Question

Can someone help me solve this problem? I want to know the solving method. Thank you! :)

Questions 1 and 2 Refer to a market with the following information to be taken as given:

?? = 3?

?D = 20 − ?

1. Calculate the producer surplus, assuming there is a monopoly supplier who is able to use first-degree price discrimination.

a. 40

b. 42

c. 48

d. 50

2. Suppose the government forces the monopolist to charge a single price. It may set any price it wishes but it is now forbidden from engaging in price discrimination of any kind. The monopolist sets its new price that applies to everyone, which of the following will occur in the redistribution of social surplus?

a. Producer surplus decreases by 8.

b. Producer surplus decreases by 10.

c. Consumer surplus increases by 4.5

d. Consumer surplus increases by 26.

Answer 1

In case of first degree price discrimination, the monopolist charges a price equal to willingness to pay of the consumer, and he keeps on charging like this until he reaches P=MC.

Through this, the entire Consumer surplus is extracted by the monopolist and it becomes a part of Producer surplus.

P= MC =3Q.

==> 3Q = 20-Q. ==> 4Q = 20 ==> Q= 5.

This gives P= 20-5=15.

Dance 25+ Demond awrue 1o Marginal Revenue Ś 10 15 20 25 Quant Quantity

The consumer Surplus is ∆ABC which is now a part of producer surplus. Total producer surplus is now ABD.

Area ABD = 0.5(BC)(AD) = 0.5(5)(20) = 50

If monopolist charges a uniform price then profit maximizing point for the monopolist will be where MC = MR ,

MC=3Q = MR

TR = PQ=(20-Q)Q

MR = 20 -2Q

Hence 20-2Q= 3Q which gives 20= 5Q ==> Q=4

Now, P=20-4=16.

Now the producer surplus will be area C'B'EDC'. Consumer surplus now increases from 0 to area AC'B'. Hence, Producer surplus also reduces by the amount of increase in consumer surplus.

Demand awrue M Carginal Revenue Ves 9 5 10 15 20 25 Quantiny

Decrease in producer surplus = area AC'B' = 0.5(4)(20-16) = 0.5 × 4 × 4 = 8

Hence option a) is correct.