies, payoffs. NOTE that a player's strategy is a "complete plan" for that player. It states what that player will do at every point (information set) in the game.
2. Draw the game tree (graph) of the game.
3. Solve the game by backward induction.
4. Can Al ever win? Explain.
11/4 Part 1 Problem
Consider a repeated game, where the players are two firms, ADM and Ajinomoto. Each firm choses to price either High or Low in each round of a infinitely repeated game. If both players play Low, their payoff is 0 each. If both play High, then their payoff is 100 each. However, if one plays High and the other plays Low, then the play that plays High gets -10 and the player that plays Low gets 150.
1. In the single round of the game, what is the Nash equilibrium? Remember an equilibrium is a description of the strategies that are played.
2. If the game was played in exactly 20 rounds, what would be the Nash equilibrium of the game?
3. Describe a Grim Trigger strategy for this game.
4. Let p be the probability that the game continues to the next round. What would p need to be for coordination to be a Nash equilibrium outcome with Grim Trigger strategies. Remember that the infinit power sum of p is 1/(1-p).
11/4 Part 2 Problem
Consider the comic strip from XKCD HERE. From the information presented in the comic, is there sufficient evidence that green jelly beans cause acne? Explain.
11/11 Problem
Consider the statement, “Walmart is pricing below cost in order to force competitors out of the market. When there are no more competitors, Walmart will charge monopoly prices.” If entry costs are low, is this proposed strategy sub-game perfect? Is the statement credible?
11/18 Problems
The problems refer to this paper: http://sticerd.lse.ac.uk/seminarpapers/ei11032005.pdf
Does the evidence from the paper suggest that ISPs tended to choose the modem that fewer of its competitors had chosen?
Why would firms do this rather than choosing the same modem as their competitors?
Did competition slow adoption?