4. (20 points) Consider the following linear version of the AA-DD model in the text: Consumption is given by C = (1 s)Y and the current account balance is given by CA = a E - 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 condition of equilibrium in the goods market is Y = C + I +G + CA = (1 - s)Y + I + G + aE mY. We will write the condition of money market equilibrium as M/P = bY DR. (a) (5 points) On the assumption that the central bank can hold both the interest rate R and the exchange rate E constant, and assuming that in- vestment I also is constant, what is the effect of an increase in government spending G on output Y? (This number is often called the open-economy government spending multiplier, but as you can see it is relevant only under strict conditions.) Explain your result intuitively. (b) (5 points) To complete the model we must add the interest parity condi- tions. Observe also that if yf is the fullemployment output level, then the long-run expected exchange rate, Ee, satisfies the equation: Yf (a E + I +G)/(s+m). (We are again taking investment I as given.) Us- ing these equations, demonstrate algebraically that if the economy starts at full employment with R=R*, an increase in G has no effect on output. What is the effect on the exchange rate? How does the exchange rate change depend on a, and why? (c) (10 points) We can express a linear approximation to the interest par- ity condition (accurate for small exchange rate changes) as: R = R* + (E E) /E. Adding this to the model, solve for Y as a function of G. What is the government spending multiplier for temporary changes in G (those that do not alter Ee )? How does your answer depend on the parameters a, b, and d, and why? 4. (20 points) Consider the following linear version of the AA-DD model in the text: Consumption is given by C = (1 s)Y and the current account balance is given by CA = a E - 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 condition of equilibrium in the goods market is Y = C + I +G + CA = (1 - s)Y + I + G + aE mY. We will write the condition of money market equilibrium as M/P = bY DR. (a) (5 points) On the assumption that the central bank can hold both the interest rate R and the exchange rate E constant, and assuming that in- vestment I also is constant, what is the effect of an increase in government spending G on output Y? (This number is often called the open-economy government spending multiplier, but as you can see it is relevant only under strict conditions.) Explain your result intuitively. (b) (5 points) To complete the model we must add the interest parity condi- tions. Observe also that if yf is the fullemployment output level, then the long-run expected exchange rate, Ee, satisfies the equation: Yf (a E + I +G)/(s+m). (We are again taking investment I as given.) Us- ing these equations, demonstrate algebraically that if the economy starts at full employment with R=R*, an increase in G has no effect on output. What is the effect on the exchange rate? How does the exchange rate change depend on a, and why? (c) (10 points) We can express a linear approximation to the interest par- ity condition (accurate for small exchange rate changes) as: R = R* + (E E) /E. Adding this to the model, solve for Y as a function of G. What is the government spending multiplier for temporary changes in G (those that do not alter Ee )? How does your answer depend on the parameters a, b, and d, and why