Factor-Price Determination
by Supply and Demand

Paul Samuelson

[An excerpt from Ch. 27 of the text, Economics: An Introductory Analysis, published by McGraw-Hill (fourth edition), 1958. Note: several tables included in the original text are not reproduced below]

Up until now we have worked only with the demand curve for a factor, taking its market price as given to the demanders. But obviously it is all the firms together who determine the factor's market price that each small firm faces. Now we must see how the total demand curve of all -- for the factor, together with the total supply curve for the factor, will interact to determine the equilibrium price tending to rule in the market place.

Figure 2 shows the total demand curve for corn land, DD; it was arrived at by adding together each and every individual firm's demand curve.

Now it is one of the peculiarities of land that, unlike most things, its total supply is relatively fixed by nature and cannot be augmented in response to a higher price for it, and its total cannot be diminished in response to lower land rentals. (Of course, this is not strictly true. Land can sometimes be created by drainage, and the fertility of the existing land can be depleted by overcropping.)

Nonetheless, we can take the complete fixity of its supply as the characteristic feature of land. By tradition, we may confine our discussion to the "original and inexhaustible gift of nature" whose total supply is by definition completely inelastic. It was the price or return to such a factor that the classical economists of the last century called "rent." This differs from ordinary usage in which rent or rental is the money paid for the use over a period of time of anything -- of a house, truck, etc.

In Figure 2, the supply curve for land SS is taken to be completely inelastic because of the fixity of its supply. The demand and supply curves intersect in the equilibrium point F. It is toward that factor-price that the rent of land must tend. Why? Because if rent rose above the equilibrium price, the amount of land demanded by all firms would be less than the existing amount that would be supplied; some property owners would be unable to rent their land at all; therefore, they would offer their land for less and thus bid down its rent.

Fixed land must work for what demanders will bid:

Fig. 2. Perfect inelasticity of supply characterizes the case of so-called "pure economic rent." We run up SS curve to demand curve to determine rent.

By similar reasoning, the rent could not long remain below the equilibrium intersection. If it did, you should be able to show how the bidding of unsatisfied firms would force the factor-price back up toward the equilibrium level. Only at a competitive price where total amount demanded of land exactly equals the total supply will there be equilibrium. It is in this sense that supply and demand determine any factor-price.

Note that the man who owns land does not have to be a particularly deserving citizen in order to receive this rental. A virtuous and poor landowner will be given exactly the same rental by competition as will a wealthy wastrel. It is the productivity of the land that is being paid for and not the personal merits of the landowner.

Even this productivity of the land is not something absolute. For example, what would happen if the price of corn were to fall greatly because people began to desire other goods? Then the derived demand for corn land would shift drastically downward and to the left. What will happen to the rentals received by landowners section. The land is not less productive in a technical sense than it was before, and the landlords are neither more nor less virtuous than they were before. But factor demand and supply intersection has changed.

A factor of production like corn land is said to earn a "pure economic rent" because: (1) its total supply is regarded as perfectly inelastic; and for the moment we shall assume that (2) the land has no other uses, such as the production of sugar or rye. Adam Smith's great follower in England of the early 1800's, David Ricardo, noted that the case of such an inelastically supplied factor could be described as follows:

It is not really true that the price of corn is high because the price of corn land is high. Actually the reverse is more nearly the truth; the price of corn land is high because the price of corn is high! Its total supply being inelastic, the land will always work for whatever is given to it under competition. Hence the value of the land is completed derived form the value of the product, and not vice versa. [A Note: Land is not the only factor whose return may be considered as economic rent. For an example where most of a wage payment is a "pure rent," see chapter 28. And in the short run, the supply of a machine or plant may be entirely fixed; thus a hydroelectric plant takes a long time to build, still longer to wear out. The return to any factor in temporarily fixed supply is sometimes called a quasi-rent because in the long run, its supply need not be fixed. Those New England farmers who petitioned OPA for higher milk price because of higher cow prices were, without knowing it, illustrating rent and quasi-rent doctrines.]


Some economists even went so far as to say that "rent does not enter into the cost of production." The last paragraph shows that there is a grain of truth in this. But still this is very dangerous terminology. If you were a farmer trying to go into the corn-raising business, you would certainly find that the landlord has to be paid like anybody else. You would certainly figure in rent in your cost of production; and if you could not pay it, you would go out of business.

Even if you were a farmer who owned your own land, it would be a mistake to think that rent does not enter into your costs of production. After you had paid all your other bills, including wages to yourself at least as great as what you could earn elsewhere in the market, there would have to be left an amount at least equal to the market rental value of your land. For what if there were not such an amount? Then you would soon find that it would be better for you to rent out your farm on the open market and hire out your own labor to somebody else.

