2 The Gains from Trade

In earlier chapters, we demonstrated the gains from trade using a production possibilities frontier and indifference curves. We now instead demonstrate the gains from trade using Home demand and supply curves, together with the concepts of consumer surplus and producer surplus. You may already be familiar with these concepts from an earlier economics course, but we provide a brief review here.

Consumer and Producer Surplus

Suppose that Home consumers have the demand curve D in panel (a) of Figure 8-1 and face the price of P₁. Then total demand is D₁ units. For the last unit purchased, the consumer buying it values that unit at close to its purchase price of P₁, so he or she obtains little or no surplus over the purchase price. But for all the earlier units purchased (from 0 to D₁ units), the consumers valued the product at higher than its purchase price: the consumers’ willingness to pay for the product equals the height of the demand curve. For example, the person buying unit D₂ would have been willing to pay the price of P₂, which is the height of the demand curve at that quantity. Therefore, that individual obtains the surplus of (P₂ − P₁) from being able to purchase the good at the price P₁.

For each unit purchased before D₁, the value that the consumer places on the product exceeds the purchase price of P₁. Adding up the surplus obtained on each unit purchased, from 0 to D₁, we can measure consumer surplus (CS) as the shaded region below the demand curve and above the price P₁. This region measures the satisfaction that consumers receive from the purchased quantity D₁, over and above the amount P₁ · D₁ that they have paid.

Panel (b) of Figure 8-1 illustrates producer surplus. This panel shows the supply curve of an industry; the height of the curve represents the firm’s marginal cost at each level of production. At the price of P₁, the industry will supply S₁. For the last unit supplied, the price P₁ equals the marginal cost of production for the firm supplying that unit. But for all earlier units supplied (from 0 to S₁ units), the firms were able to produce those units at a marginal cost less than the price P₁. For example, the firm supplying unit S₀ could produce it with a marginal cost of P₀, which is the height of the supply curve at that quantity. Therefore, that firm obtains the producer surplus of (P₁ − P₀) from being able to sell the good at the price P₁.

For each unit sold before S₁, the marginal cost to the firm is less than the sale price of P₁. Adding up the producer surplus obtained for each unit sold, from 0 to S₁, we obtain producer surplus (PS) as the shaded region in panel (b) above the supply curve and below the price of P₁. It is tempting to think of producer surplus as the profits of firms, because for all units before S₁, the marginal cost of production is less than the sale price of P₁. But a more accurate definition of producer surplus is that it equals the return to fixed factors of production in the industry. That is, producer surplus is the difference between the sales revenue P₁ · S₁ and the total variable costs of production (i.e., wages paid to labor and the costs of intermediate inputs). If there are fixed factors such as capital or land in the industry, as in the specific-factors model we studied in Chapter 3, then producer surplus equals the returns to these fixed factors of production. We might still loosely refer to this return as the “profit” earned in the industry, but it is important to understand that producer surplus is not monopoly profit, because we are assuming perfect competition (i.e., zero monopoly profits) throughout this chapter.3

Home Welfare

To examine the effects of trade on a country’s welfare, we consider once again a world composed of two countries, Home and Foreign, with each country consisting of producers and consumers. Total Home welfare can be measured by adding up consumer and producer surplus. As you would expect, the greater the total amount of Home welfare, the better off are the consumers and producers overall in the economy. To measure the gains from trade, we will compare Home welfare in no-trade and freetrade situations.

No Trade In panel (a) of Figure 8-2, we combine the Home demand and supply curves in a single diagram. The no-trade equilibrium occurs at the autarky price of P^A, where the quantity demanded equals the quantity supplied, of Q₀. Consumer surplus is the region above the price of P^A and below the demand curve, which is labeled as CS in panel (a) and also shown as area a in panel (b). Producer surplus is the area below the price of P^A and above the supply curve, which is labeled as PS in panel (a) and also shown as area (b + c) in panel (b). So the sum of consumer surplus and producer surplus is the area between the demand and supply curves, or CS + PS = area (a + b + c). That area equals Home welfare in the market for this good in the absence of international trade.

