Consider an economy with the following data: C = 400, I = 150, G = 300, T = 300, d = 5, b = .8, = .5, r = 2.

a Derive the expression of the IS, MP, and AD curves.

b Calculate the real interest rate and and aggregate output for = 2 and = 4.

c Draw a graph of the IS. MP, and AD curves. Label the points given in (b)

d Suppose the Fed lowers r to 1. Calculate the new equilibrium values of income and interest rates for this new level of r and the inflation rates in (b). Show the shifts of the curves using the same graphs as in (c).