Sometimes economists call rent paid by a man to himself "implicit" rather than "explicit" rent. Very clearly, implicit rent is as much a part of long-run competitive costs as are any other costs, and the same can be said of the implicit wages or implicit interest earned on any other factors that you could sell rather than use personally.


When some economists claim rent doesn't enter into society's cost of production, what are they driving at? They are saying: Since rent is the return to an inelastically supplied factor that would be supplied to the community even at much lower prices, the direction of causation goes as follows, "Goods prices really determine land price-rather than having land price determine goods prices."

We must avoid our old enemy the "fallacy of composition." What appears as a cost of production to each and every firm may to the industry as a whole be really a derived price-determined expense rather than a price-determining one. More than that, suppose we now assume that the corn-producing industry is just one of very many industries which can use the same land. Then to each small industry -- such as the buckwheat or rye industry -- the supply curve of land may appear to be almost completely horizontal or elastic. This is because that one industry may be too small a part of the total market picture to have any appreciable influence on land rents.

Now put yourself in the shoes of someone who takes the viewpoint of that industry as a whole. Will land then appear to be an element determining the price of rye? Or will it seem like a cost that is determined by the final price for rye? The answer must definitely in such a case be the former: To a small industry using relatively little of a factor, the factor-price is an important determiner of the industry's commodity price, and not vice versa. At the same time to the economy as a whole, the rent of a factor whose total quantity is inelastic can still be said to be more the result than the cause of the values of the various final products. (The Davenport poem hints at all this.)

To conclude: Whether rent is or is not a price-determining cost depends upon the viewpoint from which we look.


In the last part of the nineteenth century, a western frontier still existed in this country. As more and more people came here from Europe, each acre of land had more and more people to work it. In a sense, therefore, the land be-came more productive. In any case its competitive rental value certainly tended to rise. This created handsome profits for some of those who were lucky enough to get in on the ground floor and buy land early.

Nor was this true only in agriculture. Men still alive in the Middle West can remember when towns first began. They will tell you how they might have been rich if only they had recognized 70 years ago that the corner of State and Madison would eventually become the center of town and would grow tremendously in value as a result of the great increase in urban populations.

Sites with good locations earn rents in the same sense that fertile areas do. Many people began to wonder why lucky landowners should be permitted to receive these so-called "unearned land increments." Henry George, a printer who thought much about economics, crystallized these sentiments in the single-tax movement. This had a considerable following a half century ago or more, and there are still some adherents to it; but it is not likely that anyone running on the single-tax ticket will again come so close to being elected mayor of New York City as did George in 1886. Nor is it likely that anyone will soon come along and write so persuasive a bible for the movement as did Henry George in his Progress and Poverty, a book which sold millions of copies.

This is not the place to attempt any assessment of the merits and demerits of such a political movement. But its central tenet-that land rent is in the nature of a surplus which can be taxed heavily without distorting production incentives -- can be examined to illustrate one principle of distribution and taxation.

Suppose that supply and demand create an equilibrium land rent, as in Fig. 3 at E. Now what would happen if we were to introduce a 50 per cent tax on all land rents? Mind you, we are not taxing buildings or improvements; for that certainly would affect the volume of construction activity. All we are taxing is the yield of the naturally fixed supply of agricultural and urban land sites, assuming that this can somehow be identified.

There has been no shift in the total demand curve for land; firms are still willing to pay the same amount as before for the same amount of land. Hence, with land fixed in supply, the market price that they pay must therefore still be at the old intersection E. Why? Because supply has not changed and neither has demand. Because at any higher price than before, some land would have to go without any demanders. And hence in the absence of any monopoly on the part of landlords, rents could not permanently be raised to land users.

Tax on fixed land is shifted back on landlords, skimming off pure rent:

Fig. 3. A tax on fixed land leaves rentals paid by users unchanged at E but reduces rent retained by landowners to E'. (What can the landowners do but accept less return?)

Of course, what the farmer pays and what the landlord receives are now two quite different things. As far as the landlords are concerned, once the government steps in to take its cut of 50 per cent, the effect: is just the same as if the net demand to the owners had shifted down from DD to D'D'. Landowners' equilibrium return after taxes is now only as high as F', or only half as high as F. The whole of the tax has been shifted backward onto the owners of the factor in inelastic supply! The landowners will not like this. But under competition there is nothing they can do about it, since they cannot alter the total supply and the land must work for whatever it can get.

Whether or not it is a fair thing to take away part of the return of those who own land is quite another question. Perhaps many voters will feel that such owners are not less deserving than are investors who have put their money into other things, but such a political question has no place in the present discussion. What is relevant is to point out that a similar 50 per cent tax, put upon a factor of production whose total supply is not completely inelastic, will certainly produce definite effects on the factor-prices charged in a competitive market. To some extent this tax would distort the pattern of production, and it would shift part of the burden forward onto the users of the factor and onto consumers. Thus, if the same acre of land were to be taxed differently when used for wheat rather than corn production, this would certainly have distorting effects on the price of wheat relative to that of corn.