Free Trade for a Small Country Now suppose that Home can engage in international trade for this good. As we have discussed in earlier chapters, the world price P^W is determined by the intersection of supply and demand in the world market. Generally, there will be many countries buying and selling on the world market. We will suppose that the Home country is a small country, by which we mean that it is small in comparison with all the other countries buying and selling this product. For that reason, Home will be a price taker in the world market: it faces the fixed world price of P^W, and its own level of demand and supply for this product has no influence on the world price. In panel (b) of Figure 8-2, we assume that the world price P^W is below the Home no-trade price of P^A. At the lower price, Home demand will increase from Q₀ under no trade to D₁, and Home supply will decrease from Q₀ under no trade to S₁. The difference between D₁ and S₁ is imports of the good, or M₁ = D₁ − S₁. Because the world price P^W is below the no-trade price of P^A, the Home country is an importer of the product at the world price. If, instead, P^W were above P^A, then Home would be an exporter of the product at the world price.

Gains from Trade Now that we have established the free-trade equilibrium at price P^W, it is easy to measure Home welfare as the sum of consumer and producer surplus with trade, and compare it with the no-trade situation. In panel (b) of Figure 8-2, Home consumer surplus at the price P^W equals the area (a + b + d), which is the area below the demand curve and above the price P^W. In the absence of trade, consumer surplus was the area a, so the drop in price from P^A to P^W has increased consumer surplus by the amount (b + d). Home consumers clearly gain from the drop in price.

Home firms, on the other hand, suffer a decrease in producer surplus from the drop in price. In panel (b), Home producer surplus at the price P^W equals the area c, which is the area above the supply curve and below the price P^W. In the absence of trade, producer surplus was the area (b + c), so the drop in price from P^A to P^W has decreased producer surplus by the amount b. Home firms clearly lose from the drop in price.

Comparing the gains of consumers, (b + d), with the losses of producers, area b, we see that consumers gain more than the producers lose, which indicates that total Home welfare (the sum of consumer surplus and producer surplus) has gone up. We can calculate the total change in Home welfare due to the opening of trade by adding the changes in consumer surplus and producer surplus:

The area d is a measure of the gains from trade for the importing country due to free trade in this good. It is similar to the gains from trade that we have identified in earlier chapters using the production possibilities frontier and indifference curves, but it is easier to measure: the triangle d has a base equal to free-trade imports M₁ = D₁ − S₁, and a height that is the drop in price, P^A − P^W, so the gains from trade equal the area of the triangle, · (P^A − P^W) · M₁. Of course, with many goods being imported, we would need to add up the areas of the triangles for each good and take into account the net gains on the export side to determine the overall gains from trade for a country. Because gains are positive for each individual good, after summing all imported and exported goods, the gains from trade are still positive.

Home Import Demand Curve

Before introducing a tariff, we use Figure 8-3 to derive the import demand curve, which shows the relationship between the world price of a good and the quantity of imports demanded by Home consumers. We first derived this curve in Chapter 2, for the Ricardian model. We now briefly review the derivation of the import demand curve before analyzing the effect of an import tariff on prices and welfare.

In panel (a) of Figure 8-3, we again show the downward-sloping Home demand curve (D) and the upward-sloping Home supply curve (S). The no-trade equilibrium is at point A, which determines Home’s no-trade equilibrium price P^A, and its no-trade equilibrium quantity of Q₀. Because quantity demanded equals quantity supplied, there are zero imports of this product. Zero imports is shown as point A′ in panel (b).

Now suppose the world price is at P^W, below the no-trade price of P^A. At the price of P^W, the quantity demanded in Home is D₁, but the quantity supplied by Home suppliers is only S₁. Therefore, the quantity imported is M₁ = D₁ − S₁, as shown by the point B in panel (b). Joining points A′ and B, we obtain the downward-sloping import demand curve M.

Notice that the import demand curve applies for all prices below the no-trade price of P^A in Figure 8-3. Having lower prices leads to greater Home demand and less Home supply and, therefore, positive imports. What happens if the world price is above the no-trade price? In that case, the higher price would lead to greater Home supply and less Home demand, so Home would become an exporter of the product.