代做ECN 100B WQ 2025 Problem set 2

日期：2025-02-13 03:06

ECN 100B WQ 2025 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) = 16Q2 .  Imagine the inverse demand function for smartwatches is p(Q) = 1600 - 4Q.

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

Suppose two players are playing a game,  Even and Odd. Each player has a quarter and must secretly turn the quarter to heads or tails. The players then reveal their choices simultaneously. If the quarter match (both heads or both tails), then Even keeps both quarter, so wins one from Odd (+25 for Even, -25 for Odd).  If the quarters do not match (one heads and one tails) Odd keeps both quarter, so receives one from Even (-25 for Even, +25 for Odd).

2.1    Please draw the payof matrix for this game.

2.2    Does Even have a dominant strategy?  Why or why not?

2.3    Does Odd have a dominant strategy?  Why or why not?

2.4    What is the Nash Equilibrium of this game?

2.5    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?

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 lowefort, medium efort, high efort, or max efort into studying for the exam. Both players decide simultaneously. Payofs are as follows (Professor,Students):

Students

Max efort      High efort          Medium efort       Low efort

    Professor    Easy         32,24              24,32                 16,40                 8,16

Hard        48,32               40,24                  8,16                   0,8

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 2,3 Stud. show up to 1st class, Prof. threatens quiz, Stud. show up to 2nd class, Prof. does not give quiz 3,4 Stud. show up to 1st class, Prof. threatens quiz, Stud. don’t show up to 2nd class, Prof. gives quiz 2,2 Stud. show up to 1st class, Prof. threatens quiz, Stud. don’t show up to 2nd class, Prof. does not give quiz 4,3 Stud. show up to 1st class, Prof. does not threaten quiz, Stud. show up to 2nd class, Prof. gives quiz 2,3 Stud. show up to 1st class, Prof. does not threaten quiz, Stud. show up to 2nd class, Prof. does not give quiz 3,4 Stud. show up to 1st class, Prof. does not threaten quiz, Stud. don’t show up to 2nd class, Prof. gives quiz 2,2 Stud. show up to 1st class, Prof. does not threaten quiz, Stud. don’t show up to 2nd class, Prof. does not give quiz 4,4 Stud. don’t show up to 1st class, Prof. threatens quiz, Stud. show up to 2nd class, Prof. gives quiz 3,2 Stud. don’t show up to 1st class, Prof. threatens quiz, Stud. show up to 2nd class, Prof. does not give quiz 4,3 Stud. don’t show up to 1st class, Prof. threatens quiz, Stud. don’t show up to 2nd class, Prof. gives quiz 2,1 Stud. don’t show up to 1st class, Prof. threatens quiz, Stud. don’t show up to 2nd class, Prof. does not give quiz 5,2 Stud. don’t show up to 1st class, Prof. does not threaten quiz, Stud. show up to 2nd class, Prof. gives quiz 3,2 Stud. don’t show up to 1st class, Prof. does not threaten quiz, Stud. show up to 2nd class, Prof. does not give quiz 4,3 Stud. don’t show up to 1st class, Prof. does not threaten quiz, Stud. don’t show up to 2nd class, Prof. gives quiz 2,1 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 5,3

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  difer  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?