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The author is grateful to Karl F. Habermeier for useful comments on an earlier draft.
Many empirical studies corroborate these facts. See, for example, Woo (1984), Krugman (1987), Hooper and Mann (1987), and Ohno (1989). The Economic Report of the President of 1988 also offers a good review.
This proposition is opposite to the celebrated Dixit-Stiglitz model where the consumer values variety. While this may be true where food, drinks, and other entertainment goods and services are concerned, a majority of durable manufactured goods seem to be purchased in the way described in the text, where no more than one per customer is needed.
Various models have been presented to explain incomplete pass-through based on the concept of hysteresis, including Baldwin (1988), Dixit (1987, 1988), Foster and Baldwin (1986), and Froot and Klemperer (1988). The present model, however, is unique in its formulation of linear promotional cost and emphasis on corporate planning horizon.
Marston (1989) shows that when home and foreign countries are two separate markets and when marginal cost is constant (as we assume here), one can consider the pricing of Japanese goods abroad independently of that at home. We will therefore ignore the Japanese market in this model.
If the firm is a short-term maximizer, output will be equal to x0 set when the yen is strong. If the firm is a long-term maximizer, such x will be chosen as to maximize Π0 + Π1 in (2) after setting x1=x0.
The opposite asymmetry, where only the American firm adjusts output, will never take place. It can be seen from (5) that, if x0=x1 the American firm faces identical profit maximization problems in both periods, and therefore x*0=x*1 must hold.