Many students rst encounter the government spending multiplier during their initial exposure to macroe conomics. The multiplier measures the size of the increase in output caused by an increase in government spending: BIC/6G. Here, we'll consider its size in the open economy. Consider the following linear version of the AADD model in the text: Consumption is given by C = {1 s)Y and the current account balance is given by CA 2 (1E mY. {In macroeconomics textbooks, s is sometimes referred to as the marginal propensity to save and m is called the marginal propensity to import.) Then the conditions of equilibrium in the goods market and the money market are: Y=C+I+G+CA={13)Y+I+G+aEmY MS/szYdR (a) On the assumption that the central bank can hold both the interest rate R and the exchange rate E constant, and assuming that investment I also is constant, what is the effect of an increase in gov ernment spending G on output Y? (This number is often called the openeconomy government spending multiplier, but as you can see it is relevant only under strict conditions.) Explain your result intuitively. [b] Notice that, to complete the model described there, we must add the interest parity conditions. We can use our usual linear approximation of UIP: R = 3* + (E'3 E) f E. Also observe also that if Y} is the full employment output level, then the longrun expected exchange rate, E5, satises the equation: Y; 2 [GE6 +I +G)/(s+ m]. (We are again taking investment I as given.) Using these equations, demon strate algebraically that if the economy starts at full employment with R = R', a permanent increase in G has no effect on output. \"lhat is the effect on the exchange rate? How does the exchange rate change depend on a, and why? (c) Using the model from part b, solve for Y as a function of G. What is the government spending multiplier for temporary Changes in G {those that do not alter E5)? How does your answer depend on the paramieters a, b, and d, and why