Text: Question 13 (20 points)
Consider the following closed economy:
Consumption: C = 325 + 0.5(Y - T) - 500r
Investment: I = 200 - 500r
Real money demand: L(i, Y) = 0.5Y - 1000i
Expected inflation: πe = 0
Money supply: MS = 6000
Full-employment level of output = 1000
Note: In this economy, consumption is not only dependent on disposable income (as we normally assumed) but also on the real interest rate. Interest rates, i and r, are expressed in decimal points, i.e., if r = 0.5, then r = 50%.
a) Derive the IS and LM equations as functions of exogenous variables. (4 points)
b) The government runs a balanced budget; government purchases (G) and taxes (T) are both equal to 150. Calculate the full-employment values of the real interest rate, price level, consumption, and investment. (6 points)
c) Now suppose that government purchases increase to 250 and there is no change in taxes. Assuming that the economy was initially at full employment, what are the new values of output, the real interest rate, price level, consumption, and investment in the short run? In the long run? (10 points)