Question

# If the inverse demand curve is P = 120 – 20Q and the marginal cost is...

If the inverse demand curve is P = 120 – 20Q and the marginal cost is constant at $20, how does charging the monopoly a specific tax of$10 per unit affect: a. the monopoly’s profit maximizing level of output, price, and profit, and b. consumer surplus producer surplus and total welfare (where society’s welfare includes the tax revenue?

p = 120-20Q; MC = 20, r = 10 per unit.

Total revenue is TR = P*Q = 120Q - 20Q^2.

Marginal revenue is MR = TR' = 120 - 40Q.

Monopolist quantity produced is maximized, if MR = MC.

120 - 40Q = 20.

or, Q = 2.5

We find optimal price from the demand curve: P = 120 - 50 = \$70.

TR = 70 * 2.5 = 175.

If the tax is imposed, new demand curve will be: P - 10 = 120 – 20Q.

P = 130 - 20Q

TR = 130Q - 20Q^2

MR = 130 - 40Q.

We find new equilibrium, where MR = MC.

130 - 40Q = 10

or, 40Q = 120

or, Q = 3.

P = 130 - 20Q

or, P = 70 .

TR = 210.

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.

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