The following set of equations describe an economy: a. Find a numerical equation

Question

The following set of equations describe an economy:

a. Find a numerical equation relating planned aggregate expenditure to output and to the real interest rate.

Instruction: Enter the value for mpc rounded to two decimal places.

PAE = _____ plus or minus? ___r plus or minus?  ____Y.

b. At what value should the Fed set the real interest rate to eliminate any output gap? (Hint: Set output Y equal to the value of potential output given above in the equation you found in part a. Then solve for the real interest rate that also sets planned aggregate expenditure equal to potential output.)

Instruction: Enter your response as an integer value.

Real rate of interest: ____%.

C = 14,400 + 0.75(Y – T) – 50,000r I p = 7,000 – 24,000r G = 8,500 NX = 2,000 T = 9,000 Y* = 65,080

Explanation / Answer

(a)

PAE = C + I + G + NX

= 14,400 + 0.75(Y - 9,000) + 7,000 - 24,000r + 8,500 + 2,000

= 31,900 + 0.75Y - 6,750 - 24,000r

PAE = 25,150 - 24,000r + 0.75Y

(b)

When Y = 65,080, and equating Y with PAE,

Y = 25,150 - 24,000r + 0.75Y

0.25Y = 25,150 - 24,000r

0.25 x 65,080 = 25,150 - 24,000r

16,270 = 25,150 - 24,000r

24,000r = 8,880

r = 0.37

Real rate of interest = 37%

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