In Econland,the components of planned aggregate expenditure are given by:
C = 500 + 0.75(Y - T)- 500r
I = 300 - 500r
G = 400
NX = 30
If potential output equals 4,680,net taxes equal 40 and the central bank sets the interest rate at 0.05 (5%),then the bank must _______ the interest rate to ________ to restore full employment.
A) raise;6%
B) raise;7%
C) lower;4%
D) lower;3%
E) lower;2%

Question

Quizplus · Accepted Answer

To restore full employment, we need to find the equilibrium level of output where aggregate expenditure equals potential output.

AE = C + I + G + NX

Substituting the given values:

AE = (500 + 0.75(Y - T)- 500r) + (300 - 500r) + 400 + 30

AE = 1230 + 0.75(Y - T) - 1000r

At full employment, Y = 4680. Substituting that in, we get:

4680 = 1230 + 0.75(4680 - 40) - 1000r

Simplifying, we get:

1000r = 2930

r = 2.93%

Since the central bank has set the interest rate at 5%, they need to lower it by 2.07 percentage points to 2.93% to restore full employment. Rounded to the nearest whole number, this is a decrease of 3%.

Therefore, the answer is D) lower;3%.

In Econland,the Components of Planned Aggregate Expenditure Are Given By