The welfare costs of market restrictions.

• Author: Colander, David
• Position: Targeted Teaching

1. Introduction

   Many of the central ideas in economics are conveyed to students in graphs that provide a visual picture of economists' insights. One of the most well known of these pictures is the Harberger triangle, which is used to illustrate the deadweight loss from market restrictions such as monopoly power, quantity restrictions, and price ceilings and floors. Although it is generally known that the Harberger triangle misses important elements of these restrictions' inefficiency costs (see, for instance, Friedman and Stigler 1946; Glaeser and Luttmer 2003), this insight has not been integrated into economic textbooks. This is problematic because these overlooked inefficiency costs are theoretically important and in many cases are larger than the inefficiencies conveyed by the Harberger triangle.

   In this short article we show why the Harberger triangle significantly understates the efficiency costs of any restriction that does not inherently direct (or provide incentives for) agents to efficiently deal with it. We then provide a simple graphical method of capturing the additional deadweight loss in the form of a second triangle that can be seen as a measure of this additional deadweight loss. This graphical method should make it easier to integrate these insights into the textbooks and thereby help remedy the deficiencies of presentations based only on the Harberger triangle, (1) We focus on the example of price controls but discuss how the analysis caries over to other restrictions such as quotas. We argue that, together, the second triangle and the Harberger triangle provide students with a much better picture of the costs of these market restrictions, a better sense of the relative magnitudes of the two types of deadweight loss, and a better segue into a discussion of the costs of market restrictions.

   The problem with using the Harberger triangle--the area between the demand and supply curve and between the pre- and post-control quantities--as a measure of the inefficiency resulting from, for example, a price floor is that it captures only one type of restriction-induced inefficiency: the inefficiency that arises because the market restriction prevents some mutually beneficial trades from taking place. Such inefficiencies might be called "top-down" inefficiencies because they would exist even if each side of the market consisted of a single representative agent reacting optimally to restrictions and dealing with the restriction in as efficient a manner as possible. When there are many agents affected by a price control, representative agent assumptions are inappropriate, and such controls will impose additional "bottom-up" costs on society. This bottom-up inefficiency occurs because, in addition to preventing mutual beneficial trades, price controls remove incentives for the right trades to take place. They therefore impose wrong-trade, bottom-up, social costs: They lead some of the wrong agents to do the supplying or demanding. A price floor, for example, both causes an inefficiently low quantity of the good to be supplied and fails to incentivize the lowest-cost potential suppliers to do that supplying. For example, faced with a minimum wage restriction, jobs will have to be rationed, but McDonald's and other minimum wage employers will have no incentive to ration those jobs in the most efficient manner--for example, to those who benefit the most from receiving them.

   Similarly, a price ceiling can be expected to drive the highest-cost suppliers out of the market, but it fails to provide incentives to efficiently allocate the supply-limited quantity to the highest marginal benefit demanders. It (along with assorted shady political dealings) can therefore lead to Congressman Charles Rangel's (D-NY) renting and maintaining four rent-stabilized New York apartments at approximately half of their fair market value, even when other potential tenants might value those apartments significantly more highly (Kocieniewski 2008).

   The problem could be partially resolved if the Harberger triangle was accompanied by a discussion of bottom-up inefficiency, but, because pictures tend to guide the discussions, that often does not happen. (2) Because bottom-up costs are not captured in the standard textbook graph, often the full costs of price controls are not conveyed to students. The contribution of this article is to motivate and advocate for a simple way of visually capturing these additional costs and thereby to provide a picture that will be more conducive to a broader discussion and conceptual understanding of the welfare costs of price controls and other market restrictions. We illustrate our suggested picture in the context of imposing a minimum wage in the labor market for fast food workers.

   [FIGURE 1 OMITTED]

2. Illustrating the Two Types of Inefficiency: The Effective Marginal Cost Curve

   Figure 1 illustrates our suggested method with an example of a market for jobs at fast food establishments such as McDonald's in the presence of a minimum wage [P.sub.min].

   In Figure 1, the Harberger Triangle (EFC) captures the top-down inefficiency caused by the minimum wage. There are [Q.sup.*] mutually beneficial trades to be made in this market, because the [Q.sup.*] highest-benefit employers have higher marginal benefits than the [Q.sup.*] lowest opportunity cost workers. The minimum wage prevents some of these trades from taking place by reducing the quantity demanded to [Q.sup.D]([P.sub.min]). If the market could somehow ensure that this reduction occurred by removing only the highest opportunity cost workers from the market, the type of trade being eliminated would be trades such as the one between the worker just to the right of point F and the employer just to the right of point E; summing up the lost benefits from these eliminated trades would then yield the Harberger triangle.

   However, because the market is not a top-down process, it typically will not lead to only the highest opportunity cost workers being rationed out of the market. This means that there will be additional costs resulting from the wrong workers receiving the jobs. Our goal is to depict these additional costs. Toward doing that, we first note that this minimum wage leads to an excess supply [[Q.sup.S]([P.sub.min]) - [Q.sup.D]([P.sub.min])] of workers. Fast food establishments will thus get [Q.sup.S]([P.sub.min])/[Q.sup.D]([P.sub.min]) applications for each of their job postings.

   If workers differ only in their reservation wages--so that employers are otherwise indifferent as to whom they hire--then it is reasonable to assume that jobs will be randomly allocated to willing workers. The probability that any willing worker will receive a job therefore will be [Q.sup.D]([P.sub.min])/[Q.sup.S]([P.sub.min]). This means that [Q.sup.D]([P.sub.min])/[Q.sup.s]([P.sub.min]) measures the expected fraction of any subset of willing workers who will actually receive jobs. In particular, because [Q.sup.S](P) of the willing workers have reservation wages below any price P, {[[Q.sup.D]([P.sub.min])]/[[Q.sup.S]([P.sub.min])]} x [Q.sup.S](P) of hired workers will have reservation wages below P, at least in expectation.

   This reasoning motivates the curve labeled "Effective Marginal Cost" (EMC) in Figure 1. The EMC curve is calculated by taking the supply curve and compressing it horizontally by the probability-of-receiving-a-job factor [Q.sup.D]([P.sub.min])/[Q.sup.S]([P.sub.min]). It therefore captures the schedule of the expected number of hired workers with reservation wages below any given wage P.

   Inverting this reasoning allows one to think of the supply and EMC curves in terms of marginal social costs--which is why we give it the "effective marginal cost" moniker. Imagine taking the [Q.sup.D]([P.sub.min]) workers actually hired and arranging them in order of increasing reservation wages. The height of the EMC curve will then give the expected...