If planned aggregate spending in an economy can be written as PAE = 15,000 + 0.6Y - 20,000r, and potential output equals 36,000, what real interest rate must the Federal Reserve set to bring the economy to full employment? 2 percent 3 percent 4 percent 5 percent

3 percent.

Explanation:

Given that,

Potential output, Y = 36,000

Planned aggregate expenditure:

PAE = 15,000 + 0.6Y - 20,000r

We can rewrite the above equation as follows:

Y = 15,000 + 0.6Y - 20,000r

Y - 0.6Y = 15,000 - 20,000r

0.4Y = 15,000 - 20,000r

Now, we are substituting the value of potential output,

0.4 (36,000) = 15,000 - 20,000r

14,400 = 15,000 - 20,000r

20,000r = 15,000 - 14,400

r = 600 : 20,000

= 0.03 or 3%

Therefore, the Federal Reserve must set the real interest rate at 3% to bring the economy to full employment.