3 An economy is described by the following equations: Desired consumption Cd = 600 + 0.8(Y - T) - 500,.. Desired investment Id = 400 - 500r. Real money demand L = O.5Y - 200i, for i > O. Government purchases G and taxes T both equal 1000. The initial price level P equals 2.0, and expected inflation It' is zero. Full-employment output y is 8000. Notice that the real money demand function above is defined only for positive values of the nominal interest rate. We assume that, when the nominal interest rate equals zero, people are willing to hold as much money as the central bank wishes to supply; this assumption implies that the LM curve becomes horizontal for zero values of the nominal interest rate. n. Show that in this economy the requirement that the nominal interest rate must be greater than or equal to zero is not consistent with full employment. That is, the economy is in a "liquidity trap" (refer to the Application "The Zero Bound", pp. 424-427). Can monetary policy alone restore full employment in this economy? Why or why not? h. Find a combination of the money supply M and government purchases G that restores full employment while keeping the nominal interest rate at zero. Discuss the relevance of this policy to the case of Japan in the 1990s. Assume that the price level and inflation expectations are unchanged.