Some remarks on purchasing power parity and exchange rate determination mechanism1

¹ This article was originally written as a term paper for a graduate course (SUNY Buffalo) in May 2005.

Abstract

This article shows how larger, under a Cournot oligopoly model with international linkage, a long-run equilibrium exchange rate deviates from the purchasing power parity (PPP) in factor prices than the PPP in product prices does, with the asymmetry in the degree of competitiveness, consumer's preference and market volume between countries, or with the asymmetry in the marginal costs between firms, although into the same direction. Our result may well explain the phenomenon of so-called ‘overshooting’ from a different angle from the existing related literatures.

¹ This article was originally written as a term paper for a graduate course (SUNY Buffalo) in May 2005.

Acknowledgement

I would like to thank my dear parents, Masao and Setsuko.

Notes

¹ This article was originally written as a term paper for a graduate course (SUNY Buffalo) in May 2005.

² The welfare is calculated as the equally-weighted sum of producer's surplus (PS) and consumer's surplus (CS) in each country.

³ For example, consider the case where in a single market there exists two types of n firms (x) and m firms (y) with marginal costs c_x and c_y (c_x  < c_y ), respectively. Clearly, as the degree of competitiveness increases (n → ∞, m → ∞), m firms (y) exit from the market. On the other hand, Proposition 1 shows that in the long run equilibrium, an exchange rate is always adjusted so that each type may have an incentive to enter both countries, regardless of the asymmetry in market's attributes, or regardless of the disparity in firm's marginal costs.

⁴ n = m = 5 is a more competitive case than n = m = 1.

⁵ This larger deviation in exchange rate seems to explain the mechanism of so-called ‘overshooting’, from a different angle from existing related literatures, although here we are calculating a long-run sustainable equilibrium.

⁶ This does not necessarily imply that a fixed exchange rate regime is ‘better’ than a free exchange rate regime, because normally there is no guarantee that e =  holds, and also because the weight of each country in welfare is equally set at 0.5.