The following set of equations describe an economy C 1600008

The following set of equations describe an economy: C 16,000+0.8(Y-T)-40,000r ,p = 8.000-24.000 G 8,500 NX 2,000 T9,000 Y 85,300 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- 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 (Click to select Click to select) Y. interest rate that also sets planned aggregate expenditure equal to potential output.) Instruction: Enter your response as an integer value. Real rate of interest:

Solution

Use the fact that PAE = C + I + G + NX and that PAE = Y at equilibrium

a) PAE = 16000 + 0.8(Y - 9000) - 40000r + 8000 - 24000r + 8500 + 2000

PAE = 16000 + 0.8Y - 7200 - 64000r + 18500

PAE = 27300 - 64000r + 0.8Y

This is the required equation

b) At Y* = 85300, we find that the value of r is

PAE = Y

85300 =  27300 - 64000r + 0.8*85300

10240 = 64000r

r* = 16%.

The required value of interest rate is 16%