In an economy in which planned aggregate expenditure is given by PAE = 5,500 + 0.6Y - 20,000r,the central bank is currently setting the interest rate at 0.06 (6%).If potential output equals 9,750,the central bank must _______ the interest rate to ________ to restore full employment.
A) lower;4%
B) lower;5%
C) raise;7%
D) raise;8%
E) raise;9%

Question

Quizplus · Accepted Answer

Full employment corresponds to output being equal to potential output. We can find the equilibrium level of output by setting PAE equal to output Y:

PAE = Y
5500 + 0.6Y - 20000r = Y
0.6Y = 5500 + 20000r
Y = (5500 + 20000r)/0.6

To find the interest rate that restores full employment, we need to solve for the interest rate that makes Y equal to potential output:

9750 = (5500 + 20000r)/0.6
0.6*9750 = 5500 + 20000r
5850 = 5500 + 20000r
350 = 20000r
r = 0.0175 or 1.75%

The current interest rate of 6% is higher than the interest rate that restores full employment, so the central bank must raise the interest rate. The closest option is choice D, which says that the interest rate should be raised to 8%.

In an Economy in Which Planned Aggregate Expenditure Is Given