Question

1. For each the following economies, calculate equilibrium Y*, the multiplier, and the size of the recessionary or inflationary gap, if any.

• a) AE= 250 +.75Y , Yf= 1200
• b) AE= 400+ .9 Y, Yf= 3000
• c) AE= 300 +. 8Y, Yf=1500
• d) AE= 300+ .67 Y, Yf=1000

Answer 1

AE= Aggregate Expenditure, Yf= Anticipated output , Output=Y

a) AE= 250+.75Y, Yf= 1200

Y= 250 +.75Y

Y- 0.75Y = 250

0.25Y = 250

Y = 250 / 0.25

Y = 2500 / 25

Y = 1000

Multiplier = 1 / (1 - MPC)

= 1 / (1 - 0.75) = 1 / 0.25 = 100 / 25 = 4

Inflationary gap = Actual Output - Anticipated output

= 1000 - 1200 = 800

Therefore; Output (Y) = 1000, Multipiler = 4, Inflationary gap = - 800

b)

AE= 400 + 0.9Y, Yf= 3000

Y= 400 + 0.9Y

Y- 0.9Y = 400

0.1Y = 400

Y = 400 / 0.1

Y = 4000 / 1

Y = 4000

Multiplier = 1 / (1 - MPC)

= 1 / (1 - 0.9) = 1 / 0.1 = 10 / 1 = 10

Inflationary gap = Actual Output - Anticipated output

= 4000 - 3000 = 1000

Therefore; Output (Y) = 4000, Multipiler = 10, Inflationary gap = 1000

c)

AE= 300 + 0.8Y, Yf= 1500

Y= 300 + 0.8Y

Y- 0.2Y = 300

Y = 300 / 0.2

Y = 3000 / 2

Y = 1500

Multiplier = 1 / (1 - MPC)

= 1 / (1 - 0.8) = 1 / 0.2 = 10 / 2 = 5

Inflationary gap = Actual Output - Anticipated output

= 1500 - 1500 = 0

Therefore; Output (Y) = 1500, Multipiler = 5,  Inflationary gap = 0

d)

AE= 300 + 0.67Y, Yf= 1200

Y= 300 +.67Y

Y- 0.33Y = 300

0.33Y = 300

Y = 300 / 0.33

Y = 30000 / 33

Y = 909

Multiplier = 1 / (1 - MPC)

= 1 / (1 - 0.67) = 1 / 0.33 = 100 / 33 = 3.03

Inflationary gap = Actual Output - Anticipated output

= 909 - 1000 = - 91

Therefore; Output (Y) = 91, Multipiler = 3.03, Inflationary gap = - 91