Oskar Morgenstern and Gerald L. Thompson, A Note on “An Open Expanding Economy Model” (1972)

Morgenstern and Thompson’s research note corrects and clarifies their earlier extension of the von Neumann growth model to an open economy embedded in a world economy. Its scope is precise: it records changes between the original 1969 article and its 1971 French translation, explains their consequences for an existence proof, and situates subsequent criticisms and applications within the developing model. The central claim is that a revised assumption gives the proof an economically meaningful foundation without invalidating the original theorems. The note thus connects a technical correction to the larger question of what makes an economy genuinely open, rather than merely permitting trade formally.

The correction follows criticisms by Mrs. L. Mardon, communicated through Professor J. Los, concerning Assumption (A6). The authors acknowledge their correctness and replace the import-price vector (p^-) with the export-price vector (p^+), making the assumption (t^-Ap^+>0). Here (t^-) denotes lower bounds on production intensities, while (A) represents input requirements. The revised condition requires positive input valuation even at the economy’s minimum intensities and at the lowest admissible prices. Export prices therefore provide the relevant lower bound for the argument, rather than the higher import prices used in the original formulation.

To explain the economic significance of this revision, the authors first revisit the companion assumption (A5), (t^-Bp^+>0), concerning output. An open economy must produce something with positive export value even when operating at minimum intensity:

In order to have an economic solution to the open model which is essentially different from a solution to the closed model, then, even when it is operating at its minimum intensities, the economy must produce at least one product having a positive export price.

This condition distinguishes economically consequential trade from an empty permission to exchange goods. Without it, the economy would export nothing or export only free goods; the balance-of-payments condition would then permit only free imports. The resulting economy would be closed for practical purposes. Openness, in this account, depends on a positive-valued connection between domestic production and external exchange, not simply on the presence of import and export variables.

Assumption (A6) provides the corresponding restriction on inputs. At minimum production intensities, the economy must demand at least one input with a positive export price. The authors explain that this prevents high-intensity operation of an industry using only inputs whose export prices are zero while producing positively valued goods. The conceptual move is to constrain both sides of the production process: (A5) secures economically meaningful exportable output, while (A6) supplies a positive input term needed in the limiting argument. These are presented as substantive economic restrictions, not merely convenient algebraic devices.

The revised proof examines what happens when the expansion parameter (\alpha) becomes very large. From the relation ((B-\alpha A)y-z^++z^-=0), together with the price bounds (p^+\leq y\leq p^-), the authors derive an inequality containing (-t^-Bp^-+\alpha(t^-Ap^+)). The corrected assumption makes the coefficient of (\alpha) strictly positive, so this expression can be made arbitrarily large. They then compare it with the dual programs’ objective function, (-t^+z^++t^-z^-), arguing that the correction term does not prevent that objective from also becoming arbitrarily large. The replacement passage repairs the large-(\alpha) step rather than restating the entire earlier existence proof.

The statement of Theorem 1 is unaffected by these changes and Theorem 2 was independent of (A6) at any rate.

This distinction limits the correction’s reach. The authors preserve the theorem statements while revising an assumption and its supporting argument; they also identify a theorem whose validity does not depend on that assumption. Their next sentence turns the repair into an invitation to investigate the model’s foundations:

This raises the question of under what still more general assumptions our results are correct.

The remaining remarks distinguish established properties from possible additional restrictions. The authors credit R. L. Weil with a proof that the relevant linear-programming value is continuous in (\alpha). They then address Moeschlin and Rauhut’s observation about complementary variables. The products (w_i^+w_i^-) and (z_j^+z_j^-) vanish in basic solutions, as the original article’s footnote stated, but nonbasic solutions need not satisfy those conditions. Consequently, the conditions can be imposed as additional assumptions if desired. A property of basic solutions is thus not silently promoted into a property of every solution.

The closing discussion shifts from validity to economic control. Production-intensity bounds and import prices are not only parameters in an existence argument; they can also regulate the economy’s exposure to trade and industrial losses:

In a very interesting paper [1] A. Moeschlin has applied the model to show that by changing the control variables $t^+$ and $t^-$ it is possible to impose bounds on imports of goods, and that by changing import prices $p^-$ it is possible to impose bounds on losses of industries.

The note reports these applications without reproducing their derivations. Similarly, it directs readers to the authors’ Warsaw symposium paper for the question of how the economy should fix its production-intensity bounds and how that choice relates to long-term planning. Its final announcement of a unifying book places the correction within a broader research program. The note’s relevance lies in its disciplined linkage of mathematical validity, economic interpretation, and policy control: it repairs a specific proof while clarifying what the open-economy model requires and which questions remain for further work.