A monopolist faces a demand curve given by: P = 200 - 10Q, where P is the price of the good and Q...
Question:
A monopolist faces a demand curve given by: {eq}P = 200 - 10Q, {/eq} where {eq}P {/eq} is the price of the good, and {eq}Q {/eq} is the quantity demanded. The marginal cost of production is constant and is equal to $60. There are no fixed costs of production.
a. What quantity should the monopolist produce in order to maximize profit?
b. What price should the monopolist charge in order to maximize profit?
c. How much profit will the monopolist make?
d. What is the deadweight loss created by this monopoly?
Monopoly
A monopoly is a market structure with no competition. There is only one producer and the producer makes above-normal profits by charging higher prices.
Answer and Explanation: 1
P = 200 - 10Q
So, revenue R = P * Q = 200Q - 10Q^2
MR (marginal revenue) = dR/DQ = 200 - 20Q
MC = 60
At maximum profit, MR = MC
200 - 20Q = 60
a) Q=7 -> this is the quantity it should produce
b) P = 130 -> this is the price it should produce
c) profit = R - Total cost
R = 200Q - 10Q^2 = 1400-490 =910
Total cost = Q * 60 =420
profit = 910-420 =490
d) Deadweight loss is given by total surplus under perfect competition - total surplus under monopoly
If there was perfect competition, price and quantity would be as follows
price = marginal cost = 60
Q = (200-P)/10= 140/10 = 14
Thus, price would be lower than monopoly price of 130 and quantity higher than monopoly quantity of 7
Surplus in perfect competition:
consumer surplus = 1/2 * 14* (200-60) = 980
producer surplus = 0
total surplus = 980
Surplus in monopoly:
consumer surplus = 1/2* 7 * (200-130)= 245
producer surplus = 7 * (130-60) = 490
total surplus = 735
Deadweight loss = drop in surplus = 245
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What is a Monopoly in Economics? - Definition & Impact on Consumers
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Chapter 7 / Lesson 2
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Understand the meaning of a monopoly in economics and what it does. Also, know the characteristics of a monopoly and the different types of monopolies.
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