For the economy described below C 2600 05Y T 12000r I p

For the economy described below:

C

= 2,600 + 0.5(Y – T) – 12,000r

I ^p

= 1,800 – 12,000r

G

= 2,200

NX

= 0

T

= 3,500

a. Suppose that potential output Y* equals 5,860. What real interest rate should the Fed set to bring the economy to full employment? You may take as given that the multiplier for this economy is 2.

Instruction: Enter your response as an integer value.

Real rate of interest: ________ %.

b. Suppose that potential output Y* equals 4,900. What real interest rate should the Fed set to bring the economy to full employment? You may take as given that the multiplier for this economy is 2.

Instruction: Enter your response as an integer value.

Real rate of interest: ______%.

c. Show that the real interest rate determined in part a sets national saving equal to planned investment when the economy is at potential output. This result shows that the real interest rate must be consistent with equilibrium in the market for saving when the economy is at full employment.

Instruction: Enter your response as an integer value.

Planned investment I ^p =____ .

National saving S = ____.

Solution

a. Real rate of interest: 8%.

Explanation:

Y = C + Ip + G +NX

   5860 = 2,600 + 0.5(5860 –3500) – 12,000r + 1,800 – 12,000r + 2200 + 0

5860 = 2,600 + 1180 – 24,000r + 1,800 + 2200

    5860 = 7780 – 24,000r

    24,000r = 1920

   r = 1920 / 24000 = 0.08 = 8%

b.  Real rate of interest: 10%.

    Explanation:

     Y = C + Ip + G +NX

   4900 = 2,600 + 0.5(4900 –3500) – 12,000r + 1,800 – 12,000r + 2200 + 0

   4900 = 2,600 + 700 – 24,000r + 1,800 + 2200

   4900 = 7300 – 24,000r

    24,000r = 2400

   r = 2400 / 24000 = 0.1 = 10%

c. Planned investment I ^p = 840.

     National saving S = 840.

Explanation:

     When real interest \'r\' = 0.08 and Y = Y^* = 5860:

    C = 2,600 + 0.5(5860 – 3500) – 12,000(0.08)

       = 2820

   I_p = 1,800 – 12,000(0.08)

      = 840

S = Y^* - C - G

= 5860 - 2820 - 2200

= 840

National saving equals planned investment when the economy is in equilibrium at potential output, consistent with equilibrium in the market for saving. This tells you that the natural real interest rate, the one that sets Y=Y* is also the one that sets S=I.