This question is about AD and AS that we briey 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 sulnnizn'ized by Y : 9'30 + 1.563 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 {rmstThe 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 = Sill-71' 31' + 2r where M is money supply and P is the price level. {a} (b) Derive the equation for the AD (aggregate demand) curve (3points) Denoting the full employment output by 37, solve the expression for the natural real interest rate {interest rate when output is at full employment) and comment. on how changes in government expenditure1 taxes' real money balance (ii-I P), and full employment affect this rate [look at the sign of the coefcients and explain their economic: intuitions). (3 points} Assume G = T = 100st = 3115, then what will be the reduced form AD equation? (3 points} If the equation for the SEAS is given by Y = "i7 + 2[P P9],where P is actual price and Peis expected price and Y is full employment. output. Show the the graph for the SEAS and explain what happens to the. curve if expected price increases (4 points) Assuming i7 = 800 and expected price is P\" = 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) Is the SR equilibrium situation shown in question e an inationary gap or a recessionary gap? \"That will happen to the economy in the long run (how does it move to the long run?) (3 points)