With rising rates of inflation, price controls have been floated as a possible solution. I guess the idea is that if prices are rising, you should just make it illegal to raise prices and the problem will go away. Seems pretty straightforward. We should consider repealing the laws of supply and demand while we are at it, I guess.

The problem with using price controls to fight inflation is that they do not work. A lot of countries try this and it doesn’t help. In fact, it tends to make things worse. To understand why, it might be useful to provide a price theoretic analysis of the problem. Thus, let’s think about what happens when governments institute a maximum legal price, or price ceiling, on a particular good.

To do so, let’s think about the fundamental nature of exchange. Consumers have a particular willingness to pay for a good. The Law of Demand says that the consumer’s marginal willingness to pay (what they are willing to pay for one more unit of the good) declines with the quantity of the good. In other words, I might be willing to pay $1 for my first piece of pizza, but I would only be willing to pay $0.25 for the fourth piece. We also know that a firm is not going to be willing to sell a good for a price that is lower than its marginal cost. Furthermore, we know that if production is subject to diminishing marginal returns, the marginal cost of producing another unit of the good within the same period of time is increasing in the quantity produced.

If none of that makes sense, let’s think about a simple numerical example. Suppose that there is some good. The marginal willingness to pay (WTP) of buyers for a particular quantity and the marginal cost (MC) of producing the good are listed in the table below for each quantity.

We can think about how this good is allocated in terms of gains from trade. If the firms only produce 1 unit of the good, it costs them $3. The firm would like to charge the highest price possible, but they won’t accept a price below $3. Consumers would like to pay the lowest price possible, but there is someone willing to pay as much as $10 for that one unit of the good. The maximum price that consumers are willing to pay is much greater than the minimum price the firm is willing to charge. This means that there are possible gains from trade. This is true any time that the marginal willingness to pay is greater than the marginal cost. There is room for negotiation.

From the firm’s perspective, they would prefer not only to set their price, but also to charge different prices to different people. Based on the table, the firm would like to charge $10 for the first unit of the good produced, $9 for the second unit produced, $8 for the third unit produced, etc. At these prices, the consumer is indifferent between using the money for something else and getting the good. Thus, the consumer is no worse off than they were before. Meanwhile, the firm captures all of the gains from trade (the difference between the willingness to pay and marginal cost).

Of course, charging different prices to different people is difficult. The firm doesn’t necessarily know what people are willing to pay. Furthermore, if there is competition, these competitors might come in and undercut their prices. Thus, for the remainder of this post, I will assume that the firm (or firms) use uniform pricing (they charge the same price to every buyer).

Under uniform pricing, the equilibrium quantity is 4 units of the good. Why? The easiest way to answer this question is to consider alternatives. The marginal willingness to pay is greater than the marginal cost for all quantities up to 4 units. Thus, if the price is set at say $6.50, every unit of the good that is traded up to a quantity of 4 generates gains from trade. Each party is better off with the trade than without it. Buyers are paying less than what they are willing to pay (generating consumer surplus) and sellers are receiving more than it costs to produce (generating producer surplus). However, the fifth unit of production yields no possible gains from trade. The most consumers are willing to pay is $5 and the lowest price that sellers are willing to accept is $7. Thus, the trading stops at four units.

This is just basic supply and demand. Prices adjust until the gains from trade are exhausted.

Now, suppose that the government comes along and declares any price above $4 to be illegal. At $4, the firm is only willing to produce 2 units of the good instead of 4. However, consumers are willing to buy 6 units of the good for $4. There is now a shortage of the good. Consumers want 6 units, but there are only 2 units being produced. Ordinarily, prices increase when there is excess demand. In this case, increasing the price above $4 is illegal. The shortage will therefore persist.

Textbooks often stop the story here, but I’m not sure why. There is plenty to be gained by taking things further.

Let’s take stock of what is going on when the price is $4. Consumers want 6 units of the good and firms are only going to produce 2 units. This means that some consumers are not going to get the good at all, or at least won’t get as much as they want. How is society to determine who gets the 2 units of the good? One thing that we know for certain is that competition for the good isn’t going to stop just because the price cannot adjust.

