Sometimes, lawmakers determine that the market price is “too high” for consumers to pay, so they use their power to impose a ceiling on price below the market equilibrium price. Some examples of ceilings include rent controls (limits on increases in the rent paid for apartments), limits on the prices of medicines, and laws against “price gouging” after a hurricane (i.e., charging opportunistically high prices for goods such as bottled water or plywood). Certainly, price limits benefit anyone who had been paying the old higher price and can still buy all they want at the lower ceiling price. However, the story is more complicated than that. Exhibit 16 shows a market in which a ceiling price, P_c, has been imposed below equilibrium. Let’s examine the full impact of such a law.

Exhibit 16. A Price Ceiling

Prior to imposition of the ceiling price, equilibrium occurs at (P*, Q*), and total surplus equals the area given by a + b + c + d + e. It consists of consumer surplus given by a + b, and producer surplus given by c + d + e. When the ceiling is imposed, two things happen: Buyers would like to purchase more at the lower price, but sellers are willing now to sell less. Regardless of how much buyers would like to purchase, though, only Q′ would be offered for sale. Clearly, the total quantity that actually gets traded has fallen, and this has some serious consequences. For one thing, any buyer who is still able to buy the Q′ quantity has clearly been given a benefit. They used to pay P* and now pay only P_c per unit. Those buyers gain consumer surplus equal to rectangle c, which used to be part of seller surplus. Rectangle c is surplus that has been transferred from sellers to buyers, but it still exists as part of total surplus. Disturbingly, though, there is a loss of consumer surplus equal to triangle b and a loss of producer surplus equal to triangle d. Those measures of surplus simply no longer exist at the lower quantity. Clearly, surplus cannot be enjoyed on units that are neither produced nor consumed, so that loss of surplus is called a deadweight loss because it is surplus that is lost by one or the other group but not transferred to anyone. Thus, after the imposition of a price ceiling at P_c, consumer surplus is given by a + c, producer surplus by e, and the deadweight loss is b + d.8

Another example of price interference is a price floor, in which lawmakers make it illegal to buy or sell a good or service below a certain price, which is above equilibrium. Again, some sellers who are still able to sell at the now higher floor price benefit from the law, but that’s not the whole story. Exhibit 17 shows such a floor price, imposed at P_f above free market equilibrium.

Exhibit 17. A Price Floor

At free market equilibrium quantity Q*, total surplus is equal to a + b + c + d + e, consisting of consumer surplus equal to area a + b + c, and producer surplus equal to area e + d. When the floor is imposed, sellers would like to sell more, but buyers would choose to purchase less. Regardless of how much producers want to sell, however, only Q′ will be purchased at the new higher floor price. Those sellers who can still sell at the higher price benefit at the expense of the buyers: There is a transfer of surplus from buyers to sellers equal to rectangle b. Regrettably, however, that’s not all. Buyers also lose consumer surplus equal to triangle c, and sellers lose producer surplus equal to triangle d.9Once again, no one can benefit from units that are neither produced nor consumed, so there is a deadweight loss equal to triangle c plus triangle d. As a result of the floor, the buyer’s surplus is reduced to triangle a.

A good example of a price floor is the imposition of a legal minimum wage in the United States, the United Kingdom, and many other countries. Although controversy remains among some economists on the empirical effects of the minimum wage, most economists continue to believe that a minimum wage can reduce employment. Although some workers will benefit, because they continue to work at the higher wage, others will be harmed because they will no longer be working at the increased wage rate.

EXAMPLE 11

Calculating the Amount of Deadweight Loss from a Price Floor

A market has demand function given by the equation Q^d = 180 – 2P, and supply function given by the equation Q^s = –15 + P. Calculate the amount of deadweight loss that would result from a price floor imposed at a level of 72.

Solution:

First, solve for equilibrium price of 65 and quantity 50. Then, invert the demand function to find P = 90 – 0.5Q, and the supply function to find P = 15 + Q. Use these functions to draw the demand and supply curves:

Insert the floor price of 72 into the demand function to find that only 36 would be demanded at that price. Insert 36 into the supply function to find the price of 51 that corresponds to a quantity of 36. Because the price floor would reduce quantity from its equilibrium value of 50 to the new value of 36, the deadweight loss would occur because those 14 units are not now being produced and consumed under the price floor. So deadweight loss equals the area of the shaded triangle: 1/2 Base × Height = (1/2)(72 − 51)(50 – 36) = 147.

