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Model of output, exchange rate, and interest rate de- termination The equations of the model we developed in class are: (1) : Money Market Clearing: ? = bile. Y ) Et-F E (2) : Uncovered Interest Parity: = i* + EPpP* (3) : Goods Market Equilibrium: Y =C (Y -T)+1({)+G+TB (Y T, 5 Y*) I is the nominal exchange rate (units of domestic currency per unit unit of foreign currency), E is the expected nominal exchange rate, P is the domestic price level, 7 is the domestic interest, * is the foreign interest rate, Y* is foreign output, and M? is the money supply. We assume that E* is constant unless told otherwise. L ('money demand') is decreasing in its first argument and increasing in its second ar- gument. C' ('consumption demand') is increasing in Y T, and T'B ('trade balance') is decreasing in Y, increasing in Y*, and increasing in the real exchange rate, %. We also have C(Y = T) +TB (Y - T, %,Y*) is increasing in Y, but it increases (decreases) by less than 1 when Y increases (decreases) by 1. G denotes government expenditures and [ denotes investment, which is decreasing in 7. In the short run, the price level is sticky. The LM schedule represents Y, combinations such that equation (1) is satisfied. The IS schedule represents Y, i combinations such that equation (2) and (3) are satisfied. Under a flexible or floating exchange rate, the equilibrium nominal exchange rate is free to adjust and money supply is constant (unless told otherwise). Under a credible fixed exchange rate, money supply adjusts so that the nominal exchange rate is constant at the target level. Question 2 Assume that initially the IS curve is given by IS:Y =14- 15T 30t +2G and that the price level P is 1, and the LM curve is given by: LM;: M=Y(12) The home central bank uses the interest rate as its policy instrument. Initially, the home interest rate equals the foreign interest rate of 10%. Taxes and government spending both equal 2. Call this case 1. 1. According to the I5; curve, when = 0.1 what is the level of output Y? Assume that this is the desired full-employment level of output. 2. According to the LM; curve, at this level of output, what is the level of the home money supply? 3. Assume that the forex market equilibrium is given by 1-F = 7 + E where the two terms on the right are the foreign interest rate and the expected de- preciation of the home currency (the expected future exchange rate is 1), respectively. What is the equilibrium spot exchange rate? 4. There is now a foreign demand shock such that the IS curve shifts left by 1.5 units at all levels of the interest rate. The new IS curve is given by 1Sy : Y =125 -15T 301+ 2G The government asks the Central Bank to stabilize the economy at full employment. To stabilize and return output back to the desired level, according to this new IS curve, by how much must the interest rate be lowered from its initial level of 0.1, assuming that T and G remain at 2. 5. At the new lower interest rate and at full employment, on the new LM curve (LM;), what is the new level of the money supply? 6. According to the foreign exchange rate equilibrium, what is the new level of the spot exchange rate? 7. Return to part 4. Now assume that the Central Bank keeps the interest rate fixed at 10%. In this case, what is the new level of output? What is the money supply? 8. Return to part 4. Assume again that the Central Bank keeps the interest rate at 10%. Moreover, assume also the government decides to use fiscal policy G to stabilize output. Using the new IS curve, by how much must government spending be increased to achieve this goal