64. Equilibrium in a Market for Inputs
Labour market
The price of labor is the wage(w), and the quantity demanded is the number of labor-hours employed(L). The demand for labor is the MRP, the price of output times the marginal productivity of labor in units of output. As usual, the equilibrium price (wage) and the equilibrium quantity demanded and supplied (employment) are at the point where the supply and demand curve intersect.
Figure 3: Supply and Demand for Labor
Land market
Land is not a homogenous resource, and that important complication cannot be skipped over. It is the basis of the theory of rent(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.
: Marginal Productivity of Land with Different FertilitiesThe demand for good land is pMPA, for fair land pMPB, and for bad land pMPC. 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 acr. of each sort of land, three kinds of land have identical supply curves,all shown by the vertical line S.
In a supply-and-demand equilibrium, then, the rent per acre of good land will be RA. For fair land it will be RB, and for bad land zero.
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.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.
Capital market
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 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. 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.
The horizontal red line is the supply curve of capital to the firm, green-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 profit-maximizing 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.