Consider a closed economy with the following goods and money market equilibrium equations: Y = AE = C(Y) + 1(i) + G .. (1) M L(Y,I) == (2) Further, assume the following functional forms for the consumption, investment and liquidity preference curves, respectively. C(Y) = Co + C(YT) I(i) = a - bi L(Y,i) = kY-hi + u .(3) .(4) .(5) ****** (a) Assume the tax function includes only an autonomous component (T = To) and price i. Derive the goods and money market equilibrium income (Y) and interest rate (i) ii. Derive the slopes of the IS and LM curves. Indicate the sign in each case and provide an intuitive explanation. iii. How does the slope of the IS curve compare to that of the investment curve? iv. How does the slope of the LM curve compare to that of the liquidity preference curve? v. Derive the government expenditure multiplier and explain. (b) Using the results in (a), derive the simultaneous goods and money market equilibrium income (Y") and interest rate (i") (c) From your results in (b) derive the fiscal and monetary policy multipliers and explain them. (d) What is the relationship between the fiscal and monetary policy multipliers and i.The interest sensitivity of the investment curve? ii. The interest sensitivity of the liquidity preference curve? (e) How does the fiscal policy multiplier compare to the government expenditure multiplier? (f) Now, assume the tax function includes a proportional component (T = To + tY). i. How does the fiscal policy multiplier in this case compare to that in (c) above? ii. If the Central Bank increases the nominal money supply by 1%, what will be the impact on the domestic interest rate? Provide the numerical magnitude of the impact for the given values of MPC=0.7, MTR=0.3, elasticity of investment with respect so the interest rate=0.2, elasticity of money demand with respect to the income= 0.5, and elasticity of money demand with respect to interest rate=0.2