Taxation and subsidies as competition remedies

Overview

Taxation be used as a response to market power and subsidising a struggling competitor be self-defeating as a competition policy.

What you need to know

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Questions from this subtopic

Each one with the model answer underneath.

1. 1

   How can taxation be used as a response to market power?

   Model answer

   A tax can be levied on the profits that market power generates, transferring them to the government so that they can be redistributed or used to fund public spending. A tax can also be placed on each unit sold, which raises the firm's marginal cost and changes the price and output it chooses. The two work quite differently, and only the second alters the firm's behaviour.

2. 2

   A monopolist faces demand P = 100 - 2Q and has total cost TC = 30 + 10Q + Q squared, producing 15 units at £70 with profit £645. A one-off tax of £100 is levied on its profits. Calculate the new price, output and profit.

   Model answer

   A lump-sum tax adds a constant to total cost, so marginal cost is still 10 + 2Q and marginal revenue is still 100 - 4Q. The profit-maximising output is therefore unchanged at 15 units and the price remains £70. Profit falls from £645 to £545. Consumers are no better off at all; the whole effect is a transfer from shareholders to the government.

3. 3

   Why does a lump-sum tax on a monopolist's profits leave price and output unchanged?

   Model answer

   The firm chooses output by comparing the extra revenue from one more unit with the extra cost of producing it. A lump sum does not vary with output, so it changes neither of those margins and the output that was best before is still best. It reduces profit at every level of output equally, so it cannot make any other output preferable.

4. 4

   A monopolist facing demand P = 100 - 2Q with total cost TC = 30 + 10Q + Q squared has a tax of £6 per unit imposed on it. Calculate the new price and output.

   Model answer

   The tax raises total cost to 30 + 16Q + Q squared, so marginal cost becomes 16 + 2Q while marginal revenue stays at 100 - 4Q. Setting 100 - 4Q = 16 + 2Q gives 6Q = 84, so Q = 14 and the price is 100 - 28 = £72. Output falls by one unit and price rises by £2.

5. 5

   With a £6 per unit tax raising the price of a monopolist's product from £70 to £72, calculate the incidence of the tax between consumers and the firm.

   Model answer

   Consumers pay £2 more per unit, so they bear £2 of the £6. The firm now receives £72 but hands £6 to the government, keeping £66 against £70 before, so it bears £4. Consumers therefore bear one third and the producer two thirds. The reason is not that demand is the less responsive of the two — the demand curve and the marginal cost curve have the same slope here, and a competitive market with that supply curve would split the tax evenly. It is that a monopolist sets output where marginal revenue meets marginal cost, and marginal revenue falls twice as steeply as demand, so a given rise in cost moves output, and therefore price, by less.

6. 6

   Calculate the government revenue and the firm's remaining profit when a £6 per unit tax is imposed on a monopolist with demand P = 100 - 2Q and pre-tax total cost TC = 30 + 10Q + Q squared, given that output falls to 14 units at a price of £72.

   Model answer

   Tax revenue is 6 × 14 = £84. Total revenue is 72 × 14 = £1,008 and pre-tax total cost is 30 + 140 + 196 = £366, giving pre-tax profit of £642, so post-tax profit is 642 − 84 = £558. Compared with the £645 earned before the tax the firm loses £87 while the government collects £84, and the £3 difference is the profit given up by producing one unit fewer — the firm's own share of the loss. Consumer surplus falls as well, from £225 to £196, so the total value destroyed by the lower output is £32.

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