2. Consider a monopolist that faces the following equations: Market demand for m
ID: 1122745 • Letter: 2
Question
2. Consider a monopolist that faces the following equations: Market demand for monopolist’s product: Q = 100 – P TC for monopolist: TC = 20Q + (3/10) Q2
a. Write the demand equation in terms of Q.
b. Given the above 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
a. Write the demand equation in terms of Q.
It is written as P = 100 - Q
b. Given the above information, what is the profit maximizing price and quantity for the monopolist?
Profit = TR – TC
=100Q – Q^2 - 20Q - (3/10)Q^2
Profit is maximum when marginal profit is zero
100 – 2Q – 20 – 6Q/10 = 0
80 = 26Q/10
Qm = 30.77
Pm = 100 – 30.77 = 69.23
c. Calculate the monopolist’s total profits.
Profits = 100*30.77 – (30.77)^2 – 20*30.77 - (3/10)*( 30.77^2) = 1230.77
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.
ATC = TC/Q = 20 + (3/10)Q
100 – Q = TC/Q = 20 + (3/10)Q
80 = 13Q/10
Qm1 = 61.54, Pm = 100 – 61.54 = 38.46
e. Calculate the level of profits for the regulated monopoly.
Profits are zero when price is equal to average total cost.
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?
To a regulated monopolist, DWL will be eliminated and the consumer surplus will increase.
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