Question

A monopolist has a cost function given by c(?)=?² and faces a demand curve given by P(?)=120−y.

(a)What is its profit-maximizing level of output? What price will the monopolist charge?

(b)Calculate the deadweight loss imposed by the monopolist. Show also the deadweight loss in a graph

(c)If you put a lump sum tax of $100 on this monopolist, what would its output be?

(d)Suppose that you put a specific tax on the monopolist of $20 per unit output. What would its profit-maximizing level of output be?

Answer 1

In part (a) to find the profit-maximizing output, the condition for monopoly is Marginal revenue (MR)= Marginal cost (MC). On the basis of this, the values are given in the question and plugin those to get y.

In part (c) when lumpsum tax is imposed on monopolists so, this tax is like a fixed cost, it doesn't matter how much units will be produced the fixed amount will be charged anyways. So the total cost will increase due to an increase in fixed cost, which will shift the Average Cost curve upwards only. So the output produced by monopolists will remain unaffected at y=30.

In part (d) the per-unit tax affects the variable costs which result in an upwards shift of the MC and AC curve as well. So, the profit-maximizing output will be produced at y=25.