In this chapter we characterize the exchange rate in a general-equilibrium setting using an extended version of the model described in Chapter 3. Relative to the monetary models of the exchange rate, equilibrium models offer the advantage of being based on strong microeconomic foundations. However, existing equilibrium models of the exchange rate, like the basic model described in the previous chapter, often depend on very specific assumptions about the number of goods and countries, the utility functions and production processes, and the type of frictions in the international-goods markets. See, for example, Stockman (1980), Lucas (1982), Domowitz and Hakkio (1985), Svensson (1985a, 1985b), Hodrick and Srivastava (1986), Stulz (1987), Stockman and Dellas (1989), Dumas (1992), Engel (1992a, 1992b), Backus and Smith (1993), Bekaert (1994), and Sercu, Uppal, and Van Hulle (1995). In contrast, the framework we develop in this chapter is one where utility functions are quite general and can differ across countries, and where commodity markets may be imperfect. We find that with financial markets that are complete and integrated, the nominal exchange rate mirrors differences in initial wealths and marginal indirect utilities of nominal spending. Differences in marginal indirect utilities may arise from commodity market imperfections and/or differences in consumption preferences, time preferences, or risk aversions.

To relate these marginal indirect utilities to observable variables so that one can evaluate the model empirically, we then restrict utility functions to be homothetic with constant relative risk aversion (CRRA).