Suppose that the economy is characterized by the following behavioural equations: Consumption: C = 1000 + [1.9 (Y - T) Real investment: I = 210 + [1.1V li Government spending: G = 150+&1Y Tax revenue: 1' = 250 + OESY Central bank policy: i = E + &5(n-ET) Aggregate supply (AS) relation: 1': = are + 0.0005(Y - Y\") The neutral rate of interest is in=0.035, the inflation target of the central bank is =0.025, the natural level of output is Y\" = 8800. and the current expected value of'inflation is f=0.01. a} Derive the IS relation, and draw it in {i, Y} space. Explain its meaning in words. (Hint: rewrite the goods market equilibrium as an equation with i on the lefthand side use the parameter numbers given above). (2 marks) b} Substitute the central bank policy relation into the real investment relation, and then derive the AD relation and draw it in {E,Y} space. Explain its meaning in words. (Hint: solve for an equation with E on the lefthand side - use the parameter numbers given above). (2 marks) {:1 Using the AS and AD relations. solve for the current shortrun equilibrium inflation rate, m and output, Y. Are these shortrun equilibrium values greater or less than their mediumrun values? (3 marks) d} Solve for the Current short-run equilibrium interest rate, i. Is it greater or less than the neutral interest rate. in (=.035}. (1 mark) e} Calculate the medium-run equilibrium values of real investment, I, consumption. C, and government expenditure, G. Confirm that Yn = C+I+G in the medium run. (2 marks)