1. The demand equation of local movie theater in Kolkata for
balcony seats and dress circle seats are given respectively as: Qb
= 60 2Pb and 3Qdc = 56- Pdc. The total cost of running show by
multiplex is TC = 40 + 20Q. What would be the price of tickets with
price discrimination? What would be the price of multiplex decides
to charge the same price across both the types of seats.
Answer : With price discrimination Pb = 25, Pdc = 38
Without price discrimination: Pdc = 26.9
2. Suppose that the market demand function for a two firm equal
market-sharing cartel is,Q = 120-10P and that the total cost
function of each duopolist is,TC = 0.1 Q2. Determine the best level
of output of each duopolist, the price at which each will sell the
commodity and the total profits of each.
Answer :The half share market faced by each duopolist is Q =
60-5P, or P = 12-0.2Q
TR = PQ = (12- 0.2Q) Q = 12Q 0.2Q2 And MR = d (TR)/dQ =
12-0.4Q
The marginal and average total cost of each duopolist is
MC = d (TC)/dQ = 0.2Q And ATC = TC/Q = 0.1Q2/Q = 0.1 Q
Setting MC =MR, we get 0.2 Q = 12-0.4Q, or, 0.6Q = 12,or, Q =
20
P = 12-0.2(20) = 8 Therefore, TR = 12(20) 0.2(20) 2 = 240-80 =
160
And ( = TR TC = 160 0.1(20) 2 = 160-40 = 120
3. Cost function of a monopolist is TC = 1000 + 20Q.The demand
function for the monopolist is estimated to be P = 200 4Q.
a. Compute the profit maximizing output and the profit at that
level of output for the monopolist. Q =22.5 units, Profit = 1025b.
If the industry transforms into a duopoly, what would be the
equilibrium output for the industry? Q = 30 units
