Assume the following equations summarize the structure of an economy.
C = Ca + 0.85(Y - T)
Ca = 260 - 10r
T = 200 + 0.2Y
(M > P)d = 0.25Y - 25r
Ms > P = 2,125
Ip = 1,500 - 30r
G = 1,700
NX = 500 - 0.08Y
(a) Compute the value of the multiplier.
(b) Derive the equation for the autonomous planned spending schedule, Ap.
(c) Derive the equation for the IS curve.
(d) Calculate the slope of the IS curve, ∆r/∆Y. (Use the equation of the IS curve to compute ∆Y/∆r. Then use the fact that the slope of the IS curve, ∆r/∆Y equals the inverse of ∆Y/∆r.)
(e) Derive the equation for the LM curve.
(f) Calculate the slope of the LM curve, ∆r/∆Y. (To do this, use the same hint as in part d.)
(g) Compute the equilibrium interest rate (r).
(h) Compute the equilibrium real output (Y).