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122 CHAPTER 4. THE LUCAS MODELRearranging (4.54) gives the nominal exchange rateS t = u 2(c xt ,c yt ) M t y t. (4.55)u 1 (c xt ,c yt ) N t x tAs in the monetary approach, the fundamental determinants of thenominal exchange rate are relative money supplies and relative GDPs.The two major differences are Þrst that in the Lucas model the exchangerate depends on preferences (utility), and second that it doesnot depend explicitly on expectations of the future.(94)⇒The solution under constant relative risk aversion utility. Using theutility function (4.22), the equilibrium real exchange rate is q t = ((1 −θ)/θ)(x t /y t ). The income terms cancel out and the exchange rate isS t =The Euler equations are" µCt+1e t= βE tx tC te ∗ " µCt+1t= βE tq t y t C t" µCt+1r t= βE tx tC t(1 − θ) M t. (4.56)θ N t (1−γ)ÃMt (1−γ)ÃNt (1−γ)Ã∆Mt+1rt∗ " µCt+1 (1−γ)Ã1 − θ= βE tx t C t θ+ e !#t+1, (4.57)M t+1 x t+1!#+ e∗ t+1, (4.58)N t+1 q t+1 y t+1+ r !#t+1, (4.59)M t+1 x t+1!#∆N t+1+ r∗ t+1. (4.60)N t+1 x t+1Just as you can calculate the equilibrium price of nominal bondseven though they are not traded in equilibrium, you can compute theequilibrium forward exchange rate even though there is no explicit forwardmarket. To do this, let b t be the date t dollar price of a 1-periodnominal discount bond that pays one dollar at the beginning of periodt+1, and let b ∗ t be the date t euro price of a 1-period nominal discountbond that pays one euro at the beginning of period t+1. By coveredinterest parity (1.2 ), the one-period ahead forward exchange rate is,F t = S tb ∗ tb t. (4.61)