Oskar Morgenstern and Gerald L. Thompson, An Open Expanding Economy Model (1969)

Morgenstern and Thompson’s journal article extends the generalized von Neumann growth model to an economy trading at externally determined prices. Its central result is that openness, combined with domestic controls on production, permits a continuous range of expansion factors where the earlier closed model admitted only finitely many. Trade also allows profitable activities to sustain loss-making ones without abandoning balanced long-run growth. The article proceeds from an account of earlier generalizations through a review of the closed model, seven axioms for the open economy, existence proofs using linear programming, economic interpretations, and numerical examples.

The starting point is the authors’ 1956 work with J. G. Kemeny. That generalization replaced von Neumann’s restrictive assumption that every good enters the production of every other good with the requirement that production yield something of value. It allowed interconnected sub-economies with distinct, bounded expansion factors, each equal to its corresponding interest factor. Their subsequent treatment of consumption and savings challenged the assumption that growth automatically reaches an efficient point. The present article continues this investigation of how economic choices affect the direction and rate of expansion.

Openness is defined narrowly: the outside world supplies unlimited opportunities to import and export at stated prices, without itself becoming a system of strategic actors.

The sole effect of the outside world in this model shall be to provide the possibility of exporting and importing various goods in any amounts at stated export and import prices.

Domestic equilibrium prices must lie between export and import prices. Production intensities likewise lie between lower and upper bounds, but these bounds originate inside the economy. The distinction separates external trading conditions from domestic decisions about which activities must operate and which may expand. These decisions are not reduced to government planning alone.

That is, they are selected by a combination of decisions by government agents, managerial agents, and consumers.

The intensity bounds are thus control variables rather than merely technical constraints. They can represent compulsory support for services, restrictions on particular industries, or choices favouring capital accumulation. The authors leave their optimal selection unresolved: the article establishes consequences of admissible controls, not a comprehensive account of how an economy should choose them.

The seven axioms connect physical production, valuation, and finance. Production plus imports must cover domestic requirements and exports; output values and input costs are reconciled through profits and losses. Export receipts must equal import expenditure, while profitable activities must finance the losses of unprofitable activities, evaluated at their prescribed intensity bounds. A further condition requires valuable output, and the remaining axioms impose the price and activity bounds. This arrangement replaces the closed model’s strict exclusion of profitable processes and its assignment of zero prices to overproduced goods. Exportable surpluses can retain positive value, while socially desired deficit activities can remain in operation.

We wish to emphasize here that the term “unprofitable industry” does not have a derogatory connotation.

“Unprofitable” denotes an activity whose output value falls below its input value, not one without economic or social justification. Defence, entertainment, and services illustrate why such activities might be maintained. The balance-of-profits condition requires financial provision for them; the authors interpret taxation of profitable industries as one mechanism. Government therefore influences growth partly through the demands that supported activities impose on the profitable sector.

The mathematical core translates the axioms into a pair of dual linear programs. The primal minimizes import expenditure minus export receipts; the dual represents losses and profits subject to the domestic price bounds. Under four assumptions—ordered nonnegative price and intensity bounds, positive export-valued output at minimum activity, and positive import-valued input requirements—the authors establish solutions with equal expansion and interest factors. Their construction selects an expansion factor at which the common objective value becomes zero, simultaneously satisfying the two financial balance conditions. Conversely, every axiomatic solution with equal factors supplies optimal solutions to these programs.

Complementary slackness gives the mathematical formulation its economic content. Positive exports require the domestic price to equal the export price; positive imports require equality with the import price. Profitable processes operate at their upper intensity bounds, and loss-making processes at their lower bounds. The comparative-static results associate tighter minimum activity requirements or higher import prices with a weakly lower expansion factor; relaxed upper bounds or higher export prices have the opposite effect.

Hence we shall see that the resulting value of $\alpha$ can vary continuously in an interval.

This continuity is the decisive departure from the closed model. With world prices fixed, varying domestic activity bounds permits intermediate expansion factors between attainable extrema. Choosing a factor indirectly selects a functioning sub-economy and its trade pattern. The examples illustrate this flexibility: an essentials-and-inessentials economy achieves an intermediate factor of (8/3), while the final example raises a closed-economy factor of approximately 1.81 to 2 through trade. Openness can therefore improve attainable expansion, not merely interpolate between earlier closed-economy possibilities.

The article’s relevance lies in joining growth theory, external trade, and the financing of non-profit-making activities within a tractable equilibrium framework. Its methodological qualification is equally important: using game theory does not make the economy a strategic game, and using linear programming does not establish comprehensive central control. The results concern a neutral external market and specified domestic controls. They provide conditional answers about feasible expansion, leaving strategic international interaction and the rational selection of controls for further analysis.