Question

The following functions describe the behavior of major macroeconomic variables in an economy where prices are fixed: C = 400 + 0.9Yd I = 270 – 2000r G = 70 T = -40 + 0.2Y X = 45 IM = 41 + 0.12Y r=3% Y* = 1,725

c. Calculate the cyclical deficit/surplus. d. Suppose the government wants to close the recessionary gap and move us back to Y* using changes in G. Calculate the change in G necessary to close the gap. Is this an increase or decrease in G? e. Suppose instead the Federal Reserve wants to close the recessionary gap and move us back to Y* using changes in the interest rate. Calculate the change in the interest rate that will be necessary to close the gap. Is this an increase or decrease in the interest rate?

Answer 1

C = 400 + 0.9Yd; I = 270 – 2000r; G = 70; T = -40 + 0.2Y;

X = 45; IM = 41 + 0.12Y; r=3%; Y* = 1,725

Que(c) For cyclical deficit/surplus, we need to find the value of Y and compare with Y* -

C = 400 + 0.9Yd = 400 + 0.9(Y-T) = 400 + 0.9(Y- (-40+0.2Y) = 400 + 0.9 ( Y + 40 - 0.2Y)

C = 436 + 0.72Y

I = 270 - 2000* 0.03 = 210

We know - Y = C+ I + G + X - IM = 436 + 0.72Y + 210 + 70+ 45-41+ 0.12Y

Y = 720 + 0.84Y 0.16Y = 720 Y = 4500

Since Y* is 1725, the economy has an economic surplus of 4500-1725 = 2775 units

Que(d)   From above we have -

Y = 436 + 0.72Y + 210 + G+ 45-41+ 0.12Y

To reduce the gap, Y = Y* = 1725

Y = 650 + 0.84Y + G G = 0.16*1725-650= -374 units

To remove the gap G has to decrease from 70 to -374 units.

Que (e) Y = Y* to close the gap and the rest is the same except r. Since we have -

Y = C+ I + G + X - IM = 436 + 0.72Y + 270-2000r + 70+ 45-41+ 0.12Y

Y = 780+ 0.84Y-2000r 2000r = -0.16*1725+780 = 504

   r = 0.252 = 25.2% ; interest rate should increase from 3% to 25.2% to remove the gap.