Question

Q2) A monopolist has variable costs of VC = q² and faces a demand curve of P = 24 – q, where P is price and q the quantity sold. If the monopolist sets a single price, what is the resulting loss in the gains from trade?

a) $8

b) $6

c) $12

d) $4

e) None of the above

Answer 1

Ans ) Option b

A monopolist produces where ,

Marginal revenue = marginal cost

Marginal revenue = d(total revenue)/d(q)

total revenue = price × quantity = q(24 - q)

Total revenue = 24q - q²

Marginal revenue = 24 - 2q

Marginal cost = d(total cost)/d(q)

Marginal cost = 2q

Put, marginal revenue = marginal cost

24 - 2q = 2q

24 = 4q

q = 24/4

quantity = q = 6

Price = 24 - q = 24 - 6 = $18

Competitive equilibrium

In competitive equilibrium,

Price = marginal cost

24 - q = 2q

24 = 3q

q = 24/3

quantity = q = 8

Price = 24 - 8 = 16

In the below diagram, the area 'a' and 'b' represent the deadweight loss when the monopolist operates in an economy.

It can be calculated as follows:

[(1/2)×(2)×(18-16)] + [(1/2)×(2)×(16-12)]

= 2 + 4

= $6

8 a b 6 62 1 aoud 1