Question

if the inverse demand curve is p=120-Q and the marginal cost is constant at 10, how does charging the monopoly a specific tax of r= 10 per unit affect the monopoly optimum and the welfare of consumers, the monopoly, and society ( where society's welfare includes the tax revenue)? What is the incidence of the tax on consumers? (15 marks)

Answer 1

Answer on Question #40775 – Economics - Microeconomics

p = 120-Q; MC = 10, r = 10 per unit.

Total revenue is TR = P*Q = 120Q - Q^2.

Marginal revenue is MR = TR' = 120 - 2Q.

Monopolist quantity produced is maximized, if MR = MC.

120 - 2Q = 10.

Q = 55 units.

We find optimal price from the demand curve:

P = 120 - 55 = $65.

TR = 65*55 = $3575.

If the tax is imposed, new demand curve will be:

P - 10 = 120 - Q.

P = 130 - Q.

MR = 130 - 2Q.

We find new equilibrium, where MR = MC.

130 - 2Q = 10.

Q = 60 units.

P = 130 - 60 = $70.

TR = 70*60 = $4200.

So, we can see, that monopolist would be better off, because its total revenue increased.

Nevertheless, as the price increased, consumers will pay more, which is not good result of imposing tax either for consumers, or for society.