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118 CHAPTER 4. THE LUCAS MODELIn equilibrium, this is offset by the discounted expected marginal utilityof the one-dollar payoff, βE t [u 1 (c xt+1 ,c yt+1 )/P t+1 ]. Under the constantrelative risk aversion utility function (4.22) we have" µCt+1 (1−γ)#M tb t = βE t . (4.39)C t M t+1If i t is the nominal interest rate, then b t =(1+i t ) −1 . Nominal interestrates will be positive in all states of nature if b t < 1 and is likely to betrue when the endowment growth rate and monetary growth rates arepositive.4.3 The Two-Money Monetary EconomyTo address exchange rate issues, you need to introduce a second nationalcurrency. Let the home country money be the ‘dollar’ and theforeign country money be the ‘euro.’ We now amend the transactionstechnology to require that the home country’s x—goods can only bepurchased with dollars and the foreign country’s y—goods can only bepurchased with euros. In addition, x−dividends are paid out in dollarsand y−dividends are paid out in euros. Agents can acquire the foreigncurrency required to Þnance consumption plans during securitiesmarket trading.Let P t be the dollar price of x, Pt∗ be the euro price of y, andS tbetheexchangerateexpressedasthedollarpriceofeuros. M t is theoutstanding stock of dollars, N t is the outstanding stock of euros andthey evolve over time according toM t = λ t M t−1 , and N t = λ ∗ t N t−1,where (λ t , λ ∗ t ) are exogenous random gross rates of change in M andN.If the domestic household received transfers only of M, it faces foreignpurchasing-power risk because it it also needs N to buy y-goods.Introducing the second currency creates a new country-speciÞcriskthathouseholds will want to hedge. The complete markets paradigm allowsmarkets to develop whenever there is a demand for a product. The