Still other policies can interfere with the ability of prices to allocate society’s resources. Governments do have legitimate functions to perform in society, and they need to have revenue to finance them. So they often raise revenue by imposing taxes on various goods or activities. One such policy is a per-unit tax, such as an excise tax. By law, this tax could be imposed either on buyers or on sellers, but we shall see that it really doesn’t matter at all who legally must pay the tax, the result is the same: more deadweight loss. Exhibit 18 depicts such a tax imposed in this case on buyers. Here, the law simply says that whenever a buyer purchases a unit of some good, he or she must pay a tax of some amount tper unit. Recall that the demand curve is the highest price willingly paid for each quantity. Because buyers probably do not really care who receives the money, government or the seller, their gross willingness to pay is still the same. Because they must pay t dollars to the government, however, their net demand curve would shift vertically downward by t per unit. Exhibit 18 shows the result of such a shift.

Exhibit 18. A Per-Unit Tax on Buyers

Originally, the pre-tax equilibrium is where D and S intersect at (P*, Q*). Consumer surplus is given by triangle a plus rectangle b plus triangle c, and producer surplus consists of triangle f plus rectangle d plus triangle e. When the tax is imposed, the demand curve shifts vertically downward by the tax per unit, t. This shift results in a new equilibrium at the intersection of S and D′. That new equilibrium price is received by sellers (P_rec’d). However, buyers now must pay an additional t per unit to government, resulting in a total price paid (P_paid) that is higher than before. Sellers receive a lower price and buyers pay a higher price than pretax, so both suffer a burden as a result of this tax, even though it was legally imposed only on buyers. Buyers now have consumer surplus that has been reduced by rectangle b plus triangle c; thus, post-tax consumer surplus is (a + b + c) − (b + c) = a. Sellers now have producer surplus that has been reduced by rectangle d plus triangle e; thus post-tax producer surplus is (f + d + e) − (d + e) = f. Government receives tax revenue of t per unit multiplied by Q′ units. Its total revenue is rectangle b plus rectangle d. Note that the total loss to buyers and sellers (b + c + d + e) is greater than the revenue transferred to government (b + d), so that the tax resulted in a deadweight loss equal to triangle c plus triangle e as (b + c + d + e) − (b + d) = c + e.

How would things change if the tax had legally been imposed on sellers instead of buyers? To see the answer, note that the supply curve is the lowest price willingly accepted by sellers, which is their marginal cost. If they now must pay an additional t dollars per unit to government, their lowest acceptable price for each unit is now higher. We show this by shifting the supply curve vertically upward by t dollars per unit, as shown in Exhibit 19.

Exhibit 19. A Per-Unit Tax on Sellers

The new equilibrium occurs at the intersection of S′ and D, resulting in the new equilibrium price paid by buyers, P_paid. Sellers are paid this price but must remit t dollars per unit to the government, resulting in an after-tax price received (P_rec’d) that is lower than before the tax. In terms of overall result, absolutely nothing is different from the case in which buyers had the legal responsibility to pay the tax. Tax revenue to the government is the same, buyers’ and sellers’ reduction in surplus is identical to the previous case, and the deadweight loss is the same as well.

Notice that the share of the total burden of the tax need not be equal for buyers and sellers. In our example, sellers experienced a greater burden than buyers did, regardless of who had the legal responsibility to pay the tax. The relative burden from a tax falls disproportionately on the group (buyers or sellers) that has the steeper curve. In our example, the demand curve is flatter than the supply curve (just slightly so), so buyers bore proportionately less of the burden. Just the reverse would be true if the demand curve had been steeper than the supply curve.

All of the policies we have examined involve government interfering with free markets. Other examples include imposing tariffs on imported goods, setting quotas on imports, or banning the trade of goods. Additionally, governments often impose regulations on the production or consumption of goods to limit or correct the negative effects on third parties that cannot be captured in free market prices. Even the most ardent of free market enthusiasts recognize the justification of some government intervention in the case of public goods, such as for national defense, or where prices do not reflect true marginal social value or cost, as in externalities such as pollution. Social considerations can trump pure economic efficiency, as in the case of child labor laws or human trafficking. What does come from the analysis of markets, however, is the recognition that when social marginal benefits are truly reflected in market demand curves and social marginal costs are truly reflected in supply curves, total surplus is maximized when markets are allowed to operate freely. Moreover, when society does choose to impose legal restrictions, market analysis of the kind we have just examined provides society with a means of at least assessing the deadweight losses that such policies extract from total surplus. In that way, policy makers can perform logical, rigorous cost benefit assessments of their proposed policies to inform their decisions.

