Consider an economy in which taxes, planned investment, government spending on goods and services, and net exports are autonomous, but 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 Ca = 1,400 - 15r c = 0.5 Ip = 2,350 - 35r; G = 1,940 NX = - 200 Ta = 1,600.
(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) Using the equation for the IS curve, calculate the equilibrium levels of income at interest rates equal to 0, 3, and 6.
(e) Using your answers to part d, calculate the slope of the IS curve,
(f) Suppose that autonomous consumption rises by $40 billion, so that Ca = 1,440 - 15r. Explain whether this increase in autonomous consumption is caused by a rise or fall in consumer confidence. Derive the new equation for the IS curve.
(g) Using the equation for the new IS curve; calculate the new equilibrium levels of income at interest rates equal to 0, 3, and 6.
(h) Using your answers to parts d and g, explain whether the IS curve shifts to the left or right when autonomous consumption rises. Explain why the horizontal shift of the IS curve equals the multiplier times the change in autonomous planned spending.