Question

3. Assume that a monopolist produces a good at constant marginal cost MC(q) = 1. Demand is given by pºq) = 10 - 2q. There are no other pre-existing distortions in the market. (a) What is the privately optimal quantity and price chosen by the monopolist? For parts (b) and (c), assume that a tax of $t is imposed on every unit of output produced by the monopolist. (b) Derive the optimal quantity and price chosen by the monopolist as functions of T. (c) How much does the price increase when T is raised from $0 to $1? For part (d), assume that a tax t is imposed on each dollar of the monopolist's profits, while the tax on output is removed (t = 0). This means that if the monopolist earns $t in profit, it must pay t x $n to the government. (d) What is the effect of this tax on the price and quantity chosen by the monopolist? Now suppose the government is deciding whether to raise revenue by taxing the mo- nopolist's output (T>0), or by taxing its profits (t > 0). (e) Derive expressions for the government's revenue as a function of the tax rate, for each of these two kinds of taxes: R(t) and R(T). For this part of the question, assume that if one kind of tax is used, the other is not. So if t > 0 then t = 0, and vice-versa. (f) Suppose that the government only cares about the welfare of consumers. Calculate the change in consumer surplus due to each type of tax (1 or t), compared to the equilibrium in part (a) where the monopolist is not taxed. Remember that these should be expressed as functions of the relevant tax rate. (g) Can the government increase consumer surplus by taxing both output and profits (t > 0 and 7 > 0) rather than only using one kind of tax?

Answer 1

Solution-

Optimal condition for any monopolist would be when the marginal revenue earned by him is equal to the marginal cost incurred by him.

b) Marginal cost incurred by the monopolist is increased by the tax imposed on each unit of output. Thus new marginal cost = 1+t

c) price is increased by $0.5

d) Since the tax is being imposed on the profits and not on output, marginal cost incurred on producing an extra unit of output is not changed. In any case, monopolist will try to maximize his profits, thus Optimal Quantity and price charged by the monopolist doesn't change.

As per the HOMEWORKLIB RULES we are required to solve till d subparts, for the rest of the subparts post separately.