By their very essence, models and theories assume that certain elements are held constant so that they will not influence the behavior of the variables in the model. In the physical sciences, where the laboratory method has proved so fruitful, the researcher conducts repeated experiments in which all variables except two are held constant. One variable—for example, the heat applied to a mass of water—is permitted to vary, and the effect on the other variable is observed. If the water is observed to boil at 212 degrees Fahrenheit in repeated experiments, we conclude that with certain factors held constant—in this case constant pressure would be crucial—water boils at that temperature.
Economists distinguish between partial and general equilibrium models in terms of the degree of abstraction in the model. More factors are assumed to be held constant in partial equilibrium analysis than in general equilibrium analysis. Partial equilibrium analysis allows only a small number of variables to vary; all others are assumed constant. General equilibrium analysis allows many more variables to change. It does not allow all variables to vary, and thus to influence the model, however, but only those regarded as being within the scope of economics. General equilibrium models, for example, assume as given the tastes or preferences of individuals, the technology available for producing goods, and the institutional structure of the economy and society. Because the scope of economics as a social science has historically been limited by orthodox theory to variables that appear to be quantifiable, a mathematical general equilibrium model appears feasible.
Most partial equilibrium models, following the tradition of Alfred Marshall, limit themselves to the analysis of a particular household, firm, or industry. Suppose we want to analyze the influence on beef prices of a reduction in costs in the beef industry. Using the partial equilibrium approach, we would start with the industry in assumed equilibrium, disturb the equilibrium by making the cost reduction, and then deduce'the new position of equilibrium. During this analysis, all other forces in the economy are assumed to be fixed and to have no influence on the beef industry. The reduction in costs in the beef industry would result in the supply of beef increasing and the price of beef falling to a new equilibrium level. Now suppose we make our model less restrictive and include in the analysis both the pork and the beef industries. The immediate effect of lower costs in the beef industry is to lower beef prices as the supply of beef increases. However, the fall in the price of beef will also influence the demand for pork. As beef prices fall relative to pork prices, the demand for pork will decrease as the quantity of beef demanded increases: consumers will substitute beef for pork. The decrease in demand for pork will result in a fall in the price of pork, which will result in a decrease in the demand for beef and a further fall in its price. This fall in the price of beef will further decrease the demand for pork and, again, lower its price. The interaction between prices and demands for the two goods will continue, with the resulting changes in prices and outputs becoming smaller and smaller, until new equilibrium conditions are established in both industries.
In our partial equilibrium model, the beef industry is assumed to be isolated from the rest of the economy. We can plot a simple graph showing the consequence of a reduction in costs in the beef industry by means of supply-and-demand curves. The supply curve of beef moves out and to the right, and a new equilibrium emerges. But if we show the interactions between the beef and the pork industries, the resulting graphs become more complex.
Partial equilibrium analysis is an attempt to reduce a complex problem to a more manageable form by isolating one sector of the economy, for example one industry, and ignoring the interaction between that sector and the rest of the economy. It is useful for contextual argumentation. The gains in clarity and analytical neatness, however, are achieved at the expense of theoretical rigor and completeness.
If we were to move toward a more general equilibrium model by adding a third and fourth industry to our example, the analysis would become so complex that diagrammatic representation would produce more confusion than clarity. Walras's great contribution was his recognition that the complex interdependence of industries could best be understood and communicated mathematically. His general equilibrium analysis is useful for noncontextual argumentation.