A subsidy is a payment by the government to a buyer or seller of a good or service. It is, in essence, the exact opposite of a tax. In fact, when we analyze the effects of subsidies on markets, we can treat the subsidy as a negative tax. Thus, the price the buyer pays is lower than the price the supplier receives after the subsidy. If the government subsidizes gasoline by $1 per gallon, for example, then buyers might pay $3.50 per gallon at the pump, but gas stations receive $4.50 per gallon because they get to add the government dollar to the $3.50. This relationship is P_b + subsidy = P_s, where P_b is the price the buyer pays (the market price) and P_s is the price the seller receives after the subsidy is paid.

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Governments tax a lot, but they also subsidize the production of many different goods and services. Let’s look at the effects of the U.S. government subsidy for the domestic production of ethanol, a corn-based fuel additive that can be mixed with gasoline. (A common rationale given for the subsidy is to reduce the dependence of the United States on imported oil, though not coincidentally politicians from large corn-producing states have been vocal backers of the policy.) Let’s say the government gives fuel producers $1 for every gallon of gas–ethanol mix they sell. This means that if the original supply curve S₁ is what suppliers receive, the supply curve that buyers face will be shifted down by the amount of the subsidy, to S₂ (Figure 3.15). The supply curve that buyers face is lower because the amount people pay to fill their tank is less than the amount the gas station receives, since the government is footing part of the bill (the effects of a tax are just the opposite).

Before the subsidy was in place, consumer surplus was everything below the demand curve and above the price that consumers pay (P₁), area A + B + C in Figure 3.15. After the subsidy, consumer surplus will change. But it will not get smaller, as in the case of a tax. It will get larger. The new consumer surplus is the area below the demand curve and above the price that the consumers have to pay (the new lower price, P_b ). This is the old consumer surplus A + B + C plus the new part F + G + H. This additional surplus comes from the lower price and the additional sales at that price.

Before the subsidy, the producer surplus was everything above the supply curve but below the price the suppliers received (P₁ ), area F + G + J. After the subsidy, producer surplus gets bigger, too. The area above the producers’ own supply curve S₁ and below the price that the suppliers receive (P_s ) is now F + G + J plus B + C + D. [We calculate producer surplus using the producers’ supply curve (S₁) because this is the supply curve that embodies the suppliers’ costs of production.]

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Note that parts of the consumer and producer surplus areas overlap in this case (areas B + C + F + G ) because both sides are getting more surplus than before. The only way this is possible, however, is if someone else foots the bill. In this case, it’s the government. The subsidy costs money. The cost of the subsidy is the subsidy amount times the quantity produced, Q₂ × (P_s – P_b), which amounts to the rectangle B + C + D + E + F + G + H + I.

This isn’t the only cost of the subsidy, however. Like any other price regulation, a subsidy also creates deadweight loss. It might seem odd at first that there would be DWL when both consumers and producers are better off after the subsidy. The key is to compare how much their surplus goes up to how much the subsidy costs the government. While consumer surplus went up by F + G + H and producer surplus by B + C + D, total government outlays for the subsidy were (F + G + H ) + (B + C + D ) + (E + I ). Therefore, the subsidy’s DWL is E + I. Society as a whole pays more for the subsidy than the added benefit it gave to consumers and producers. If somehow the government could just turn over the subsidy revenue to consumers and producers without changing the price, society would be better off. By changing the price, it gets some extra people to buy gasoline (with ethanol added) who really were not interested in buying before.

When we looked at the market interventions earlier in this chapter, the DWL derived from the surplus lost by people who would have bought if there were no tax or regulation, but do not buy when the tax is in place and the price is too high. Here, it is the other way around. The DWL comes from people who would not have made a purchase in a competitive market. They only make a purchase because the subsidy lowers the price. The amount they value the extra quantity is less than it costs the government to move them to buy it.

A different way to understand this deadweight loss is to think about people giving presents to each other. Economist Joel Waldfogel asked microeconomics students who received Christmas presents how much they thought the gifts they received cost the people who bought them.12 Then he asked the students how much the gifts were worth to them, apart from the sentimental value. The students valued the presents they got by about 15% less than the presents’ cost to purchase. This 15% DWL from Christmas presents is just like the DWL from a subsidy. When the government subsidizes a product, it gives consumers a gift: The consumers value the gift (as measured by the consumer surplus) less than it costs the government to buy it (as measured by the revenue cost).