(40pts) 2. Consider the following model of s closed economy in the short run: CIGTPEYMd/P=540+0.8(YT)=37040r=500=100+0.25Y=C+I+G=PE(Equilibriumconditionforthegoodemarket).=0.5Y60r Suppose that the central bank sets the nominsl money supply M=1500. Goods msrket equilibrium is obtained when Y=C+I+G, while money market equilibrium is obtained when M/P=Md/P. NOTE: In this problem taxes have two components: a lump-aum component and a component that depends on income Y. You must take this into accosnt when deriving the IS equation. (20pta)s) (4pts)(i) What is the "tsox multiplier" for this economy? Find its slgebraic expression snd then find its numerical value. (4pta) (ii) Find the IS equation and the LM equation (as a function of P ) for this economy. (We do not yet know the value of P ) (6pts) (iii) Using the expressions you found in question 2(s)(ii) find the aggregate demand equation (which is a function of P ). Drsw a graph to illustrate the AD equation. (10pts) (iv) Now asume that P=2. Using the numerical IS snd LM equations for the economy solve for the equilibrium values of Y and r. What would be these equilibrium values if we had P=3 instead? Find these new equilibrium values of r and Y, and draw a graph (in Yr space) to explsin the impact of the incresse in the price on output and the interest rate. (7pts) b) Astuming again that P=2, consider an improvement in consumer confidence, such that sutonomous consumption expenditures incresse from 540 to 640 units. (That is, C=100 ). What is the impset of this change on the equilibrium output, on the equilibrium intereat rate and on consumption? Calculate. Explain your zesult. Draw a graph to illustrate. (8pta) c) If the central bank wanted to maint ain the interest rate constant after the change in C, by how much would it have to change the money supply? (Asume again that P=2.) Csleulate. Explain yous result. Drsw a graph to illustrate