Chapter 3:Problem 2
2. 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=1500-10r ,c=0.6 ,T=1800
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b. Autonomous planned spending, Ap, equals Ca − cTa + Ip + G + NX = 1,500 − 10r −.6(1,800) + 2,400 − 50r + 2,000 − 200 = 4,620 − 60r. Therefore, at an interest rate equal to 3, autonomous planned spending equals 4,620 − 60(3) = 4,440.
c. Since the marginal propensity to save equals 0.4 and the equilibrium level of income equals Ap /s, the equilibrium level of income equals 4,440/.4 = 11,100, given the interest rate equals 3.
d. Since autonomous consumption changes by 4 percent of any change in household wealth and the decline in the housing market in 2006–09 and drop in the stock market of 2007-09 reduces household wealth by 3 trillion dollars, the decrease in autonomous consumption that results from the decline in household wealth equals .04(3) = 120 billion.
e. Since the decrease in autonomous consumption that results from the decline in household wealth equals 120 billion, autonomous planned spending decreases by that amount as well. Therefore, the new amount of autonomous planned spending equals 4,440 – 120 = 4,320. Therefore, the new equilibrium level of income equals 4,320/.4 = 10,800, given the interest rate equals 3.
f. Using your answer to parts c-e, compute the value of the multiplier. The multiplier, k, equals ΔY/ΔAp = (10,800 − 11,100)/(4,320− 4,440) = (-300)/(-120) = 2.5.