## I I I

1,500,000

ness to pay, that is, in value in use (the value in exchange is zero if the toll is zero).

3. If the bridge costs less than the money value of the satisfaction it brings (that is, willingness to pay), it should be built. Otherwise, as when it costs a dollar more than \$10,000,000, it should not. A society that indulged in such projects would fill in the Great Lakes for ski resorts or level the Rockies for farmland.

ing those who use the bridge pay for it. The purpose is efficiency. We want to induce people to use the bridge in a way that will maximize the value in use gotten from it and from the alternative uses of resources. For this purpose the relevant fact is that Molly McClelland as the extra crosser causes no sacrificed opportunities elsewhere. So McClelland should cross free. If her crossing wore off 8 cents worth of paint and bridge, it would be desirable to make her pay this cost in an 8-cent toll, to induce her to forgo the crossing unless it were worth in use at least the 8 cents of sacrificed opportunities it cost. But if not, then the past cost of the Golden Gate Bridge (incurred, say, to build it) is irrelevant to

The method of value-in-use, then, is a guide to whether Mars landings, aqueducts, radar systems, and the like should occur at all. Of course, in many cases it would require the aid of a wizard to know the demand curve to evaluate the projects. But the method gives general guidance to how they should be paid for.

Crossings Figure 10.3

Price The Best Toll on a Bridge Is Zero

marginal cost—that is, it is irrelevant to the additional by the shaded triangle of willingness to pay (see Figure cost of one more crossing. By the assumption of the 10.3). So, false; the average cost of constructing the question the marginal cost is zero, and so should be bridge is beside the point, the toll. The toll of 50 cents reduces society's happiness

With a 50-cent toll the consumers get area A in surplus (the excess of value in use, A + B, over value in exchange, B). The B area is the part of willingness to pay extracted from crossers and given to whoever owns the bridge. From the social point of view the crossings that still take place with a 50-cent toll cause happiness in the value of A + B. The distribution of income is changed by the toll, shifting B dollars of purchasing power from crossers to owners. The critical point is that the shaded triangle is sheer waste. Crossings not worth at least 50 cents do not take place, even though these crossings have some value and no opportunity cost. "The distribution of wealth among members of the community is affected by the mode of payment adopted for the bridge, but not the total wealth, except that it is diminished by tolls. . . . This is such plain common sense that toll bridges have now largely disappeared from civilized communities."3

3 Harold Hotelling, "The General Welfare in Relation to Problems of Taxation and of Railway and Utility Rates," first published in 1938, reprinted in Musgrave and Shoup, eds., p. 158. He added: "But New York City's bridge [sic] and tunnels across the Hudson are still operated on a toll basis, because of the pressure of real estate interests anxious to shift the tax burden to wayfarers, and the possibility of collecting considerable sums from persons who do not vote in the city." Today 6 out of 19 roads off the island of Manhattan charge tolls, and all the roads to New Jersey do. Yet New York does not fall below San Francisco in civilization; all four of the bridges across San Francisco Bay charge tolls. As we shall see in the next chapter, however, assigning degrees of civilization is not quite so easy when it is realized that the taxation to pay for the bridges (if tolls are to be zero) itself creates triangles of net social loss under the demand curves for the taxed goods. It is a choice between two evils.

Producers' Surplus Is Analogous, the Producers' Gain from Trade

Consumers' surplus, then, is the consumers' net gain from trade, namely, a triangle equal to their gross gain (the trapezoid of value in use) minus their cost (the rectangle of value in exchange). Consumers imply producers. A producers' surplus, therefore, ought to exist, similar to consumers' surplus. In fact it does, and like consumers' surplus is the producers' net gain from trade. Consider, for example, American exports of wheat.

Q: When the crop is poor and wheat is expensive in America, it seems reasonable to restrict American exports. After all, our own citizens should be fed first, shouldn't they?

A: Our own citizens will be best off when the trade in grain is free. The supply curve of wheat to the rest of the world slopes upward in Figure 10.4 because more wheat is producible only at the expense of ever more costly resources in shipping, growing, and the like, and because more wheat from a given production is suppli-able to the rest of the world only at the expense of ever more valuable uses in consumption at home. That is, the supply curve is the marginal (opportunity) cost.

