For the next question, consider a monopolist. Suppose the monopolist faces the following demand...
Question:
For the next question, consider a monopolist. Suppose the monopolist faces the following demand curve: {eq}P = 100 - 3Q {/eq}. The marginal cost of production is constant and equal to $10, and there are no fixed costs.
What is the value of the deadweight loss created by this monopoly?
a. Deadweight loss = $412.5
b. Deadweight loss = $250
c. Deadweight loss = $675
d. Deadweight loss = $750
e. Deadweight loss = $337.5
f. None of the above
Monopoly:
Monopoly is a market structure in which there is a single seller and large number of buyers in the market. The monopolist has the freedom to decide the price and output in the market. Being a single seller the monopolist cater to the entire market demand.
Answer and Explanation: 1
e. Deadweight loss = $337.5
Reason:
P = 100 - 3Q (Demand Function)
TR = P * Q
Multiplying Q on both sides of demand equation we have,
{eq}P * Q = 100Q - 3Q^{2} {/eq}
{eq}TR = 100Q - 3Q^{2} {/eq}
MR = Change in TR/ Change in Q = dTR/ dQ
Differentiating the TR equation with respect to Q
dTR/dQ = 100 - 6Q
MR = 100 - 6Q
MC = $10 (GIven)
The monopolist will maximise his profits at the level where MR = MC
Equating MR with MC we have,
100 - 6Q = 10
6Q = 90
Q = 15 units
Putting the value of Q in the demand equation we have,
P = 100 - (3* 15)
P = 100 - 45
P = $55
MC = $10 (Given)
P = 100 - 3Q (Given)
Equating the demand equation with MC we have,
10 = 100 - 3Q
3Q = 90
Q = 30 units
Dead Weight Loss (DWL) = 1/2 * (30 - 15) * (55-10)
DWL = 1/2 * 15 * 45
DWL = $337.5
Hence the dead weight loss in monopoly will be equal to $337.5
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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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