The Capital Market
The previous chapter described how labor effort is not fixed in supply, but is a variable factor of production. By introducing the worker's preference function for leisure and income, the model of the market economy expands.
In this chapter capital is no longer treated as fixed in supply but instead is shown to be a variable factor of production. To show this, time must be made an explicit variable. It allows consumers to choose how they will vary their consumption over time, that is, how they decide whether or not to save. Also, businessmen who create capital must devote current income to investment in plant and equipment and inventory. Thus, the savings behavior of consumers and the investment behavior of entrepreneurs leads to the introduction of variable amounts of capital into the model of the market economy.
9.1 VARIABLE AMOUNTS OF CAPITAL
In the model so far all of each good that is produced is also sold each period. This market-clearing assumption gives two equations that show that none of the quantities of goods 1 and 2 remain unsold. If we admit that some amounts of goods 1 and 2 are not sold but rather added to the stock of inventories of goods on hand, then there exists some postponement of consumption and these added inventories represent one form of the existence of capital goods.
One of the goods being produced may also be a capital good; that is, good 2 may be factor Y in reality and may be bought, not by consumers but by producers of goods 1 and 2 for use in their production. If some goods are produced but not directly consumed, then those individuals who receive money income from the sale of their ownership of factor supplies must have saved some of their income and lent it to producers, who, if turn, used it to purchase capital goods that flowed into the producers' market. Again both markets are cleared, but both saving and investment occur and in equilibrium they will be equal to each other.
In the model of the consumers' market, the sum of the incomes of Mr. A and Mr. B represents the total income of the two-person community. That is, P1QA.1 + P2QA,2 = IA and P1QB,1 + P2QB,2 = IB; therefore, IA + IB = I. Since the condition was imposed that each consumer spend all of his income on the two consumers' goods, if C represents consumption, one can say that C = I. If Mr. A and Mr. B each saves part of his income, the new budget equations for consumers might read P1QA.1 + P2QA,2 + SA = IA and P1QB.1 + P2QB.2 + SB = IB, where S refers to saving. From these two equations one can now note that I = C + S for the entire community. (There is no government and therefore no taxes or government expenditures in this abstract model. Furthermore, it is a closed economy, which means merely that we abstract from the existence of international trade as well.)
If, in addition, we note the expenditures of producers on factors X and Y, and if some of the supplies of these factors are devoted to the production of investment or capital goods INV, the producers' budget equations, when added together, become (PXX1 + PYY1) + (PXX2 + PYY2) + (PXXINV + PYYINV) = Q1 + Q2 + INV = C + INV. Since the left-hand side of the equation also measures total income I, again we have I = C + INV. From the consumers' market with saving behavior we found I = C + S; therefore, saving must equal investment. This is an important proposition in...