Assume the following equations summarize the structure of an economy.
C = Ca + 0.8(Y - T)
Ca = 260 - 10r
T = 200 + 0.2Y
(M > P)d = 0.25Y - 25r
Ms > P = 2,000
Ip = 1,900 - 30r
G = 1,800
NX = 700 - 0.14Y
(a) Derive the equation for the IS curve.
(b) Derive the equation for the LM curve.
(c) Compute the equilibrium interest rate (r) and real output (Y).
(d) Suppose consumer and business confidence decline, resulting in decreases in the amounts of autonomous consumption and planned investment by 40 and 60, respectively. Derive the new equation for the IS curve and compute the new equilibrium interest rate (r) and real output (Y).
(e) Suppose that natural real GDP equals the amount of real output that you computed in part c. Compute the amount of a cut in autonomous taxes that would be necessary in order to overcome the declines in consumer and business confidence and restore real output to natural real GDP.
(f) Suppose that instead of fiscal policy, monetary policy is used to restore real output to natural real GDP. Compute by how much the Fed would have to increase the money supply in order to do so.
(g) Compute the amounts of autonomous consumption and planned investment associated with each of the policies described in parts e and f. Explain which policy is likely to result in
a higher rate of growth in real output over the long run.