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106 CHAPTER 4. THE LUCAS MODEL(76)⇒equilibrium.In order to study the exchange rate, we need to have a monetaryeconomy. The problem is that there is no role for Þat money in theArrow—Debreu environment. The way that Lucas gets around thisproblem is to require people to use money when they buy goods. Thisrequirement is called a ‘cash-in-advance’ constraint and is a popularstrategy for introducing money in general equilibrium along the linesof the transactions motive for holding money. A second popular strategythat puts money in the utility function will be developed in chapter9.The models we will study in this chapter and in chapter 5 haveno market imperfections and exhibit no nominal rigidities. Marketparticipants have complete information and rational expectations. Whystudy such a perfect world? First, we have a better idea for solvingfrictionless and perfect-markets models so it is a good idea to start infamiliar territory. Naturally, these models of idealized economies willnot fully explain the real world. So we want to view these models asproviding a benchmark against which to measure progress. If and whenthe data ‘reject’ these models, take one should note the manner in whichthey are rejected to guide the appropriate extensions and reÞnementsto the theory.There is a good deal of notation for the model which is summarizedin Table 4.1.4.1 The Barter EconomyConsider two countries each inhabited by a large number of individualswho have identical utility functions and identical wealth. People maybelieve that they are individuals but the respond in the same way tochanges in incentives. Because people are so similar you can normalizethe constant populations of each country to 1 and model the people ineach country by the actions of a single representative agent (household)in Lucas model. This is the simplest way to aggregate across individualsso that we can model macroeconomic behavior.‘Firms’ in each country are pure endowment streams that generatea homogeneous nonstorable country-speciÞc good using no labor or