Private and Public Consumption and Savings in the von Neumann Model of an Expanding Economy

Oskar Morgenstern and Gerald L. Thompson’s 1966 research report extends the von Neumann growth model by making private and public consumption and savings explicit determinants of expansion and interest. Building on their earlier collaboration with John G. Kemeny, the authors investigate how these decisions affect balanced growth, connect productive sectors, and permit multiple equilibria. They state their central contribution directly:

The new model answers the question of the influence upon the expansion of varying private and public savings and consumption rates, conditions so far not investigated in any of the previous models listed in Table 1 below.

The report moves from methodological positioning through a private-sector formulation, an existence proof, numerical examples, and a public-sector extension. Its concern is the logical structure of economic equilibrium rather than immediate empirical prediction. The authors delimit their inquiry:

In particular, we are not concerned with the so-called "Turnpike Theorem" which is a special application of the von Neumann model.

The private-sector model supplements input and output matrices with a matrix of real remuneration, interpreted through workers’ wages and extended to stockholders and firms. Consumption and saving coefficients enter separate conditions governing physical expansion and the valuation of investment. Equilibrium also requires that surplus goods receive zero prices, inefficient activities operate at zero intensity, and something of positive value be produced. Allowing consumption and saving coefficients to vary independently accommodates hoarding and capital consumption.

This generalization separates the expansion factor from the interest factor, whose equality characterized the original model. When consumption exceeds saving, expansion cannot exceed interest; when saving exceeds consumption, the ordering reverses. Equality is recovered when the coefficients coincide. These relationships depend on the model’s formal assumptions, rather than constituting universal empirical laws.

Consumption also changes the economy’s connectivity. An illustration involving wheat, entertainment, and diamonds begins with technologically distinguishable sub-economies and different feasible growth factors. Remuneration distributed across all three products then ties their activities together. The distinction between technological, private-consumption, and public-consumption connections shows that economic unity need not arise from production requirements alone. Private tastes and public demand can connect sectors that technology leaves separate. In the computed illustration, incorporating private consumption and investment produces unique expansion and interest factors and positive prices for all three goods.

The existence analysis uses two associated matrix games to establish conditions under which their strategies jointly satisfy the economic equilibrium requirements. For the general case, the authors provide a finite elimination algorithm that successively constrains activity or price components until a solution is obtained. Existence under the stated assumptions does not guarantee uniqueness. Numerical examples explore hoarding, consumption of all earnings, extreme saving, nonlinear relationships between expansion and interest, and computational feasibility.

Non-uniqueness becomes economically consequential when the same technological and preference data admit two distinct solutions without an internal rule selecting between them. An external authority or additional considerations would be needed to determine the outcome. The authors connect this indeterminacy to cooperative game theory’s sets of mutually undominated imputations. Game theory thus serves both as mathematical machinery and as a way to interpret the limits of equilibrium selection.

The final section introduces government receipts in real goods and separate public consumption and saving coefficients. Taxation and spending are represented through commodity allocations within a moneyless model. Public demand can connect sectors otherwise left disconnected, while government can influence expansion and interest through spending, saving, and receipts. Yet introducing public decisions does not automatically establish agreement over economic objectives:

If a conflict exists between the consumers and the government we have a true game situation which has to be treated as such.

This distinction separates the use of matrix games to prove equilibrium from strategic conflict among economic decision-makers. A concluding deficit-spending example lowers expansion while leaving interest unchanged, underscoring that public intervention need not move both factors together. The report integrates consumption, savings, and public activity into a rigorous growth framework while distinguishing equilibrium existence from uniqueness, selection, and agreement over outcomes.