Note that if only 2 units of the good are produced, the marginal willingness to pay for that second unit is $9. While buyers are legally prohibited from paying more than $4 for the good, there is nothing to stop a consumer from paying $4 to the firm for the good and an addition $5 on other resources to make sure to get the good instead of other consumers.

Suppose for example that all of the consumers of this good earn $15 per hour at their job. This suggests that the marginal buyer would be willing miss 20 minutes of work to wait in line to buy the good for $4. In this case, the consumer is paying $9 for the good ($5 of his or her time and $4 in terms of money, or more accurately, the next best use of that $4).

This is the first lesson to really understand about price ceilings. Normally, competition for resources occurs with the context of markets. Prices adjust to market conditions (supply and demand). The people who get the good are the people who have a willingness to pay that is greater than or equal to the price. When the price is not legally allowed to adjust above a particular point, the competition for the good doesn’t stop. Competition just takes another form.

But think about the consumer waiting in line. Who benefits? The marginal consumer is paying more than $6.50, despite the fact that the price is legally restricted to $4. Meanwhile, the firm does not capture any of the consumer’s willingness to pay beyond $4. Time spent waiting in line outside the store does not convey any benefit to the store.

Firms want to capture some of this surplus (the difference between the willingness to pay of $9 and the price of $4). One way to do this might be to take payments from the customer under the table or to sell some of the good on the black market. Of course, this type of behavior is a violation of the law.

Other, legal alternatives might take place as well. Firms, faced with a smaller producer surplus might try to increase their surplus in other ways. At the price of $4, the firm is producing 2 units at a total cost of $7. Thus, the producer’s gain is only $1. The firm could reduce its costs by reducing the quality of the good. Suppose that by reducing the quality of the good, the firm saves $1 per unit of production. Now, the firm is willing to produce 3 units of the good at $4. But this isn’t the end of the story.

A lower quality good will tend to reduce the willingness to pay of the consumers. To make thing simple, suppose that the willingness to pay falls by $1 for every unit of the good. This means that the consumer is now willing to purchase only 5 units of the good instead of 6.

Let’s think about the implication of this change. First, the shortage is smaller. The firm increased their production by one unit. Consumers reduced their demand by one unit. Now, instead of the shortage being 4 goods, the shortage is 2 goods.

The firm sells 3 units of the good for $4 each. This generates $12 in revenue. It costs the firm $9 to produce these 3 units. The benefit to the firm from producing is $3. This is greater than the $1 benefit with the higher-quality good.

For the consumer, it is possible that they benefit, but this depends on how much of this benefit is dissipated through non-price competition like waiting in line. The maximum possible surplus for this low-quality good is $12, which occurs if and only if there’s no non-price competition. However, the marginal buyer is willing to pay $7 dollars for this new lower-quality good. Non-price competition for the good will tend to drive the total cost of the good to each consumer to $7. This implies a surplus of only $3.

Now, let’s compare this with our initial equilibrium. Under the equilibrium price of $6.50, the total expenditure is $26. Consumers are willing to pay $34 for 4 units of the good. This is a consumer surplus of $8. The cost of producing these 4 units is $18. This means that the firm gets a benefit of $8. The total surplus from trade is $16.

So, let’s compare the different situations here. With the allocation determined by prices in the market, the benefit to society from trade is $16. With the price ceiling, consumers get a lower-quality good and there is a shortage. Since non-price competition will tend to increase the total cost of obtaining the good to $7, the total surplus from trade is $6. The net cost to society of the shortage and the lower-quality goods is $10, or over 60% of the original surplus.

This is the problem with price ceilings. Resources have to be allocated somehow. Eliminating the price mechanism just means that some other mechanism has to emerge to allocate resources. This could be black market activity or under-the-table payments. This could be through forms of non-price competition and reductions in the quality of the good. While price ceilings might reduce monetary expenditures of the average consumer, they tend to raise the combined total of monetary and non-monetary costs due to competition for the good that results from the shortage.

A price ceiling gives one the impression that something has been done to solve the problem of high prices. Observed prices are lower. Monetary expenditures on that good are lower. However, the increased cost of non-market competition and reductions in the quality of the good are also part of the cost. As the example I have given illustrates, these costs tend to outweigh any savings in monetary costs. The solution to “high” prices isn’t lower quality goods, long lines, and empty shelves. But that is what price ceilings tend to deliver.

Economic Forces

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