In a certain economy, the components of aggregate spending are given by: C = 100 + 0.9(Y - T) - 500r
I = 150 - 1,000r
G = 200
NX = 50
T = 100
Given the information about the economy above, the immediate impact on aggregate expenditures of a one-percentage-point increase in the real interest rate (r) from 5 percent to 4 percent is ___, and the eventual impact on short-run equilibrium output is ______.

Question

Quizplus · Accepted Answer

Recall that Y = C + I + G + NX. Substituting into the equation gives Y = 100 + 0.9(Y - 100) - 500r + 150 - 1,000r + 200 + 50. Collecting terms yields Y= [410 -1,500r] + 0.9Y. Thus, a one-percentage-point decrease in r would immediately increase aggregate expenditure by 1,500 × (0.01) = 15. At a real interest rate of 5 percent, we get Y = [410 -1,500(.05)] + 0.9Y or Y = 335 + 0.9Y. Solving for Y, we get Y - .9Y = 335 or 0.1Y = 335 or Y = 3,350. At a real interest rate of 4 percent, we get Y = [410 -1,500(.04)] + 0.9Y or Y = 350 + 0.9Y. Solving for Y, we get Y - .9Y = 350 or 0.1Y = 350 or Y = 3,500. So the short-run equilibrium changes from 3,350 to 3,500, an increase by 150 units. In other words, the multiplier in this economy is 10 (150/15).

In a Certain Economy, the Components of Aggregate Spending Are