A protected monopoly which is unregulated makes profit by restricting production to raise the price of its product. It makes a profit but the gain in profit from monopolization of a market is less than the cost to consumers as a result of the higher price. Therefore there is a net social loss from a protected monopoly.

To prove this proposition let us start with a special historical case. In the Middle Ages and later kings often granted a monopoly for the sale of salt to one organization because it was easier to collect a tax on salt from one enterprise than from the many salt producers and sellers that would exist under competition.

The socially optimum output and price are given by the intersection of the demand schedule and the marginal cost curve. The demand curve represents the marginal benefit curve so the intersection corresponds to the level of production and consumption such that marginal benefit is equal to marginal cost and both correspond to the market price. These are represented in the above graph by Q_opt and P_opt.

The monopolist maximizes its profit where marginal cost is equal to marginal revenue. In the graph the level of output of the monopolist is shown as Q_m and the price the monopolist establishes is P_m. Although the monopolist has a monopoly on the sale of salt it does not necessarily have to produce the salt itself. It could get the amount Q_m by offering the price P_p. The monopoly's profit would then be the difference between the price it sells the salt and the price at which it purchases times the amount sold; i.e., monopoly profit equals (P_m-P_p)Q_m. The level of the monopoly profit can be compared with the loss to the consumers and the salt producers, as is shown in the diagram below.

The loss to the consumers is the area of the gray-colored uppertrapezoid. The loss in producers surplus to the salt makers is the area of the gray-colored lower trapezoid. The profit of the monopolist is the rectangle described previously. Clearly the loss of consumer and producer surpluses is greater than the amount of the monopoly profit by the area of the two triangles.

If the monopolist does not purchase the quantity it sells but instead produces it itself then the purplish colored area is the profit the monopolist would lose in functioning as a monopolist rather than as a price-taking firm producing at the socially optimum level of production. Thus the net gain in profit for the monopolist is the monopoly profit less the area of the purplish trapezoid.

The net social welfare loss of the economy due to the monopoly is the area of the gray trapezoid less the rectangle representing the monopoly profit. The result is the same as before; the net social loss due to the monopoly is the area of the two triangles.

It is very important to remember that the above analysis applies only to the protected monopoly; i.e., a firm which is protected by the State from competition. If there is a small town which there is only a single grocery store despite freedom of entry then that store has a monopoly but it is not a protected monopoly. Even if that store exploits its monopoly power there is no economic welfare loss due to monopoly. When the town grows enough it will get another store. The town will get another store when someone sees that the revenue it will generate exploiting all the opportunities for price setting and discrimination will be greater than the cost. For the people of the town it is not a choice between perfect competition and monopoly it is a choice between mon-opoly and zero-opoly. The town's people are clearly better off with the exploitative monopoly than they were with no store because they can if they ignore the existence of the store and continue to do whatever they did before the store located there.

The above point harkens back to the French engineer, Jules Dupuit, who essentially founded cost benefit analysis. He asked when should a bridge be built in a particular location. His answer was that it should be built when the revenues that would be generated if the bridge were operated as a monopoly taking advantage of price discrimination exceeds the costs of building it. In building and operating it the costs may be reduced taking advantage of monopsonistic advantages at the location. Dupuit did not assert that the bridge should actually be operated that way, he was only looking for a criterion about when or if the bridge should be built. However, any other mode of operation would require government subsidies financed out of taxes which would involve a transfer of welfare from one segment of the economy to another.

On this matter of possible welfare losses due to competition deemed not to be perfect the Austrian School of Economics deviates sharply from the Neoclassical School. Clearly in this matter the Austrian School is correct; freedom of entry and exit is the essential criterion of competitiveness.

For the debate in ancient China on the issue of the welfare loss due to protected monopolies see The Debate on Iron and Salt.