Answer to Question #194934 in Microeconomics for Lena

Question

Consider a monopolist that sells a single good. The demand for the good is represented by the inverse demand function (price, p, as function of quantity, q) p = 10 − 2q. Suppose that there are no costs of production.

1. Suppose that demand consists of individual consumers whose willingness to pay is given by the value of the inverse demand function. Suppose the monoppolist can identify whether a consumer has a willingness to pay below or above 3. The monopolist can set two different prices to the two resulting groups. Determine the demand for each of the two groups. Then calculate the optimal price for each group for the monopolist.

Answer 1

It has been given that there is no cost of production. Therefore we can consider that TC=0

1.

Suppose that demand consists of individual consumers whose willingness to pay is given by the value of the inverse demand function

TC=0

MC=0

p=10-2q

TR=p*q

TR=(10-2q)q

MR=10-4q

At equilibrium MC=MR

10-4q=0

10=4q

q=2.5

p=10-2*2.5

p=5

2.

Suppose the monopolist can identify whether a consumer has a willingness to pay below or above 3.

It is given that there are two groups therefore it can be said that Q=Q1+Q2

Now it is given that some some customers are willing to pay above or below 3

Therefore, there are two prices.

Let us consider P1=P+3

                          P2=P-3

Therefore demand for 1st consumer will be ,

P1=10-2(q1+q2)

P+3=10-2(q1+q2)

P=7-2(q1+q2)

And demand for the second consumer might be, 

P2=10-2(q1+q2)

P-3=10-2(q1+q2)

P=13-2(q1+q2)