## Do Farm Subsidies Increase or Decrease Food Prices?

A reader asks:

Stiglitz said “The heavy subsidization of corn, for instance, means that many unhealthful foods are relatively cheap. So grocery shopping on a tight budget often means choosing foods that are not nutritious.”

Please correct me if I’m wrong. I’ve been telling [people] that farm subsidies make food more expensive, not cheaper (sugar is a really good example).

If you ask an economist, you shouldn’t be surprised when the answer is “it depends.”

### Price-Decreasing Agricultural Subsidies

Letting p denote price, f(.) denote the production function, L denote how much labor is employed on the farm, and w denote the wage, we know that the producer maximizes profit by choosing how much labor L to employ on his farm, such that

pf(L) – wL,

where the first term is total revenue (price times quantity produced) and the second term is total cost (wage times labor), with the associated first-order condition (FOC)

pf’ – w = 0,

so at L*, i.e., the optimal quantity of labor, the value of the marginal product of labor (left-hand side) equals the marginal cost of labor (wage, or right-hand side).

If the state subsidizes labor by paying, say, 20% of each unit of labor, then the maximization problem becomes

pf(L) – 0.8wL,

because 0.2wL is paid for by the government. The associated FOC is then

pf’ – 0.8w = 0,

so L* is now such that the value of the marginal product of labor is much lower than it is in the unsubsidized case (since 0.8w < w). But because marginal product of labor is decreasing in L, this means that more output is produced, which leads to lower prices in the aggregate.

### Price-Increasing Agricultural Subsidies

Now, that’s only *one kind* of subsidy. Another kind of subsidy is a price subsidy where the quantity produced is rationed — think of raisins in the US. In that case, if the quantity allowed is less than the optimal (i.e., market-clearing) quantity, what will happen is that prices will be artificially higher — the subsidy here is that each producer receives a higher price per unit, leading to extra-normal (i.e., above zero) profits.

The same can be accomplished by placing restrictions on how much of a commodity can be imported (e.g., sugar) by placing a tariff on it; this allows domestic producers to charge a price higher than marginal cost because of scarcity.

My understanding is that for corn, farmers directly receive money, which is more akin to my first example above and, as Stiglitz claimed, cheap corn-based foods (notice the presence of high-fructose corn syrup in almost every processed food) flooding the market instead of the other way around. Presumably, what drives the choice producers of specific commodities make (direct subsidies or trade restrictions) is whether a higher price and lower quantity demanded leads to higher profit, or whether a lower price and higher quantity demanded does (which goes through the price-elasticity of revenue, holding cost constant).