This question is about AD and AS that we briefly reviewed at the beginning and meant to allow a closer look at how AD is derived by combining IS and LM equations. Suppose the IS (goods market equilibrium given by Y = C + I + G) is summarized by Y = 900+ 1.5G 1.2T - 4r where Y is real output; G and T and are government expenditure and taxes, respectively, with the bars showing that they are endogenously given. The intercept term (500) denotes the autonomous components of consumption and investment, which can change depending on household wealth and and sentiments of consumers and investors (firms). The negative relationship between real GDP and real interest rate (r) comes from the negative relationship between investment and interest rate. Similarly, assume that the LM is summarized by Y = 3M - 3P+2r where M is money supply and P is the price level. (a) Derive the equation for the AD (aggregate demand) curve (3points) (b) Denoting the full employment output by Y, solve the expression for the natural real interest rate (interest rate when output is at full employment) and comment on how changes in government expenditure, taxes, real money balance (MP), and full employment affect this rate (look at the sign of the coefficients and explain their economic intuitions). (3 points) (c) Assume G = T = 100, M = 345, then what will be the reduced form AD equation? (3 points) (d) If the equation for the SRAS is given by Y = + 2[P = P],where P is actual price and Peis expected price and is full employment output. Show the the graph for the SRAS and explain what happens to the curve if expected price increases (4 points) (e) Assuming Y = 800 and expected price is Pe = 120,compute the SR equilibrium given the reduced demand equation derived in question C [also indicate the answers using the AD-AS diagram] (4 points) (f) Is the SR equilibrium situation shown in question e an inflationary gap or a recessionary gap? What will happen to the economy in the long run (how does it move to the long run?) (3 points)