EXAMPLE 12

Calculating the Effects of a Per-Unit Tax on Sellers

A market has a demand function given by the equation Q^d = 180 – 2P, and a supply function given by the equation Q^s = −15 + P, where price is measured in euros per unit. A tax of €2 per unit is imposed on sellers in this market.

1. Calculate the effect on the price paid by buyers and the price received by sellers.

2. Demonstrate that the effect would be unchanged if the tax had been imposed on buyers instead of sellers.

Solution to 1:

Determine the pre-tax equilibrium price and quantity by equating supply and demand: 180 – 2P = −15 + P. Therefore P*= €65 before tax. If the tax is imposed on sellers, the supply curve will shift upward by €2. So, to begin, we need to invert the supply function and the demand function: P = 15 + Q^s and P = 90 – 0.5Q^d. Now, impose the tax on sellers by increasing the value of P by €2 at each quantity. This step simply means increasing the price intercept by €2. Because sellers must pay €2 tax per unit, the lowest price they are willing to accept for each quantity rises by that amount: P′ = 17 + Q^s, where “P prime” indicates the new function after imposition of the tax. Because the tax was not imposed on buyers, the inverse demand function remains as it was. Solve for the new equilibrium price and quantity: 90 – 0.5Q = 17 + Q, so new after-tax Q = 48.667. By inserting that quantity into the new inverse demand function, we find that P_paid = €65.667. This amount is paid by buyers to sellers, but because sellers are responsible for paying the €2 tax, they receive only €65.667 – €2 = €63.667, after tax. So we find that the tax on sellers has increased the price to buyers by €0.667 while reducing the price received by sellers by €1.33. Out of the €2 tax, buyers bear one-third of the burden and sellers bear two-thirds of the burden. This result is because the demand curve is half as steep as the supply curve. The group with the steepest, less elastic, curve bears the greater burden of a tax, regardless of on whom the legal incidence of the tax is imposed.

Solution to 2:

Instead of adding €2 to the price intercept of supply curve, we now subtract €2 from the price intercept of the demand curve. This step is because buyers’ willingness to pay sellers has been reduced by the €2 they must pay in tax per unit. Buyers really don’t care who receives their money, they are interested only in the greatest amount they are willing to pay for each quantity. So the new inverse demand function is: P″ = 88 – 0.5Q. Using this new inverse demand, we now solve for equilibrium: 88 – 0.5Q = 15 + Q. (Because buyers must pay the tax, we leave the old supply curve unchanged.) The new equilibrium quantity is therefore Q = 48.667, which is exactly as it was when sellers had the obligation to pay the tax. Inserting that number into the old supply function gives us the new equilibrium price of €63.667, which is what buyers must pay sellers. Recall, however, that now buyers must pay €2 in tax per unit, so the price buyers pay after tax is €63.667 + €2 = €65.667. So nothing changes when we impose the statutory obligation on buyers instead of sellers. They still share the ultimate burden of the tax in exactly the same proportion as when sellers had to send the €2 to the taxing authority.

We have seen that government interferences, such as price ceilings, price floors, and taxes, result in imbalances between demand and supply. In general, anything else that intervenes in the process of buyers and sellers finding the equilibrium price can cause imbalances as well. In the simple model of demand and supply, it is assumed that buyers and sellers can interact without cost. Often, however, there can be costs associated with finding a buyer’s or a seller’s counterpart. There could be a buyer who is willing to pay a price higher than some seller’s lowest acceptable price, but if the two cannot find one another, there will be no transaction, resulting in a deadweight loss. The costs of matching buyers with sellers are generally referred to as search costs, and they arise because of frictions inherent in the matching process. When these costs are significant, an opportunity may arise for a third party to provide a valuable service by reducing those costs. This role is played by brokers. Brokers do not actually become owners of a good or service that is being bought, but they serve the role of locating buyers for sellers or sellers for buyers. (Dealers, however, actually take possession of the item in anticipation of selling it to a future buyer.) To the extent that brokers serve to reduce search costs, they provide value in the transaction, and for that value they are able to charge a brokerage fee. Although the brokerage fee could certainly be viewed as a transactions cost, it is really a price charged for the service of reducing search costs. In effect, any impediment in the dissemination of information about buyers’ and sellers’ willingness to exchange goods can cause an imbalance in demand and supply. So anything that improves that information flow can add value. In that sense, advertising can add value to the extent that it informs potential buyers of the availability of goods and services.