Lesson-40. Land, Capital and Natural Resources

Transcription

1 Lesson-40 Land, Capital and Natural Resources The Marginal Productivity Approach in General So far, the marginal productivity approach to analyze the demand for labor, in the Neoclassical tradition has been applied. However, the marginal productivity corresponds to the demand for any input. In general, we can define the marginal productivity of any input as the additional output as a result of adding one unit more unit of that input, with all other inputs held steady. In algebraic terms, that is approximately that is, the increase in output divided by the corresponding increase in the input, while the other inputs do not vary. We can then define the value of the marginal product for any input as VMP input =p*mp input where p stands for the price of the output, as before. In general, we may think of the VMP as the marginal productivity of the input in money terms. The rule for maximization of profits, for each input, is to increase the use of the input until Now let us apply that to the land input. Land VMP input =price input Now, let's apply the marginal productivity approach to land. We may think of a potato farmer who is considering renting additional land to farm. How much land? Of course, that will depend on the rent per acre-- the price of land. Using the general formulae for marginal productivity and the value of the marginal product from the previous page, we can define the marginal productivity of land as

2 that is, the increase in output (measured in bushels of potatoes) divided by the corresponding increase in the number of acres of land used, while the other inputs do not vary. The value of the marginal product of land will be VMP land =p*mp land where p, again, stands for the price of the output -- a bushel of potatoes, in this case. Continuing the example of producing potatoes, the value of the marginal productivity (in the potato example) is the market value of the additional potatoes produced on one additional acre of land. The farmer will increase the number of acres of land he rents until VMP land =price land And so the value of the marginal product of land is the demand curve for land of a standard quality. Differential Rent However, land is not a homogenous resource, and that important complication cannot be skipped over. It is the basis of the theory of rent, first proposed by English economist David Ricardo, and still considered the correct theory of rent by just about all economists. Some land is more fertile than other kinds of land, or more profitable because it is closer to markets; and some land is more suitable to one kind of crop than another. These differences in fertility will be reflected in the marginal productivities and therefore in the demands for the different kinds of land. Let us think of a very small economy with just three kinds of land: good, fair, and bad. There are just 10,000 acres of each kind of land. The supply and demand for each kind of land is shown in Figure 6 below:

3 Figure 1 Marginal Productivity of Land with Different Fertilities The demand for good land is pmp A, for fair land pmp B, and for bad land pmp C. The supply of land of a particular quality is always a vertical line, because "they're not making any more of it"-- the supply of land cannot be increased no matter how high the price. Since there are 10,000 acres of each sort of land, the three kinds of land have identical supply curves, all shown by the vertical line at S. In a supply-and-demand equilibrium, then, the rent per acre of good land will be R A. For fair land it will be R B, and for bad land zero. The bad land in this example is what Ricardo called "marginal" land-- good enough to be cultivated, but only if it can be had free of rent. Thus, the rent on fair land is just enough to offset its greater productivity relative to the marginal land. Similarly, the rent on good land is just enough to offset its productivity advantage over marginal land. If the rent of good land were any lower than that, no-one would want to use fair or marginal land, but all would compete for the limited supply of good land-- forcing the rent on the good land up until it is large enough to offset the productivity advantage of that good land. Similarly, the difference in rent between the good and fair land is just enough to offset the productivity differential between them. This is called the "differential" theory of rent-- that the rent of any land is just large enough to offset its differential productivity relative to marginal land. To stress the basis of land rent, it is often called differential rent. This idea-- that rent is based on differential productivity, which is given by nature and not the result of the landowner's action-- is what led the American social activist, Henry George, to propose that land rent ought to be largely confiscated by taxation.