The competitive determination of land rent by supply and demand is only one instance of the general analysis applicable to any factor of production. How is the rental value per week of a tractor to be determined in a competitive market? We first sum up the derived demands of all business firms for tractors. (Of course, these derived demands have behind them marginal-revenue-product considerations as shown in the last chapter, but this behind-the-scenes relation need not now concern us as we observe the aggregate market demand for this factor.)

In addition to the DD curve shown in Fig. 4, we must also have a supply curve such as SS. But there is now no reason why the supply curve should be perfectly vertical. It may now be positively elastic, rising upward toward the northeast --being dependent in the case of the tractors on their marginal costs of production Or if the factor of production were labor, it might be that people would feel they could afford to work fewer hours as wages rise, so that the SS curve might eventually bend backward and northwestward from the vertical, rather than rising forward.

Factor supply and derived demand together determine income distribution:

Fig. 4. Land's share in national income rises when its rent Is bid up. Skilled and unskilled labor shares are, in competitive markets, determined by interplay of factor supply and demand. Same would hold for any factor.

In any case, whether the supply curve is vertically inelastic, positively elastic, or negatively elastic, there will be an SS curve as in Fig. 4. Where the demand and supply curves intersect, the final equilibrium factor-price will be set. And if the demand curve for the factor shifts upward, its market price will tend to rise; on the other hand, if the supply offered of any factor increases, so that the supply curve shifts rightward, then the factor-price will tend to fall.

In a competitive market economy, therefore, factor-prices and the distribution of income are not determined at random. There are definite forces of supply and demand operating to create high returns to scarce factors that are very useful in producing the things wanted by people with purchasing power. But the price will drop if more of any factor should become available or if other close substitutes for it are found or if people stop wanting the goods that a factor is best suited to make. Competition gives and competition takes.


Competitive supply and demand helps determine the For Whom problem of society. Whether or not we like its answer to this distribution question-and in the case of rent Henry George certainly did not -- we have to admit that it does contribute to an efficient solution of the How problem for society.

Thus, as a result of supply and demand in markets for goods and for factors, in America where land is plentiful and labor scarce we find extensive agriculture. In Europe or Asia, where people are plentiful relative to land, we find intensive agriculture.

Why? Because of government planning? No, not necessarily.

Rather it is the signaling of market pricing that results in efficient How. Land has to be auctioned off at a low price here; labor auctioned off at a high price here. So every farmer, seeking his Least-Cost combination lest he go bankrupt, substitutes land for labor. And abroad, cheap labor: gets substituted for land. (More than that: with labor scarce here, we find that fussy vegetables which require much care get priced relatively higher than those which lend themselves to extensive methods. So the resulting high commodity prices tend to make us substitute the cheaper goods in our diet for the more expensive ones. Abroad the opposite commodity substitutions take place. Hence, the pricing system signals best commodity substitutions as well as best factor substitutions.)

Do you now believe that charging rent has a function-even if you later tax part of it away? Then you are ready to appreciate that some of the troubles in the real world come from the fact that there is no way to charge the appropriate rents. Here are some examples.

Item: The sea is free to all. So every one fishes in it until the fish are all killed off. If society could somehow charge rents for commercial fishing licenses, we might in the long run all be better off -- including fishermen!

Item: Our roads get very crowded on weekends and during the rush hour. We usually can't charge tolls or rents. If we could, we might coax shoppers and people who are getting very little pleasure from driving to do their driving at some less crowded time.

Item: In a Boston suburb, the cost of collecting money from parking meters turned out to be just equal to the revenues raised by the 5-cent charges. Many said, "Let's cut out the meters." Three economic professors who lived in town argued that the point in making charges was to make the limited parking space go around and be divided among those (nickel voters!) who desired it most. The point of the meters was not, so said the economists, to raise money. Which was right? The group who said "Down with meters," or the learned professors?

Other examples of how charging rent leads to efficient How -- even though it may lead to For Whom considered ethically dubious -- could be given. But the point has been made.


The same general principles determining land rent also determine the prices of all inputs; the rental of threshing machines or of trucks is determined in essentially the same way. We might even go so far as to say that wages are the rentals paid for the use of a man's personal services for a day or a week or a year. This may seem a strange use of terms; but if you think about it, you will recognize that every agreement to hire labor is really for some limited period of time. By outright purchase, you might avoid ever renting any kind of land. But in our society, labor is one of the few productive factors that cannot legally be bought outright. Labor can only be rented, and the wage rate is really a rental.