In a certain economy, the components of aggregate spending are given by: C = 500 + 0.8(Y - T) - 300r
I = 200 - 400r
G = 200
NX = 10
T = 150
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 6 percent is ___, and the eventual impact on short-run equilibrium output is ______.

Question

Quizplus · Accepted Answer

Recall that aggregate expenditure Y = C + I + G + NX. Substituting into the equation gives Y = 500 + 0.8(Y - 150) - 300r + 200 - 400r + 200 + 10. Collecting terms yields Y = [790 -700r] + 0.8Y, where r is the rate of real. Thus, a one-percentage-point increase in r would immediately decrease aggregate expenditure by 700 × (0.01) = 7. At a real interest rate of 5 percent, we get Y = [790 -700(.05)] + 0.8Y or Y = 755 + 0.8Y. Solving for Y, we get Y - .8Y = 755 or Y = 3,775. At a real interest rate of 6 percent, we get Y = [790 -700(.06)] + 0.8Y or Y = 748 + 0.8Y. Solving for Y, we get Y - .8Y = 762 or Y = 3,740. So the short-run equilibrium changes from 3,775 to 3,740, a decrease by 35 units. In other words, the multiplier in this economy is 5 (35/7).

In a Certain Economy, the Components of Aggregate Spending Are