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Ouiz Ouestion Solution:

1. The demand curve for karate training in a community with only two martial arts schools is P = 100 - Q, where Q is in student-Iessons. The cost of providing an additional student-Iesson is $8/lesson. Complete the table below for the four cases described in a-d. There are no fixed costs.

a.    Both schools get together and collude to price fix at a profit maximizing level.

b.    Both schools assume that the other will hołd the present tuition constant despite what the competition does.

c.    Both schools assume that the other will hołd the present enrollment constant despite what the competition does.

d.    School 1 believes school 2 will adjust to its new profit maximizing solution each time school 1 adjusts its enrollment strategy. (Show calculations below.)

Assumption	Q of School 1	Q of School2	Price ($/lesson)	Profit of School1	Profit of School2
a	23	23	54	1058	1058
b	46	46	8	0	0
c	30.67	30.67	38.67	940.44	940.44
d	46	23	31	1058	529

c) Coumot model

P= 100-(Q₂ +Q,)

MR = (100 -Q₂)-2Q,

8 = (100 - Q₂) - 2 Q,, so 2Q1 = 92 - Q₂ Qi = 46 - 0.5Q₂ School 1 reaction curve Q₂ = 46 - 0.5Q| School 2 reaction curve Q, = 46 - 0.5(46 - 0.5Qi)

Q, = 46 - 23 + .25Qi, so Qi = 30.67 students.

For the Stackelberg model, which is letter d above, take the demand curve for the Cournot model shown on the first linę of the equations on the left and substitute the reaction curve of school 2 into the Q₂ term.

This gives P = 100 - Q, - (46 - 0.5Qi). which when solved for equals 46 lessons. Substituting this into the reaction curve for firm 2 gives Q₂ = 23.

Letters a and b are the single-price monopoly model and the Bertrand and perfectly competitive models, resp.