Consider an economy in which consumption, taxes, and net exports all change as income changes. In addition, consumption and planned investment change as the interest rate changes. You are given the following information concerning autonomous consumption, the marginal propensity to consume, planned investment, government purchases of goods and services, and net exports: C = Ca + 0.85(Y - T) Ca = 225 - 10r; Ip = 1,610 - 30r G = 1,650 NX = 700 - 0.08Y; T = 100 + 0.2Y.
(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, Y = kAp.
(d) Using the equation for the IS curve, calculate the equilibrium level of income at an interest rate equal to 3.
(e) At the equilibrium level of income at an interest rate of 3, show that leakages equal injection.