A monopolist faces a market demand given by Q = 76 - P, whose marginal revenue i

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

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