The shaded area, C, under the marginal cost is therefore the whole cost of supplying the amount marked as the Equilibrium Quantity, for it is the summation of all the successive increments to cost. The rectangle C + S is the revenue from selling the Equilibrium Quantity to the rest of the world at the World Price. The unshaded triangular area, S, then, is the surplus of producers' revenues over costs. In a word, it is America's profit. In another, it is America's economic rent. In still another, it is America's producers' surplus. It reaches a maximum when trade is free and the Equilibrium Quantity is sold. At a Lower Quantity the value of wheat is lower in America than in the rest of the world. Americans could do better in terms of their own valuation

Figure 10.4

Wheat Price in Terms of All Other Goods

A quota on wheat exports prevents Americans from trading wheat for goods that Americans value more than wheat. The quota reduces producers' surplus.

Supply = Marginal Cost

World Price (demand)

Lower Quantity

Equilibrium Quantity

Wheat Sold Relative to Rest of World (quantity)

of wheat and all other goods by selling more wheat at the high World Price. The amount of all other goods they get more than outweigh in value to them the wheat they give to the rest of the world. That is, false.

The Two Surpluses Together Show That Free Trade Is Good

### Price of Motorcycles

A generalization of the argument makes the familiar point that free trade is best, and even shows how it might not be. Should there be, for instance, a free market for motorcycles in Columbus, Ohio? Well, suppose that competition would drive the market to Equilibrium in Figure 10.5. The sum of consumers' and producers' surplus is a measure of the entire gain from trade. The entire gain is the gain of student motorcyclists at Ohio State University plus the gain of Columbus motorcycle sellers. The position marked Equilibrium maximizes it. This fact is obvious for quantities Less Than Equilibrium, because the big, shaded triangular area (bounded by the three points, m, a, x) is chopped down to a smaller trapezoidal area (m, i, n, x).

It requires a little proof for quantities larger than Equilibrium. Consider Figure 10.6. Suppose, just to be definite, that the market deal takes place at a point on the demand curve (not along the supply curve or along neither). What needs to be proven is that, at More Than Equilibrium compared with Equilibrium, the gain by student motorcyclists of a large quantity and low price is more than offset by the loss by motorcycle sellers. The rise in Consumers' surplus in the move from Equilibrium to More Than Equilibrium is the horizontal trapezoid A + B + C. Is the fall in producers' surplus larger, as it should be if More Than Equilibrium is on balance bad for society? Yes. The area A + B is the fall in revenue to producers on the old quantity of motorcycles when they are sold at the new, low price. The Equilibrium quantity still costs what it did before. But its revenue is less by A + B since the market price is lower. The More Quantity out to More Than Equilibrium costs producers C + L + R, but gets them only R in revenue. So on this account, they lose C + L, to add to the loss of A + B. The whole fall in producers' surplus is A + B + C + L, which is L more than the rise in consumers' surplus. This would be true of any point

Figure 10.5

Free Markets Maximize the Sum of

Consumers' and Producers' Surplus

The point Equilibrium, which will be reached by the free market, maximizes the sum of consumers' and producers' surplus. The quantity Less Than Equilibrium would only be observed as a result of interference with the market. The social loss at Less Than Equilibrium, relative to the optimum, is the triangle ina.

Price of Motorcycles

The point Equilibrium, which will be reached by the free market, maximizes the sum of consumers' and producers' surplus. The quantity Less Than Equilibrium would only be observed as a result of interference with the market. The social loss at Less Than Equilibrium, relative to the optimum, is the triangle ina.

Motorcycles (quantity)

Motorcycles (quantity)

Price of Motorcycles

Supply

Equilibrium

Equilibrium

Supply

Equilibrium

More Than Equilibrium

Equilibrium

Figure 10.6

Too Many Motorcycles Hurts Producers More Than It Helps Consumers

If more than Equilibrium motorcycles are exchanged, the cost of supplying More Quantity, as shown by the area under the supply curve, exceeds the benefit to buyers of More Quantity, as shown by the area under the demand curve. A triangle L of social loss is the result.

More Than Equilibrium

Figure 10.6

Too Many Motorcycles Hurts Producers More Than It Helps Consumers

If more than Equilibrium motorcycles are exchanged, the cost of supplying More Quantity, as shown by the area under the supply curve, exceeds the benefit to buyers of More Quantity, as shown by the area under the demand curve. A triangle L of social loss is the result.

Motorcycles (quantity)

out of Equilibrium. So only at Equilibrium is the sum of consumers' and producers surplus maximized, which was to be demonstrated. Equilibrium, in other words, is efficient.

Notice that, in the way of efficiency, Equilibrium is not best for either consumers by themselves or producers by themselves. Consumers, for example, could do better if they could compel producers to give away the motorcycles, and short of such robbery they could do better, even if they had to stay on the producers' supply curve, by restricting their own purchases a little.4 Equilibrium is best for "society," that is, for consumers and producers together on balance.

