Using Consumer and Producer Surplus to Calculate the Cost of the Sugar Import Quota System
From our description of the US sugar market, we learned that the sugar import quota system operated to raise the price of sugar in the US to be about two times higher than the world price. US sugar producers gain from this program while US consumers of sugar (i.e.Coca Cola, Hersheys) are made worse off by the program. But additionally, the restriction on trade introduces some inefficiency to the market. Economists argue that trade is benficial to both buyers and sellers. From this it follows that restricitions on trade, like the sugar import program, will cause some loss in efficiency. Now it may be that, as a country, we are willing to incur some efficiency loss in order to pursue some other objective like preserving agricultural lifestyles. Many developed countries restrict trade in agricultural products to protect their domestic farmers. The Japanese restrict rice imports and the Norwegians restrict dairy product imports. The US restricts sugar imports. One job for economists is to calculate the costs of such programs so that more informed decisions can be made about whether it is too costly to have programs like the sugar import quota program. If the cost to the US is only $1 million per year, maybe the program is a cheap way to protect farmers and maintain a vibrant ag community. But if the cost is $100 billion, maybe not.
From our previous description of the US Sugar Import Quota and the US sugar market we gleaned these (appoximate) facts:
US Price: 20 cents per pound
World Price: 10 cents per pound
US Production: 17 billion pounds
US Imports: 3 billion pounds
US Consumption 20 billion pounds
US Average cost of production: 12 cents per pound
The diagram to the right is drawn to be consistent with these "facts".
If there were free trade in sugar: First we look at what the US market would look like if there were free trade for sugar. Given our facts, if there was free trade, the price of sugar would fall to about $ .10 per pound in the US. Given the US supply curve, if the price was $ .10 per pound the quantity supplied by US sugar beet and sugar cane growers would be ZERO...that is, the US would import all of its sugar, and consumers would expand consumption from 20 to 25 billion pounds per year. The graph to the right shows what the US market would look like if we allowed sugar to be freely imported. The price in the US would fall to $ .10, the quantity demanded would increase to 25 (probably a shift from HFCS to sugar by some food processors), quantity supplied by US producers would fall to zero, and imports would be 25. With free trade and a price of $ .10 per pound consumer surplus would be equal to the area shaded green in the diagram to the right.
Costs of the Sugar Import Quota System: As noted above the sugar import quota system causes the price in the US to be $ .20 per pound instead of the world price of $ .10 per pound. This cost is borne by sugar consumers and is quantified as a loss in consumer surplus. We can calculate the magnitude of the loss in consumer surplus geometrically as the area of the trapzoidal area shaded light green in the diagram to the right.
Benefits of the sugar import program. There are two groups of benificiaries of this program. First is the US sugar producers. If there were free trade in sugar with a price of $ .10, the quantity supplied would have been zero, but with the program, the price of sugar is $ .20, US producers supply 17 billion pounds of sugar, and earn a producer surplus shown in the diagram to the right. The magnitude of the producer surplus is calculated as the area of the shaded producer surplus triangle which is $ .10 tall, and 17 billion wide and thus the producer surplus is equal to ($ .10)(17billion)(1/2)=$.85billion.
The second beneficiary of the program are those that are allocated import quotas. These importers get the chance to buy sugar at the world price and then sell it in the US. They earn a profit of ($ .20 - $ .10)= ten cents per pound and get to import 3 billion pounds and so earn a total profit of $ .3 billion per year. This is shown as the area of the shaded rectangle in the diagram to the right.
Cost minus Benefits = Efficiciency Loss: Above we noted that the cost of the sugar import quota was the loss in consumer surplus. Then we noted some of the lost consumer surplus was captured as a benefit for US sugar producers (shown as the producer surplus) and a benefit for owners of the import quotas (shown as "Profit for Quota Owners"). But the costs of the program are greater than the benefits and the magnitude of the loss in efficiency is calculated as the size of the two shaded triangles shown in the diagram to the right.
The magnitude of the two shaded deadweight loss triangles represent that portion of the loss in consumer surplus not showing up as benefits for either US sugar producers or sugar importers. They are triangles, and we know the dimensions of the triangles, and so we can calculate their size. This is done in the diagram to the right.
The results of the sugar import program can be summarized as:
