2 A model of currency unions Consider the model we learned in class, in which tradables are endowed and the current account is exogenous: cr = yr - x, and non-tradables are produced linearly with labor, CNT = UNT = AE. Because of this, APNT = W. Agents have utility log cr + log cNT, and face the budget constraint ecr + PNTCNT = wLte(yT - x). 1. Take the first order conditions of the agent with respect to cr and CNT. UIUC 2. Plug in the market-clearing conditions for tradables and non-tradables to find an equa- tion relating employment, wages, the exchange rate, and the tradable endowment/the current account. 3. Suppose, in Archenland, yr = 3 and x = 1. If L = 1, and Wt-1 = 1, what must e, the exchange rate, be to have full employment and no wage inflation? 4. What about in Narnia, which is the same, except that x = -1? 5. Suppose Narnia and Archenland are in a currency union and that the exchange rate gets set to be e = 5. As in class, we'll assume that is must be the case that E