Question

1. (25 points) Suppose that a monopolist faces the inverse demand curve: P 100-Q and produces goods at a marginal cost of $5. Finally assume that the firm incurs no fixed costs A. Suppose the monopolist lowers the price from $90 to $89. Explain why the firm's marginal revenue is less than the price of the 11th unit sold, $89 (do not answer this question by providing a mathematical equation). B. At what price will the monopolist maximize its profit? C. (5 points) Calculate the deadweight loss to society resulting from the firm having monopoly power (rather than selling the good at the competitive levell.

Answer 1

A)

We calculate the change in quantity demanded as a result of price change.

Let first estimate the quantity demanded at P=$90

P=100-Qd

90=100-Qd or Qd=10

Now we estimate the quantity demanded at P=$89

89=100-Qd or Qd=11

We know that a monopolist needs to decrease the price of good to increase the sale of additional unit. Since price is decreased for all units sold. Marginal Revenue will be less than the price.This explains why Marginal Revenue from selling 11th unit is less than price.

(Please note that in this question, we are not required to calculate the quantity demanded to answer the question. I have done just to check if new quantity demanded is 11 units following the price change as mentioned in the question)

b)

Given Marginal Cost=MC=5

P=100-Q

Total Revenue=P*Q=(100-Q)*Q=100Q-Q2

Marginal Revenue=MR-=dTR/dQ=100-2Q

Set MR=MC for profit maximization

100-2Q=5

2Q=95

Q=95/2=47.50

P=100-Q=100-47.50=52.50

Profit maximizing price is $52.50

c)

A competitive firm sets its output level such that

MC=P

So,

5=100-Q

Q=95

and price is $5

Given demand and supply curves are linear. So,

Dead weight loss=1/2*(Change in price)*(Change in quantity)=1/2*(52.50-5)*(95-47.50)=$1128.125

Dead weight loss is $1128.13