Need help with d-f Consider a monopolist that faces the following equations: Mar

Question

Need help with d-f

Consider a monopolist that faces the following equations: Market demand for monopolist's product: Q = 100 - P TC for monopolist: TC = 20Q + 3/10 q^2 a. Write the demand equation in terms of Q. b. Given the abeve information, what is the profit maximizing price and quantity for the monopolist c. Calculate the monopolist's total profits. d. Suppose the monopolist is regulated to produce where price equals average total cost (average cost pricing). Calculate the quantity the monopolist will produce and the price that will be charged after regulation. e. Calculate the level of profits for the regulated monopoly. f. What do you think happens to the consumer surplus under regulation compared to a scenario with no regulation? What do you think happens to deadweight loss when we move from an unregulated to a regulated monopolist?

Explanation / Answer

Q = 100 - P, re-arranging, we get P = 100 - Q

TC = 20Q + 0.3Q2

d. Given that the regulated monopoly produces where P = ATC,

ATC = TC/Q

ATC = (20Q + 0.3Q2)/Q

ATC = 20 + 0.3Q

ATC = P (plugging in the values, we get)

20 + 0.3Q = 100 - Q

1.3Q = 80

Q = 61.53 units.

P = 100 - 61.53

P = $38.47

e. Profits = TR - TC.

TR = price*output

TR = 38.47*61.53

TR = $2367.05.

TC = 20*61.53 + 0.3*(61.53)2

TC = 1230.6 + 1135.78

TC = 1259.38

Profits = 2367.05 - 1259.38

Profits = $1107.67.

f. After calculating price and quantity from an unregulated monopoly in part a of the question (by equating MR and MC) we get price = $69.24 and quantity = 30.76, which is way above the regulated price.

Clearly, the consumer surplus would increase in case of regulation as compared to no regulation because the consumer surplus is the area bounded by above the price line and below the demand curve. In case of regulated monopoly, this price is below the unregulated monopoly, increasing the area of C.S thereby.

There would be no deadweight loss to the society in regulated monopoly.

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