Depicting a Free Trade Equilibrium: Large Country Case

The adjoining graph depicts the supply and demand for wheat in the US market. The supply curve represents the quantity of wheat that US producers would be willing to supply at every potential price for wheat in the US market. The demand curve represents demand by US consumers at every potential price for wheat in the US market.

The intersection of demand and supply corresponds to the equilibrium autarky price and quantity in the US. The price, , is the only price that will balance domestic supply with domestic demand for wheat.

The next graph 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 the Mexico. The price, , is the only price that will balance Mexican supply with demand for wheat.

The curves are drawn such that the US 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 US would export wheat to Mexico. Once trade is opened, the higher Mexican price will induce profit-seeking US 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 US market wheat supply falls because of US exports. The reduced supply raises the equilibrium price in the US. These prices move together as US 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 US and an import demand curve for Mexico.

Notice that at prices above the autarky price in the US, there is excess supply of wheat, i.e., supply exceeds demand. If we consider prices either at or above the autarky price we can derive an export supply curve for the US. The equation for export supply is given by,

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

Graphically, export supply is the horizontal difference between the supply and demand curve at every price, at and above the autarky price, as shown in the adjoining Figure. At the autarky price, P_Aut^US, export supply is zero. At prices, P, P and P, 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. The export supply curve gives the quantities the US would be willing to export if it faced prices above its autarky price.

In Mexico, at prices below it's 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,

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 demand is the horizontal difference between the demand and supply curve at every price at and below the autarky price as shown in the adjoining Figure. At the autarky price, P_Aut^Mex, import demand is zero. At prices, P, P and P, 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. The import demand curve gives the quantities Mexico would be willing to import if it faced prices below its autarky price.

The intersection of the US export supply with Mexican import demand determines the equilibrium free trade price, P_FT, and the quantity traded, Q_FT, where Q_FT = XS^US (P_FT) = MD^Mex(P_FT). See Figure. The free trade price, P_FT, must be that price which equalizes US export supply with Mexican import demand. Algebraically, the free trade price is that price which solves,

This implies also that world supply is equal to world demand since,

and,

International Trade Theory and Policy - Chapter 90-4: Last Updated on 4/30/98