A monopolist faces a market demand given by Q = 76 - P, whose marginal revenue i
ID: 1176594 • Letter: A
Question
A monopolist faces a market demand given by Q = 76 - P, whose marginal
revenue is MR = 76 -2Q.
a) Compute the consumer surplus at p = 0, 20, and 50.
b) If the monopolist has constant average and marginal costs AC = MC = 6, what output level
will it choose in order to maximize profits? What are the monopoly price and profits?
c) Assume instead that it has cost function given by TC = 0.25Q^2 -5Q + 300, what are the
monopoly supply, price and profits?
d) Assume now that the cost function is TC = 0.333Q^3 - 26Q^2+ 695Q - 5800, whose
marginal cost is MC = Q^2 -52Q + 695. Again, find monopoly supply, price and profits.
e) Graph the market demand curve, MR curve, and the three MC curves from parts (b-d).
f) Compute the deadweight loss in part (b).
Explanation / Answer
a) at p=0 the consumer surplus is the area of triangle formed by the price line, the quantity line and the demand line
hence the consumer surplus=1/2*76*76=2888
consumer surplus at P=20 is the area formed by P=20 line with the Q=0 line and the demand line
1/2*56*56=1568
similarly consumer surplus at p=50 will be 1/2*26*26=338
b) to maximise profit MR=MC
hence 76-2Q=6
therfore profit maximising production=35
monopoly price=76-35=41
monopoly profit=35*41(revenue)-6*35
therefore monopoly profit=1225
c) Monopoly supply will be determined by profit maximising equation MR=MC
therefore MC=0.5Q-5
hence supply will be
0.5Q-5=76-2Q
2.5Q=81
Q=32.4 or rounded to 32 units
monopoly price=76-32.4=43.6
and profit=43.6*32.4-0.25*32.4^2+5*32.4-300
profit=1012.2
d) as done in the above part Q can be found out through
MR=MC
Q^2-52Q+695=76-2Q
hence we get a quadratic in Q
Q^2-50Q+619=0
we get Q=25+-sqrt(6)
hence monopoly price can accordingly be 51+-sqrt(6)
the profit will be {25+sqrt(6)}*{51-sqrt(6)}
which is 1320+26*sqrt(6)
hence this is the maximum profit because for the other solution of the quadratic the profit will be 1320-26*sqrt(6)
so the monopoly Price=51-sqrt(6)=48.55
monopoly quantity=25+sqrt(6)=27.44
profit=1383.68
e) all the MC curves along with demand and MR curve is at he link below
http://img600.imageshack.us/img600/2/pgma.jpg
f) the link to the demand MR and MC curve are given below please check it out and contact for further queries.
http://img526.imageshack.us/img526/8458/09as.jpg