Foundations of Economic Analysis - Methods and Analysis

Methods and Analysis

Samuelson's Foundations demonstrates that economic analysis benefits from the parsimonious and fruitful language of mathematics. In its original version as a dissertation submitted to the David A. Wells Prize Committee of Harvard University in 1941, it was subtitled "The Observational Significance of Economic Theory" (p. ix).

One unifying theme, on the striking formal similarities of analysis in seemingly diverse fields, occurred only in the course of writing on them—from consumer's behavior and production economics of the firm to international trade, business cycles, and income analysis. It dawned on the author that he was prodigal "in proving essentially the same theorems" over and over. His failure of initial intuition, so he suggests, might be less surprising in light of the few economic writings then extant concerned with formulating meaningful theorems – hypotheses about empirical data—that could conceivably be refuted by empirical data (pp. 3–5).

Samuelson (pp. 5, 21–24) finds three sources of meaningful theorems sufficient to illuminate his purposes:

• maximizing behavior of economic units (as to utility for a consumer and profit for a firm)
• economic systems (including markets and economies) in stable equilibrium
• qualitative properties between two or more variables, such as an alleged technological relation or psychological law (indexed by the sign of the relevant functional relationship).

Part I conjectures that meaningful theorems for economic units and for their respective aggregates are almost all derivable from general conditions of equilibrium. The equilibrium conditions can in turn be stated as maximization conditions. So, meaningful theorems reduce to maximization conditions. The calculus of the relations is at a high level of abstraction but with the advantage of numerous applications. Finally, Part I illustrates that there are meaningful theorems in economics, which apply to diverse fields.

Part II concentrates on aggregation of economic units into equilibrium of the system. But the symmetry conditions required for direct maximization of the system, whether a market or even the simplest model of the business cycle, are lacking, in contrast to an economic unit or its corresponding aggregate. What can be hypothetically derived (or rejected in some cases) is a stable equilibrium of the system. (This is an equilibrium of the system such that, if a variable disturbs equilibrium, the system converges to equilibrium.) Stability of equilibrium is proposed as the principal source of operationally meaningful theorems for economic systems (p. 5).

Analogies from physics (and biology) are conspicuous, such as the Le Chatelier principle and correspondence principle, but they are given a nontrivially generalized formulation and application. They and mathematical constructions, such as Lagrangian multipliers, are given an operational economic interpretation. The generalized Le Chatelier principle is for a maximum condition of equilibrium: where all unknowns of the function are independently variable, auxiliary constraints ("just-binding" in leaving initial equilibrium unchanged) reduce the response to a parameter change. Thus, factor-demand and commodity-supply elasticities are hypothesized to be lower in the short run than in the long run because of the fixed-cost constraint in the short run. In the course of analysis, comparative statics, changes in equilibrium of the system that result from a parameter change of the system, is formalized and most clearly stated (Kehoe, 1987, p. 517). The correspondence principle is that the stability of equilibrium for a system (such as a market or economy) implies meaningful theorems in comparative statics. Alternatively, the hypothesis of stability imposes directional restrictions on the movement of the system (Samuelson, pp. 258, 5). The correspondence is between comparative statics and the dynamics implied by stability of equilibrium.

Chapter VIII on welfare economics is described as an attempt "to give a brief but fairly complete survey of the whole field of welfare economics" (p. 252). This Samuelson does in 51 pages, including his exposition of what became known as the Bergson-Samuelson social welfare function. Theorems derived in welfare economics, he notes, are deductive implications of assumptions that are not refutable, thus not meaningful in a certain sense. Still, the social welfare function can represent any index (cardinal or not) of the economic measures of any logically possible ethical belief system that is required to order any (hypothetically) feasible social configurations as "better than", "worse than", or "indifferent to" each other (p. 221). It also definitively elucidates the notion of Pareto optimality and the "germ of truth in Adam Smith's doctrine of the Invisible Hand" (Samuelson, 1983, p. xxiv; Fischer, 1987, p. 236).

The final pages of the book (pp. 354–55) outline possible directions analytical methods might take, including for example models that show how:

• deficit financing could produce positive short-run effects on the economy that are swamped by adverse long-run effects on capital accumulation (seriously reconsidered later as crowding out)
• declines in age-specific mortality affect the net reproductive rate (whose the implications for population growth are less abstract than they might first appear).

Samuelson closes by expressing hope in the future use of comparative dynamics to:

aid in the attack upon diverse problems – from the trivial behavior of a single small commodity, to the fluctuations of important components of the business cycle, and even to the majestic problems of economic development.