Question

Acoustek produces high-end guitar, serving the Canadian market as a monopolist. The market demand is p = 280 – 2Q and Acoustek’s marginal cost of production is $40 for each unit of guitar with the current production capacity.

1.a (4 marks) Calculate the equilibrium price, output and profit of Acoustek as a monopoly.

1.b (7 marks) Suppose a new entrant is planning to enter the market by investing $2,000 for the production facility. The entrant’s marginal cost of production will be $40 for each unit. If the entry occurs and both firms (Acoustek and the entrant) were to play a Cournot competition, what are the equilibrium output, price and profit of each firm? (Call Acoustek as firm 1 and the entrant as firm 2).

1.c (7 marks) Upon the entry by firm 2, Acoustek can also invest $2,000 to expand its production capacity, and this investment will reduce Acoustek’s marginal cost of production to $20 (while the entrant’s marginal cost is still $40). If Acoustek plays as a Stackelberg leader with the investment (and the entrant as a follower), what are the equilibrium output, price and profit of each firm?

1.d (4 marks) If Acoustek makes an investment for expanded capacity as above and the potential entrant does not enter, what are Acoustek’s equilibrium output, price and profit as a monopoly?

1.e (8 marks) Using the profits of each firm derived from the previous questions, draw a game tree of the “sequential entry and capacity expansion” game in which Acoustek first makes a capacity expansion decision and the entrant makes an entry decision. Find a subgame perfect Nash equilibrium of this game.

Answer 1

A)

(Page No. De equilibruin of monopoly at MREMC 2 2 28o - 20 MK2 2 80— 44 Mc - 10 MK - МО 2go-u Q = 40 2 Чp 2 чау се - 24° — 60 Р= 28– 2х6 от До PLE/16-40xo=120x4: 7200

B)

IP=280- 20 MR = 280 42 280 42 MC 240 M Rg =MC 28042 -9 240 2 = 60 - 0.5% < best respons Function of sound, by symmtery q2 = 60 - 0.5%, 1 best response function of firmy putting qiuto & 2 = 60 -0.5/60-0.54 2 = 60-30+ 0.2861 30 240 92 60-0.5X You 40 Q = 4 +€2²80 P= 280-2x802 120 profit firm 1 = (120-40x40=3200 profit firm 22/120-40 X Yo-2000 21200 2020.

C)

D)

D) P= 2 х 22, Чер- 2 8о -49, 9 ? ?о | МК, 2 ме, 28o 4, 2 20 9,5 26 2 2s . р, 20-25 г), а profit from 2 /150 20X65-2000 - ЧО