# 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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Chapter 7 / Lesson 2Understand 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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