Introduction. Factors to be considered, 445. — I. Time preference in a static society, 447. — The effect of invention on the interest rate, 447. — Economic expansion caused by invention, 449. — Time preference and a constructive attitude, 450. — The "price" of capital supply, 451. — II. The mechanism of finance, 454. — The interaction of gold and price levels, 455. — The effect of credit inflation, 455. — Discount and interest, 458. — Recent inflation, 459. — Conclusion, 461.

If divisible commodities in a barter market are cleared by higgling until no further exchange takes place, prices may be shown to be a simple function of the quantities traded. Assume that A, B ***, N units (pounds, bushels, yards, etc.) of various commodities are sold in portions Ai+A2+ +An =A) Bi+B2+ * +Bn=B, C1+C2+.. +Cn=C, etc., at theoretical prices, respectively, a, b, ***, n to be deduced, then barter in terms of commodities, irrespective of persons, may be expressed by the equations appearing in Table 1, in which each column as well as each row totals zero. If, therefore, the quantities AI+A2+ * * * +An=A, etc., are given, the ratios a:b:c: ... :n are determined. And if a price standard is assumed-e.g., the value of a pound of A =$1.0-then all prices may be computed.' The same market may be pictured as a money economy by assuming that each trader correctly estimates the value of the commodity he brings to market and obtains bank credit in this amount. This credit finances all the purchases, and at the end of the market day each trader is able to pay back the borrowed credit. If the services of the banker are included as one of the commodities exchanged, the market balances as before.

THE analysis of market phenomena by input-output arrays not only provides a practicable means of describing industrial interdependence, but also helps to clarify economic theory. For example, the accepted proposition that a change in the general price level as measured by index numbers is in reality a change in the monetary yardstick, may be easily demonstrated, and index number theory elucidated, by means of theoretical input-output relationships. Table i presents a theoretical input-output array in which the conventional input columns are written as rows comprising a set of simultaneous equations. It is assumed to classify exchanges of goods among certain firms, each marketing a specific commodity. The schedule merely indicates the goods and values brought to the market and the goods and values received, in the completed trading of, let us say, a single day. Monetary and other intermediate exchanges are omitted. With r rows, r i independent equations may be solved for relative, but not absolute, prices. The nature of a perfect, complete market imposes certain limitations on the relationships of the items in Table i. Since the sum of the first column is the sales value of commodity A, it must equal the sum of the first row, which itemizes the value of the goods received in exchange, and so on. to the nth column and row.1 Of course the ultimate units entering into a market are not goods, but the usances of capital and labor, broadly construed; and durable goods embody these usances discounted to their present worth. But such complexities, which have been discussed by Professor Leontief and others, would here only divert the argument. Exchanges may be simply visualized as if they were described in terms of tangible goods. Just as a gold monetary standard means that pricing throughout the economy is relative to the exchange value of a designated quantity of gold, so pricing may also be expressed in terms of physical units of each marketed commodity in turn. That is, prices may be standardized so that a is reduced to unity, then b, and finally n. Equations expressing prices in terms of a changed to unity are obtained by dividing the equations of Table i by a. Analogous equations may be obtained by similarly dividing by b and ... n. The column footings of such equations appear in Table 2. The row totals of Table 2, namely V/a, V/b, ..., V/n, may be taken to represent on a mag-