A Simplification of Multi-Country Multiplier Theory*1
IN recent years the theory of the foreign trade multiplier has been extended from the simple two-country case to the generalized n-country case, by the application of matrix algebra.2 The following notes present an alternative and simpler proof of some of the more interesting conclusions which have been established by this technique.
I. NATIONAL INCOME MULTIPLIER THEORY
An autonomous change in demand for any country’s output will have a multiplier effect on the outputs of all countries in the system. Let Kij be the multiplier relating the total change in country i’s output to an autonomous change in the demand for j’s output, so that Yi = KijDj, where Yi is the total change in ...
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