Problem 1: In this exercise, we analyze the effects of technological change on the exchange rate. Suppose that for the "domestic" country L(R,Y)=Y()R() where ,>0. Here, measures the elasticity of demand for real cash to GDP (the percentage increaseof money demand caused by a percentage increase in GDP). Suppose that the GDP of the domestic country grows at a rate of g>0 and that the GDP of the "foreign" country, the interest rates, and the money supply in both countries are constant. 1. What is the growth rate of the exchange rate according to monetary theory? How does it depend on ? Can you explain the intuition behind this result? (Hint: if xt grows at rate gx we have that log(xt+1)/(xt)=gx Moreover log(x)y=ylog(x).) 2. Imagine that for the "foreign" country L(R,Y)=Y()R() and that the 'foreign' GDP Y* grows at the same rate g as domestic GDP. What is the new rate of depreciation of the domestic currency? Explain. 3. Now consider the general model of the long-run exchange rate. How do the predictions of this model with respect to items 1 and 2 differ from the model's approach to the long-run exchange rate