Chapter 19: Problem 720

Suppose the government decides to regulate a certain monopoly with a fixed per unit tax How will this affect price output, and profits?

Short Answer

Expert verified

When the government imposes a per unit tax on a monopoly, the monopolist will experience an increase in marginal cost and a change in its cost structure. This leads to a decrease in the optimal output level, causing the monopolist to increase the price of the product, though not necessarily by the full amount of the tax. As a result, the monopolist's profits will decrease due to increased total costs and potentially reduced revenue.

Step by step solution

Understand the context of monopoly

A monopoly is a market structure where a single firm produces a particular good or service with no close substitutes. In this context, the monopolist has the ability to influence the price of the output based on the demand for the good or service. The monopolist's objective is to maximize profit by choosing an optimal output level and price.

Identify the monopolist's cost structure

To analyze the impact of a per unit tax, we need to first identify the monopolist's cost structure. The main costs associated with a monopolist's production are fixed costs (FC), variable costs (VC), and total costs (TC): - Fixed costs are the costs that do not change with the level of output. - Variable costs are the costs that change as the output level changes. - Total costs are the sum of fixed costs and variable costs: TC = FC + VC The average total cost (ATC) is the total cost divided by the quantity of output: ATC = TC/Q And the marginal cost (MC) is the increase in the total cost resulting from the production of one additional unit: MC = d(TC)/dQ

Analyze the effect of a per unit tax on cost structure

When the government imposes a per unit tax, t, it adds to the cost of producing each unit. The new total cost can be written as: New TC = FC + (VC + tQ) Note that fixed costs (FC) remain the same. The new ATC is now: New ATC = (FC + VC + tQ) / Q The new MC is the derivative of the new total cost with respect to quantity: New MC = d(FC + VC + tQ) / dQ

Assess the effect on optimal output and price

In a monopoly, the profit-maximizing output level is determined where the marginal cost is equal to the marginal revenue (MC = MR). When a per unit tax is imposed, the new marginal cost (New MC) will be higher than the original marginal cost (MC) by the value of the tax. Therefore, in order to maximize profits, the monopolist will have to decrease its output level. As a result of the decrease in output, the demand curve for the good will shift to the left, and the monopolist will increase its price. However, the price increase may not be equal to the amount of the tax, as the monopolist will balance it with the reduction in quantity to minimize the overall negative impact on demand and profits.

Assess the effect on profits

Since the monopolist is faced with an increase in marginal cost and a decrease in output, its total cost will increase. Moreover, the increased price may not fully compensate for the reduction in output, leading to a decrease in revenue. As a result, the monopolist's profits which are equal to total revenue (TR) minus total costs (TC) will decrease. In conclusion, when a per unit tax is imposed on a monopolist, the monopolist will decrease its output level, increase its price, and ultimately face reduced profits.