Question

Consider a competitive industry that the government taxes in order to raise revenue (e.g., the sale of alcoholic beverages). Show graphically that the amount of revenue generated by a per-unit tax on the industry can in principle be duplicated by reorganizing it as a state-run monopoly and using the profits as government revenue.

Answer 1

The equivalence of the effect of a per-unit tax, and a state-run monopoly, on the sale of alcoholic beverages, can be described as follows:

Consider that there is a market for alcoholic beverages, which the government wants to regulate. In the process of regulation, the government wants to achieve the following:

• reduce the equilibrium quantity bought and sold
• increase the equilibrium price
• generate government revenue

It is important to note here that a market based mechanism like a tax, or like a state-run monopoly, will be able to generate revenues for the government.

A non-market based mechanism like a ban, will not generate any revenue.

The diagram below shows two panels to explain the equivalence of outcome, if the two mechanisms are used.

In both the panels, the same market is depicted, i.e., that of alcoholic beverages. Thus, the demand curve and supply curve are the same. The second panel also shows the MR curve.

The first panel represents a per unit tax. The size of the tax is t, which is:

The reduction in quantity due to the tax is

The pink shaded area is the revenue to the government

where GR is government revenue, and represents the area of the rectangle. This rectangle has height t and breadth Qt.

Now, the second panel shows the same outcome, by creating a monopoly.

The key here is for the monopoly to charge a price in a manner that , on a quantity such that

In general, the monopoly will first equate MR = MC, to get the profit maximization quantity. It will then set a price as per the demand curve.

Profit in this case will be the blue shaded rectangle

If the market is competitive, and the demand and supply curves are the same,

and will be equivalent

In other words, the government revenue raised from tax t, will be equal to the profit generated by the monopoly.

The pink shaded rectangle will have the same area as the blue shaded rectangle.