7.2 Depicting a Free Trade Equilibrium: Large and Small Country Cases

Figure 7.1 "U.S. Wheat Market: Autarky Equilibrium" depicts the supply and demand for wheat in the U.S. market. The supply curve represents the quantity of wheat that U.S. producers would be willing to supply at every potential price for wheat in the U.S. market. The demand curve represents demand by U.S. consumers at every potential price for wheat in the U.S. market. The intersection of demand and supply corresponds to the equilibrium autarky price and quantity in the United States. The price, P_Aut^US, is the only price that will balance domestic supply with domestic demand for wheat.

Figure 7.2 "Mexican Wheat Market: Autarky Equilibrium" shows the supply and demand for wheat in the Mexican market. The supply curve represents the quantity of wheat that Mexican producers would be willing to supply at every potential price in the Mexican market. The demand curve represents demand by Mexican consumers at every potential price for wheat in the Mexican market. The intersection of demand and supply corresponds to the equilibrium autarky price and quantity in Mexico. The price, P_Aut^Mex, is the only price that will balance Mexican supply with demand for wheat.

The curves are drawn such that the U.S. autarky price is lower than the Mexican autarky price. This implies that if these two countries were to move from autarky to free trade, the United States would export wheat to Mexico. Once trade is opened, the higher Mexican price will induce profit-seeking U.S. firms to sell their wheat in Mexico, where it commands a higher price initially. As wheat flows into Mexico, the total supply of wheat rises, which will cause the price to fall. In the U.S. market, wheat supply falls because of U.S. exports. The reduced supply raises the equilibrium price in the United States. These prices move together as U.S. exports rise until the prices are equalized between the two markets. The free trade price of wheat, P_FT, is shared by both countries.

To derive the free trade price and the quantity traded, we can construct an export supply curve for the United States and an import demand curve for Mexico. Notice that at prices above the autarky price in the United States, there is excess supply of wheat—that is, supply exceeds demand. If we consider prices either at or above the autarky price, we can derive an export supply curve for the United States. The equation for export supply is given by

$$X{S}^{US}(P^{US})=S^{US}(P^{US})-D^{US}(P^{US})\text{,}$$

where XS^US(.) is the export supply function, S^US(.) is the supply function for wheat in the United States, and D^US(.) is the demand function for wheat in the United States. Each function is dependent on the U.S. price of wheat, P^US.

Graphically, export supplyThe quantity of a product a country would wish to export at a particular price. The export supply curve is the schedule of export supply at every potential price (usually prices above the country’s autarky price). is the horizontal difference between the supply and demand curve at every price at and above the autarky price, as shown in Figure 7.3 "Deriving the U.S. Export Supply Curve". At the autarky price, P_Aut^US, export supply is zero. At prices P₁, P₂, and P₃, export supply is given by the length of the like-colored line segment. To plot the export supply curve XS^US, we transfer each line segment to a separate graph and connect the points, as shown on the right in Figure 7.3 "Deriving the U.S. Export Supply Curve". The export supply curve gives the quantities the United States would be willing to export if it faced prices above its autarky price.

In Mexico, at prices below its autarky price there is excess demand for wheat since demand exceeds supply. If we consider prices either at or below the autarky price, we can derive an import demand curve for Mexico. The equation for import demand is given by

$$M{D}^{Mex}(P^{Mex})=D^{Mex}(P^{Mex})-S^{Mex}(P^{Mex})\text{,}$$

where MD^Mex(.) is the import demand function, D^Mex(.) is the demand function for wheat in Mexico, and S^Mex(.) is the supply function for wheat in Mexico. Each function is dependent on the Mexican price of wheat, P^Mex. Graphically, import demandThe quantity of a product a country would wish to import at a particular price. The import demand curve is the schedule of import demand at every potential price (usually prices below the country’s autarky price). is the horizontal difference between the demand and supply curve at every price at and below the autarky price, as shown in Figure 7.4 "Deriving the Mexican Import Demand Curve". At the autarky price, P_Aut^Mex, import demand is zero. At prices P₁, P₂, and P₃, import demand is given by the length of the like-colored line segment. To plot the import demand curve MD^Mex, we transfer each line segment to a separate graph and connect the points, as shown on the right in Figure 7.4 "Deriving the Mexican Import Demand Curve". The import demand curve gives the quantities Mexico would be willing to import if it faced prices below its autarky price.