Oskar Morgenstern and Gerald L. Thompson, Further Consideration of “An Open Expanding Economy Model”

Oskar Morgenstern and Gerald L. Thompson’s 1971 conference proceedings contribution, republished in 2013, revisits their 1969 extension of the von Neumann growth model to international trade. Its purpose is precise: to relax an assumption that helped secure an open-economy solution and to clarify the relationship between the expansion factor, α, and the interest factor, β. After reviewing the model’s axioms, the authors establish conditions distinguishing open from closed solutions, construct an example with α < β, and interpret that inequality through two accounting indices. The central distinction is between what the equations permit and what constitutes an economically efficient growth path.

The introduction situates the argument within successive generalizations of von Neumann’s model. Earlier work had introduced demand, private and public consumption, and investment; the subsequent open model allowed imports and exports at given world-market prices, subject to a balance-of-payments condition. International trade changes the possibilities of expansion without requiring a comprehensive account of relations among countries. Even a model exporting one commodity and importing another can reveal effects unavailable within a closed economy.

The review organizes this framework around seven axioms. These connect physical production and trade, output and input values, external payments, profits and losses, positive-valued production, activity bounds, and bounds on domestic prices. Domestic prices lie between export and import prices, while production activities lie between prescribed lower and upper limits. These restrictions become essential to the later argument: external payments balance at trade prices, but trade need not balance when valued at domestic prices; likewise, the stipulated balance between profits and losses need not coincide with the balance at actual activity levels.

The first substantive revision removes assumption A5, which required positive minimum activity in a process producing something with a positive export price.

If we now drop (A 5) the solution to the economy may be either open or closed and we take this step in order to determine the conditions when one or the other case obtains.

Openness thus becomes a property to establish rather than an outcome secured by the discarded assumption. To maintain existence, the authors restore two conditions used for the closed model: every process requires a positive input, and every good can be produced domestically. They define an open solution by positive export value. This is a value-based distinction: importing only free goods does not make an economy open in their stipulated sense.

Theorem 1 provides asymmetric tests. Production with positive value at export prices is necessary for openness, but not sufficient. Domestic prices strictly above export prices for every good are sufficient for closure, but not necessary. In the latter case there is no incentive to export; balanced external payments then preclude positive-valued imports. The authors explicitly deny that either test can be strengthened into an equivalence. Their revision therefore clarifies the limits of the characterization as well as extending the model’s admissible solutions.

The second problem concerns the known inequality α ≤ β. Can the expansion factor be strictly smaller than the interest factor? A three-process numerical example is offered to demonstrate that possibility. Holding β at 2.38, the authors lower α to 2.31 and reduce the activity levels of two industries relative to the earlier solution. They mention pollution control and labor difficulties as possible reasons for limiting production, but do not develop a theory of those restrictions.

Here we merely demonstrate by means of an example that solutions with $\alpha < \beta$ are, in fact, mathematically possible within the model.

The qualification matters: feasibility alone does not establish economic desirability. To interpret the gap, the authors introduce the internal balance-of-payments index, r, and the internal balance-of-profits index, s. The former values net exports at domestic prices; the latter measures net profits at actual activity levels. Price bounds and external payment balance imply r ≥ 0, while activity bounds and the stipulated profit-loss balance imply s ≤ 0. Equality between expansion and interest holds exactly when both indices vanish. Strict inequality therefore signals a departure from at least one of these internal balances, even though the model’s external and bounding conditions remain satisfied.

It is clear that the economically most interesting solutions are those with $r = s = 0$.

Their interpretation turns on efficiency over time. Drawing on Truchon, they associate positive r with failure to maximize production over time and extend that reasoning to negative s. Thus α < β is mathematically admissible but, they argue, economically uninteresting at least for a one-country economy. That qualification limits the conclusion: the contribution does not establish a general dismissal of unequal factors across interacting national economies.

The closing defense of the seven axioms connects mathematical formulation to economic intelligibility.

Axioms for an empirical field as the present one should have reasonable transparency and this frequently requires a somewhat larger number of axioms.

Rather than treating formal compression as the overriding objective, the authors favor explicit conditions whose economic meanings remain visible. The contribution’s significance lies in this disciplined separation of existence, openness, and efficiency: allowing trade does not guarantee positive-valued trade, and satisfying equilibrium restrictions does not guarantee an efficient expansion path.