Economic Growth and Change in a Material World
Appendix D: Properties of the matrix L If Ji is the ﬂow of goods, then an element Lik of the matrix L is the quantity of the ith good bought (or sold) due to the kth value-price difference. If J is interpreted as a demand vector, whose elements are demands for the ith good, then Lik expresses the purchaser’s willingness to buy/sell the ith good due to the kth value-price difference. A corresponding equation expresses the seller’s willingness to sell. The vector J is common to the buyer and seller (except for the sign) and the agreed prices are also common to the two of them. However, the L matrices for the buyer and seller must be different if their subjective (internal) values are different. Thus L reﬂects the link between subjective values and demand (from the buyer’s point of view) or between subjective values and supply (from the seller’s perspective). In brief, L can be regarded as a generalization of the conventional scalar demand function of microeconomics. For simplicity we call it the demand matrix hereafter. (The demand matrix is introduced here only for the case of trade. However, we generalize it later to account for production and consumption.) The off-diagonal elements of the L-matrix are ‘cross-effects’ due to competition or substitution interdependencies with other goods. For instance, the price of oil and the price of gas are strongly correlated because of substitution possibilities between them. The diagonal matrix elements reﬂect demand that would occur in the...
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