The Feasible Area of There is another way of exhibiting consumers' surplus and its uses.5 The land-Exchange Is the lords of New Orleans, say, have a supply curve of rental housing. It is as usual Triangle of Surplus upward sloping, because more houses are expensive to build and because the landlords themselves can be enticed to live elsewhere at a high enough price. Look at Figure 10.7. But the supply curve is a schedule of the minimum acceptable price for any quantity, such as Small. Landlords would be pleased to get more than the price Barely Acceptable to Suppliers for the quantity Small. So it is with other quantities along the supply curve. The whole vertically shaded region above the supply curve, in other words, is the region of deals acceptable to landlords. Tenants likewise would be pleased to get the quantity Small at any price less than the Price Barely Acceptable to Demanders, and the whole horizontally shaded region below the demand curve in the diagram is the region of deals acceptable to tenants. Putting the two areas together yields the cross-hatched area of possible deals compared with no deals (zero housing rented) that make both landlords and tenants better off. The crosshatched area, in other

4 As will be shown in Chapter 17 on monopoly and in a question at the end of this section.

5 The idea is Milton Friedman's in his Price Theory (Chicago: Aldine, 1976), Chapter 2.

words, is the area of mutually advantageous deals, and these are exhausted at the corner marked Equilibrium. At Equilibrium the mutually advantageous deals have been exhausted. To have larger or smaller quantities rented by landlords to tenants would make one or both worse off; at Small, for instance, the deals have not been exhausted, and more renting would make both better off.

Interference in The connection between consumers' surplus and this way of looking at curves Free Trade of supply and demand is that the areas of mutual benefit are the same money measures as consumers' surplus. The triangle des in Figure 10.7 is a money measure of the inefficiency of staying at Small.

Q: Suppose that the market for rental housing in New Orleans is in Equilibrium initially and that at the Old Price the government imposes rent control (that is, making it illegal to offer or accept a rental above the Old Price). Now suppose that the demand curve of tenants rises, perhaps because the population of New Orleans or the money income of tenants has risen. Describe the social loss from the rent control, assuming that it is enforced.

government forbids rentals above the Old Price, a landlord has no incentive to surrender more housing. Tenants are unable to express in money offers to the landlords their new and larger willingness to pay for housing. The shaded area is the money measure of inefficiency. It is the loss to everyone—tenants as well as landlords—from making new deals impossible. Or, to put it another way, the shaded area is the sum of consumers' and producers' surplus forgone.

A: The old demand curve, which determined the Old Price, is the dashed line in Figure 10.8. Because the

Housing Price

Barely Acceptable to Demanders

Barely Acceptable to Suppliers

Barely Acceptable to Demanders

Barely Acceptable to Suppliers

Figure 10.7

Competitive Equilibrium Exhausts the Opportunities for Mutually Advantageous Exchange

At Equilibrium the marginal landlord is willing to rent a house for exactly the amount that the marginal renter is willing to pay. A quantity smaller than Equilibrium will leave mutually beneficial deals unmade; a quantity larger than Equilibrium cannot be reached by purely voluntary actions of landlords and renters.

Small

Figure 10.7

Competitive Equilibrium Exhausts the Opportunities for Mutually Advantageous Exchange

At Equilibrium the marginal landlord is willing to rent a house for exactly the amount that the marginal renter is willing to pay. A quantity smaller than Equilibrium will leave mutually beneficial deals unmade; a quantity larger than Equilibrium cannot be reached by purely voluntary actions of landlords and renters.

Small

Rental Housing in New Orleans (quantity)

Figure 10.8

### Why Most Economists Disapprove of Rent Control

With a price ceiling of Old Price, suppliers will supply no more than New Housing and Old Quantity. If demand shifts to New Demand, society loses the value

Figure 10.8

### Why Most Economists Disapprove of Rent Control

With a price ceiling of Old Price, suppliers will supply no more than New Housing and Old Quantity. If demand shifts to New Demand, society loses the value

Old Quantity

Summary Consumers' surplus is the excess of value in use (accruing to the consumers) over value in exchange; likewise, producers' surplus is the excess of value in exchange (accruing to producers) over value in use elsewhere (as for example in use by the suppliers themselves). The expression "consumers' surplus" is sometimes used to stand for both surpluses. The two are the gains from trade to all the parties, that is, money values of the happiness gained over not trading. The sum of the two surpluses is the total social gain from trade. It is maximized when the quantity traded is that of supply equal to demand. The idea is unremarkable. What is remarkable is its wide applicability to social questions, from free trade in housing and grain to the desirability of building bridges.