4 Natural Resources Natural resources include such things as standing forests and schools of fish, deposits of petroleum, copper ore and gold, and similar biological and mineral resources. Traditionally, these resources are lumped with land in economics. One reason for this tradition is that the market prices of all natural resources include an element of differential rent. The case is simplest for such renewable natural resources as second-growth forests. Essentially, woodland is one crop that may be grown on the land, and if the land is best suited for woodland, its rent will be based on its value in growing timber. The productivity of land in this sort of use will also depend on the cost of extraction. If the land is very hilly or swampy, then it may be difficult to use machinery, or more costly machinery may be needed-- raising the cost of harvesting the timber. With natural resources in general, cost of extraction is inversely related to productivity and therefore rent. For mineral resources such as petroleum and gold (and old-growth forests), no renewal is possible in an economically meaningful time frame. Nevertheless, the supply-anddemand price of natural resources will include a component of differential rent. The cost of extraction of mineral resources will vary. For example, petroleum at great depth or under deep water will cost much more to drill and operate the well than shallow, dry land oil deposits. Thus the shallow, dry land deposits with lower costs of extraction are more productive. In general the cheaper deposits will be extracted first. But oil or minerals from costly deposits must sell for the same as those from deposits that are cheap to extract, so the ones from deposits with low costs of extraction will be sold at over their cost, the difference being differential rent. Capital The third of the classical "factors of production" is capital. The earliest generation of economists did not think of capital as being an independent factor. But as the nineteenth century wore on, it was increasingly clear that capital (and specifically, mechanization) is a key factor in modern production. It was Nassau Senior who pointed out that capital investment in and of itself would increase productivity. Senior wrote "That the powers of Labor, and of the other instruments that produce wealth, may be indefinitely increased by using their Products as the means of further production." As we know, capital is more than just machinery, but it may be helpful to think in terms of a specific kind of machine. We may think of a tractor to be used on the potato farm. As we increase the number of machines in use, with the same amount of land and labor, output will increase, but at a decreasing rate. Capital, like the other inputs, is subject to diminishing returns. Once again, we will focus on the "marginal productivity" of the machines. On the other hand, the costs of using the machinery will also increase as the number of machines increases.

5 The machines will gradually wear out and will have to be replaced. It is customary to deduct wear and tear from the output, so that the total and marginal productivity are net of wear and tear. But, for practical applications, we should remember that wear and tear is a real cost and must be taken into account. The resources "tied up" in the machine have an opportunity cost. The money laid out to buy the machines pays for the resources used in producing the machines. The money (and resources) will be recovered only gradually, using the machines to produce goods and services. However the money (and the resources) could be used for other purposes. For example, the investor might instead have bought a vineyard, which would produce a crop of wine grapes every year. It will not make sense to invest in the machine unless the net revenue from using the machine to produce goods and services is worth at least as much as the wine grapes. Similarly, the investor might instead have leant his money to someone else, to finance either production or consumption expenditures. It will not make sense to invest in the machine unless the net revenue from using the machine to produce goods and services is worth at least as much as the interest the investor could get on the loan. Of course, capital includes many kinds of producers' goods, from tractors and other machines through grapevines and orchards and many intangible assets. What they all have in common is the opportunity cost corresponding to the interest rate. With that in mind, we identify the price of capital as the interest rate. The demand for capital is the marginal productivity of capital (net of wear and tear) times the price of output. As for the supply of capital, that will depend on the decisions made by savers. Many economists believe that an increase in interest rates will result in an increase in saving and so in the quantity of capital supplied, giving an upward sloping supply curve of capital. However, for capital as for labor, it is logically possible that the supply curve (in the economy as a whole) could be backward sloping. For an individual industry, however, the supply of capital will probably be horizontal and correspond to the opportunity cost of capital in other industries. In the next page, we see a picture of the supply and demand for capital as many economists understand them. Demand for Capital Here is a diagram the demand for capital by an individual firm as it is sketched in the previous page. We assume that the firm uses a given quantity of labor and land and that the quantity of capital used varies. The quantity of capital used (measured in dollars' worth) is marked off on the horizontal axis. On the vertical axis is the rate of interest, which we understand as the price of capital.

6 Figure 2 Marginal Net Productivity as the Demand for Capital In the diagram, the horizontal red line, corresponding to the market interest rate, is the supply curve of capital to the firm. The green line is the demand for capital, that is, the marginal productivity of capital (net of the cost of wear and tear of specific capital goods) times the price of the output -- the value of the marginal product of capital. The profitmaximizing demand for capital for the firm is shown by K. That is, it will be profitable to expand the capital stock of the company until diminishing returns reduces the value of the marginal product to r, the market rate of interest, at K. Some economists criticize this approach to the supply and demand for capital on the grounds that "capital" really consists of many different kinds of capital goods and cannot be expressed as a single amount of "capital." If we accept that argument, we would have to think of a marginal productivity curve and demand for each respective capital good, measure the capital goods in natural units (number of machines, number of grapevines, and so on), and treat the price in a little more complicated way. But, for microeconomics, the results would be pretty much the same: the demand for a capital good, like the demand for any input, depends on marginal productivity. Now let's look at an important application of the marginal productivity approach in the economics of factors of production.