Pricing and Price Levels - Davies, George R. (Econometrica, 1946)
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.