2. Consider the IS / LM model, assuming consumption demand is C (Y) = b(Y T) and in vestment demand is I (r) = f'r, where b E (0, 1) and f > O are constants, 'r is the real in terest rate, Y is GDP, and T 2 0 is exogenous taxes. Money demand is L(Y, 'r) = Y r. The price level is xed at one, and ination expectations are zero. Exogenous govern ment purchases are G 2 0, and the exogenous money supply is M S > 0. Assume the constants and exogenous variables are such that in IS / LM equilibrium the endogenous variables are all positive. Net exports are zero. (a) (b) (C) Assuming the interest rate is xed (that is_, ignoring money demand and the LM curve), solve for GDP in terms of b, T, I, r, and G. What is the government purchases multiplier % (when r is xed)? Now reintroduce money demand and the resulting LM curve. Solve for IS / LlVI equilibrium GDP (Y*) in terms of the constants and exogenous variables. What is the equilibrium government purchases multiplier that incorporates an adjusting interest rate %)? (Hint: You'll need to solve for two unknowns, Y and i", using two equations, IS and LM.) Is it bigger or smaller than the multiplier in part (a)? Give a brief intuitive explanation for your answer in a few sentences. Returning again to the xed 'r case (in part (a)), how does GDP change (if at all) when G and T are increased by the same amount? Your answer is the Keynesian \"balancedbudget multiplier,\" which doesn't increase government debt since taxes rise in tandem with government purchases