The archive.

Can an economy sustain balanced growth while maintaining activities that lose money? Oskar Morgenstern and Gerald L. Thompson address this question by opening the generalized von Neumann growth model to trade at externally fixed prices. Their distinctive move is to combine those trading opportunities with domestic bounds on production, allowing profitable industries to finance loss-making services rather than excluding them from equilibrium. Under the model’s assumptions, these controls permit a continuous range of expansion rates where the closed model offered only finitely many. Linear-programming proofs and numerical examples show how trade prices and production requirements shape feasible growth—and how openness can raise it. The article also makes a useful distinction: establishing what specified controls make possible is not the same as deciding which controls an economy should choose.

When does a growth model describe a genuinely open economy, rather than a closed economy with trade variables attached? In this corrective note, Oskar Morgenstern and Gerald L. Thompson sharpen the answer by replacing import prices with export prices in a key positivity assumption. They acknowledge criticism of their earlier formulation and explain why the revised condition repairs an existence proof without changing the theorem statements. The economic distinction is concrete: trade must involve goods of positive value, not merely exchanges of free goods. Readers can follow how a small mathematical correction changes the interpretation of production constraints, while seeing the authors distinguish properties of basic solutions from conditions that would require additional assumptions.

When John von Neumann published his expanding-economy model in 1937, he gave economics one of its rare transformative events. Morgenstern and Thompson build on it here, synthesizing two decades of work into the KMT model, which removes von Neumann's restrictive assumption that every good figures in every process and admits multiple expansion rates, subeconomies, and game-theoretic solution methods. Across fourteen chapters they extend the framework to open economies that import and export at world prices, to consumption and savings, to trading blocks and a world model bound by a common expansion rate, and, pointedly, to contraction and compression, since resource limits make endless growth no longer self-evidently desirable. Throughout, they insist the models apply to any economy regardless of political organization, deliberately omit money and stochastic elements, and treat expansion, stationarity, and collapse as problems of structure, optimization, and computable linear programming.