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 qua ntity graph-
ically. ****Include ****the ****inverse ****demand ****curve, ****firm’s ****marg inal ****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 ****possibl e?
1.5 E. ****What ****are ****the ****equilibrium ****prices ****and ****equilibri um ****quantity
with ****perfect ****price ****discrimination?
1.6 F. ****What ****are ****consumer ****surplus, ****producer ****surplus, ****and ****dead-
weight ****loss ****at ****the ****perfect ****price ****discrimination ****equilibri um? ****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 代写ECN 100B WQ 2025 Problem set 2heads 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 ****th e ****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 ****w ill ****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 su bgame 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?
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