Is Economics an Equilibrium System?
Equilibrium in economics is between supply and demand. For simplicity, we will fix the supply side by regarding it as fixed resources. We can then focus on the demand side of the economic equilibrium.
In either the classical principles of political economy or neoclassical economics, market efficiency emerges by way of the law of demand. Here we limit demand to ‘consumer demand’. In the ideal thinking of economics, the law of demand can coordinate shortages or surplus in the market, which therefore implies the existence of the ‘invisible hand’.We denote demand at price p by f(p). We then have a formula between two distinct price vectors p1 and p2:
This is the demand law, which describes the converse relationship between a demand and its price, as discussed further in Chap. 2.
In classical economics, there is no analytical formulation for this efficiency. However, as neoclassical economics was developed, market demand was analytically designed as a summation of individualistically subjective demands, each of which is derived from a maximization of the subjective utility function. This reasoning, if successful, can provide a justification of market efficiency, in terms of subjective optimization. Each subjective plan to consume by each household is designed to generate a well-defined market demand behavior.
However, this immediately turned out to be incorrect when the Pareto-Slutsky equation was formulated in the first decade of the last century, because the sign of
income effect was not confirmed to derive the consumer demand law. A sufficient condition was not established until Hildenbrand (1994).
Lemma 1.6. The consumer demand law requires a sufficient condition that the spread of demand R(x) is greater as income x increases.
Consumer demand microscopically derived does not hold consistently by itself. That is to say, as the income size increases in a given income class, the variance of expenses between consumers in that class should increase. This heterogeneity of consumers can assure the positive nature of the income effect.
Lemma 1.7. Advocating microscopic economic behavior cannot generate a consistent macroscopic consumer demand. That is to say, ‘invisible hands’ cannot be guaranteed by individualistic behavior itself (invalidity of indivisible hand).
Thus we cannot rest upon the idea of the invisible hand, which does not work by itself, but needs to be complemented by other measures. One such measure may be an income policy or another policy measure to make up the equilibrium to eliminate the excess or deficit of consumer demand.
1.9