Tariffs vs Quotas with Domestic Monopoly

It is well-known that tariffs and quotas are equivalent under certain conditions. One of the requirements is that markets be perfectly competitive. When markets are not competitive, international trade may have what is called a pro-competitive effect. This means that opening to world markets can force an imperfectly competitive industry to price at marginal cost. Under a tariff regime the pro-competitive effect remains, but with a quota it is diluted. This sheet was designed to show how that could happen. It is partial equilibrium using linear demand and supply, with the solution embedded in the sheet. It should work in any version of Excel. Further details, including a detailed slideshow of how the model was created, can be found in Gilbert and Oladi (2007).
 

Model Layout Guide
 
 

Exercises

Pro-competitive Effects of Trade

In this sheet we assume a single price domestic monopolist. In the initial equilibrium depicted on the left the monopolist faces a fixed world price (the economy is open and small). In this context, the monopolist cannot charge any price higher than the world price, because all buyers are free to purchase from the world, which is willing to supply the whole market. In effect, the industry is forced to act as if it were competitive rather than a monopoly. This is socially desirable because monopoly introduces a deadweight loss. To see the extent of the loss, consider the equilibrium on the right. This is a zero quota equilibrium (autarky). The monopolist makes supernormal profits by restricting output, at the expense of social efficiency (compare the total surplus in cell I36 with cell S36).

Effect of Small Tariffs

Now consider the effect of a tariff (increase the value in cell E31). As the price of importing rises, the monopolist is able to charge a higher price, just as with competition. If the tariff is small, however, it is still unable to exploit its monopoly power, the price is the world price plus the tariff.

Non-Equivalence of Tariffs and Quotas

Suppose the tariff you set in the previous exercise was 50 percent, then imports (cell E36) should be 10. Under perfect competition, a quota of 10 should be equivalent to a tariff of 50 percent. To see whether this holds with monopoly, increase the quota in cell O31 to 10. The results are quite different. With the tariff, the price is 75. With the quota, the price is 97. Why? The quota allows imports of 10 units, but leaves residual demand to the monopolist. The monopolist exploits the residual demand in the usual way, by restricting output and pushing up the price. Consumers cannot respond to the move by purchasing more from the world market, because the quota has already been filled. 

Prohibitive Tariffs and Monopoly

What if the tariff imposed is large rather than small? If the tariff is large enough to push the price of importing above the price where the domestic demand curve crosses the monopolist's marginal cost, then the effect of the tariff under monopoly will diverge from the effect of the same tariff under competitive conditions. Under competition, a tariff that raises the cost of importing (the world price plus the tariff) above the autarky price is said to be prohibitive. The margin by which the cost of importing exceeds the autarky price is called water, and has no effect. The domestic price cannot be forced above the autarky price by a tariff. Under monopoly things are different. The 'just' prohibitive tariff is 70. When you have 70 in cell E31, the value in cell E36 is zero. As we keep increasing the tariff though, the domestic price rises with it. Why? The monopolist can, and prefers to, restrict its output to meet the higher price (it cannot go higher for the same reasons outlined above). If the tariff rises above 120, the monopolist is effectively unconstrained. Their optimal choice is to charge a price of 110 anyway. Hence, a very large tariff, with substantial water by the conventional interpretation, is equivalent to a zero quota. 

Effect of Falling World Prices

Consider the implications of advances in technology in foreign markets that lead to a fall in the world price. Take as our starting point a tariff of 120 percent in cell E31 and a zero quota in cell O31, since in both cases the monopolist is unconstrained. Now, decrease the world price in cell E44 to represent the technological progress. The tariff and quota are no longer equivalent in their effect. The quota fully insulates the monopolist from external competition, no matter what happens. The monopolist protected by a tariff however, must still contend with the world price decrease, it will reduce their ability to influence the domestic price.