Wednesday, June 2, 2010

What is the effect of a price cap?

Today's post is about a deceptively complicated topic: price ceilings. In an ordinary supply and demand analysis, supply slopes up and demand slopes down. Their intersection define the equilibrium price and quantity.

This is an equilibrium because -- given the market price -- neither the producers nor the consumers have an incentive to change their behavior. Everyone who is willing to pay more than the price buys the product. Every unit that costs less than the market price is sold. And, there are just as many units demanded as are units supplied.*

Turning to today's topic, what happens when the government places a cap on the price below the equilibrium price? Such a cap is called a price ceiling, and the first-order analysis looks like this:

At the regulated price, quantity demanded exceeds quantity supplied, so there isn't enough to go around. Hence, price ceilings lead to shortages. Given equations for supply and demand, it wouldn't be difficult to compute the size of the shortage. We could even tell the story in reverse for price floors (which stipulate that the price cannot go below some level). In that case, price floors cause surpluses. For many, this is where the analysis stops.

This is unfortunate because if you start thinking about it, the analysis does not make much sense if we stop here. There are still interesting questions that we have not yet answered. What happens to the excess demand? Does it just evaporate? Who among the (too-many) consumers gets the (too-few) products available for sale?

The problem is that the graph no longer depicts an equilibrium. Here's another picture to clarify the point:

At the quantity traded, there is a wedge between what buyers are willing to pay (Pd) and the maximum price allowed by the market (Ps). If you are a consumer who is willing to pay more than the maximum legally-mandated price, do you just stand by and let someone else get the good? No! You are willing to expend up to the surplus you would get at the mandated price to get your hands on one of the rare products that will be traded.

One way to resolve the shortage is to assume that individuals waste some value of their time waiting in line to help "pay" for the good. In this world, everyone who waits in line gets the good eventually, but the difference in the maximum price and the willingness to pay is covered by the costly hassle of standing in line.**

In the standard supply and demand equilibrium, whatever the buyer pays the seller receives in exchange for bringing the product to market, but this isn't so for waiting in line. When the buyer pays for a product in time, no one gets those foregone opportunities back. In this sense, waiting in line is pure waste.

There are other ways to resolve the shortage. For example, suppliers could bundle the good with other goods and services (and charge extra for those services). Under rent control, you often see that landlords charge high application fees and key fees. When the U.S. government instituted price controls on gasoline (in the 1970s), many gas stations offered complementary services that included a tank of gas. Get your oil changed (at this high price) and you also get a tank of gas without the worry of being the one who doesn't get to fill up if there is a shortage.

If you think about any price change, there are a host of other possibilities for buyers and sellers to get around price restrictions. I have only scratched the surface, but it is a surface worth scratching.

*If more consumers show up than suppliers, the price will be bid up. If there are fewer consumers than suppliers, the price will fall. The only stable price is when quantity supplied equals quantity demanded.

** In general, you could take "line" to be figuratively. Consumers need not literally wait in line. They could spend time filling out forms and making phone calls, or they could literally pay someone else to deal with the hassle.

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