ECN 100B WQ 2023 Problem set 2
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ECN 100B WQ 2023 Problem set 2
1 Price discrimination question
Imagine a firm called Bapple that is the monopoly in the market for smartwatches, with cost-function C(Q) = 8Q2 . Imagine the inverse demand function for smartwatches is p(Q) = 800 − 2Q.
1.1 A. What are equilibrium price and equilibrium quantity with a single price?
1.2 B. Show the equilibrium price and equilibrium quantity graph- ically. Include the inverse demand curve, firm’s marginal rev- enue curve, and firm’s marginal cost curve.
1.3 C. What are consumer surplus, producer surplus, and dead- weight loss at this equilibrium?
Now assume that Bapple is able to perfectly price discriminate in the market for smart- watches.
1.4 D. What three conditions must be true for this perfect price discrimination to be possible?
1.5 E. What are the equilibrium prices and equilibrium quantity with perfect price discrimination?
1.6 F. What are consumer surplus, producer surplus, and dead- weight loss at the perfect price discrimination equilibrium? How do these compare to the single price equilibrium?
2 Static game I
Sam and Jessie are deciding to play Truth or Dare. To do so, they each make simultaneous choices of what to play without colluding. If Sam and Jessie both choose Truth, then their payoffs are 2 each. If Sam and Jessie both choose Dare, then their payoffs are 1 each. If Sam chooses Truth and Jessie chooses Dare, Sam gets 0 and Jessie gets 3. If Jessie chooses Truth and Sam choose Dare, Jessie gets 0 and Sam gets 3.
2.1 Please draw the payoff matrix for this game.
2.2 Does Sam have a dominant strategy? Why or why not?
2.3 Does Jessie have a dominant strategy? Why or why not?
2.4 What is the Nash Equilibrium of this game?
2.5 Is this game a Prisoner’s Dilemma? If so, why? If not, why not?
3 Static game II
Imagine a game with a Professor and Students (who all act together as one player). The Pro- fessor is giving a final exam and has to decide whether to make it easy or hard. Students have to decide whether to put low effort, medium effort, high effort, or max effort into studying for the exam. Both players decide simultaneously. Payoffs are as follows (Professor,Students):
Students
Max effort High effort Medium effort Low effort
Professor Easy 16,12 12,16 8,20 4,8
Hard 24,16 20,12 4,8 0,4
3.1 Does Professor have a dominant strategy? Why or why not?
3.2 Do Students have a dominant strategy? Why or why not?
3.3 What is the Nash Equilibrium of this game?
3.4 If there are multiple Nash Equilibria, which one will be se- lected in the end? If there is no Nash Equilibrium, how will the game end?
4 Sequential game
Imagine the same Professor and Students are playing a sequential game. Students move first and decide to show up to class or to not show up. Professor moves second and decides whether to threaten a quiz for the next lecture or not. Students then decide whether to attend the next lecture or not. Professor, who has a quiz prepared, observes whether students attend or not and then decides finally whether or not to actually give the quiz. Payouts (Students,Professor) are as follows:
Stud. show up to 1st class, Prof. threatens quiz, Stud. show up to 2nd class, Prof. gives quiz 15,9
Stud. show up to 1st class, Prof. threatens quiz, Stud. show up to 2nd class, Prof. does not give quiz 6,3
Stud. show up to 1st class, Prof. threatens quiz, Stud. don’t show up to 2nd class, Prof. gives quiz 12,9
Stud. show up to 1st class, Prof. threatens quiz, Stud. don’t show up to 2nd class, Prof. does not give quiz 9,6
Stud. show up to 1st class, Prof. does not threaten quiz, Stud. show up to 2nd class, Prof. gives quiz 15,6
Stud. show up to 1st class, Prof. does not threaten quiz, Stud. show up to 2nd class, Prof. does not give quiz 6,3
Stud. show up to 1st class, Prof. does not threaten quiz, Stud. don’t show up to 2nd class, Prof. gives quiz 12,9
Stud. show up to 1st class, Prof. does not threaten quiz, Stud. don’t show up to 2nd class, Prof. does not give quiz 9,6
Stud. don’t show up to 1st class, Prof. threatens quiz, Stud. show up to 2nd class, Prof. gives quiz 12,12
Stud. don’t show up to 1st class, Prof. threatens quiz, Stud. show up to 2nd class, Prof. does not give quiz 6,6
Stud. don’t show up to 1st class, Prof. threatens quiz, Stud. don’t show up to 2nd class, Prof. gives quiz 9,12
Stud. don’t show up to 1st class, Prof. threatens quiz, Stud. don’t show up to 2nd class, Prof. does not give quiz 6,9
Stud. don’t show up to 1st class, Prof. does not threaten quiz, Stud. show up to 2nd class, Prof. gives quiz 12,9
Stud. don’t show up to 1st class, Prof. does not threaten quiz, Stud. show up to 2nd class, Prof. does not give quiz 6,6
Stud. don’t show up to 1st class, Prof. does not threaten quiz, Stud. don’t show up to 2nd class, Prof. gives quiz 9,12
Stud. don’t show up to 1st class, Prof. does not threaten quiz, Stud. don’t show up to 2nd class, Prof. does not give quiz 6,9
4.1 Please draw the game tree for this game.
4.2 How many subgames does this game have?
4.3 What is the subgame perfect Nash Equilibrium for this game?
4.4 Do Students believe Professor’s threat of a quiz?
5 Oligopoly
5.1 Markets differ according to what three dimensions in terms of market structure?
5.2 What is a real-life example of an oligopoly and why?
5.3 What are the three models of oligopoly?
5.4 Would a firm prefer to be in a market with an oligopoly, a monopoly, or perfect competition? Why?
5.5 Would a consumer prefer to be in a market with an oligopoly, a monopoly, or perfect competition? Why?
6 Cournot
Suppose there are two departments selling economics degrees in one market competing fol- lowing the rules of the Cournot Oligopoly Model—econ and man. econ. Suppose market demand for an economics degree is Q = 14400 − 4p. Suppose both departments marginal cost is $6000 per degree.
6.1 What is each department’s residual demand curve?
6.2 What is each department’s best response functions?
6.3 What is the Nash-Cournot equilibrium in this market?
6.4 What is the price at this equilibrium?
6.5 What are profits for the two departments at this equilibrium?
6.6 Graph the marginal cost, demand, residual demand, and marginal revenue curve for the econ department. Show the equilibrium price and quantity for the econ department.
2023-02-10