a) Compute the profit maximizing prices (p1, p2) for the monopolist to charge fo
ID: 1167493 • Letter: A
Question
a) Compute the profit maximizing prices (p1, p2) for the monopolist to charge for each product line.
b) If the monopolist was “broken up” into a duopoly so that each of the two product lines are in competition with one another, compute the Nash equilibrium prices (p1, p2) for the new firms to charge if their competition is characterized as a static, price setting game.
c) If the firm in control of product line 2 agrees to set the cartel price and firm 1 optimally deviates from the cartel arrangement, what price will firm 1 set? (hint: you shouldn’t have to solve the cartel problem to figure this out)
Explanation / Answer
q1= 60-p1+ 1/2p2 and c(q1)= 1/2q1^2
for monopolist quantity is set at MR=MC
multiply q1 by p1, we get total revenue TR and then differentiating the equation with respect to q1, we get
MR= 60-2p1+1/2p2
C(q1)= 1/2q1^2 =1/2(60-p1+1/2p2)
differentiating wrt p1 we get MC= -60+p1-1/2p2
we know MR=MC for profit maximisation then we get
120-3p1+p2=0...................................... equation 1
similarlly with the second product line
we again equate MR=MC of product 2 after doing the same thing, we get
120+p1-3p2=0 ................................................equation 2
from equation 1, p2= 3p1 - 120
substituting p2 in equation 1, we get
p1=p2= 60
b) If monopoly is broken up into duopoly it acts as bertrand game in nash equilrium is at p1=p2= mc because the products are homogeneous, consumers will always purchase from the cheapest seller. If prices are the same, p p1 = p2=MC , consumers are indifferent between purchasing from firms 1 and 2.
c) If the firm 1 deviates from cartel price it will set a price less than firm 2,s price but higher than marginal cost to attract consumers at a slightly lesser price than firm 2.
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