Question

Question1 Suppose there is a market for heroin in Eugene. The demand curve for heroin is 140-2Q. The marginal cost of heroin is $4. What is the competitive market price?

Question2 What is the competitive market quantity?  

Question3  What is the price if a single monopoly firm enters the market?

Question4

Suppose 1 person overdoses for every 2 units of heroin purchased. How many more people overdose in a competitive market than in a monopoly market?  

Can you solve those questions and explain step by step?

Answer 1

Demand function: P = 140-2Q

Marginal cost = $4

Question 1

We know that a competitive market is the one where there are many sellers and buyers in the market and firm is the price taker. In a competitive market profit-maximizing output is at a point where the Price = Marginal cost. In a perfectly competitive market, Price= Average revenue = Marginal revenue.

Thus for finding the competitive market price, we will equate Price with the Marginal cost.

P = Price

Marginal cost = $4

Thus market price = $4

Question 2

We know that the demand function is given by: P = 140-2Q

Price = $4

By putting this value in the equation we get,

4 = 140- 2Q

2Q = 136

Q = 68 units

Thus the competitive market quantity is 68 units.

Question 3

A monopoly is a market structure where there is only one seller of a product in the market, in that case, it becomes the price maker of the firm. The profit-maximizing level is attained at the point where Marginal revenue = Marginal cost.

The demand curve is given by the equation:

P=140-2Q

Price = Average revenue

AR = 140 - 2Q

Total revenue = 140Q - 2Q²

Marginal revenue = 140 - 4Q (differentiation of TR with respect to Q)

Now equating marginal revenue with marginal cost we get,

MR = MC

140- 4Q = 4

136 = 4Q

Q = 34

Thus the monopoly market quantity is 34 units.

Putting these units in the demand function we will get the price charged by the monopoly.

P =140-2Q

P = 140 - 2(34)

P = $72

Thus the price charged by a single monopoly will be $72.

Question 4

1 person overdoses for every 2 units purchased.

In a competitive market total units purchased are 68. Thus (68/2) = 34 person overdoses for 68 units purchased.

In a monopoly market total units purchased are 34. Thus (34/2) = 17 person overdoses for 34 units purchased.

Thus in a competitive market, (34 -17) = 17 more people overdose than in a monopoly market.