W3P1 Keynesian Cross

Question 1

Keynesian Cross Consider a closed economy to which the Keynesian Cross applies so that Y = AE (1) and aggregate expenditure is AE = C + I + G (2). Consumption is given by the equation C = 200 + 0.75 (Y − T). (3). I=300, G=300 and T=300.

What is equilibrium income Y?

Answer 1

Step 1 = combine equation 1,2 and 3 to get Y=C+I+G so Y=200+0.75(Y-T)+I+G
Make income Y the subject and plug in I=300, G=300 and T=300
Y-0.75Y=200-0.75T+I+G
Y=(200-0.75T+I+G)/(1-0.75)
Y=(200-0.75(300)+300+300)/(1-0.75)
Y=2300

Question 2

How much does equilibrium income Y decrease when G is reduced to 200? What
is the multiplier for government spending?

(So Y = AE (1) and aggregate expenditure is AE = C + I + G (2). Consumption is given by the equation C = 200 + 0.75 (Y − T). (3). I=300, G=200and T=300.)

Answer 2

Y=(200-0.75T+I+G)/(1-0.75)
Sub in T,I and G vals:
Y=(200-0.75(300)+300+200)/(1-0.75)
Y=1900
When G was 300, Y =2300, therefore income has decreased by 400
Gov multiplier is ΔY/ΔG=1/1-MPC
When the marginal propensity to consume MPC=0.75
ΔY/ΔG=1/1-0.75 = 4

Question 3

How much does equilibrium income Y decrease when T is increased by 100? What
is the multiplier for taxes?

(So Y = AE (1) and aggregate expenditure is AE = C + I + G (2). Consumption is given by the equation C = 200 + 0.75 (Y − T). (3). I=300, G=300 and T=400.)

Answer 3

New equilibrium with T = 400 gives Y=(200-0.75T+I+G)/(1-0.75)
Sub vals in: Y=(200-0.75(400)+300+300)/(1-0.75)
Y=2000
Income (Y) has decreased by 300
The tax multiplier is: ΔY/ΔG = MPC/1-MPC
When the marginal propensity to consume MPC=0.75, ΔY/ΔG = 0.75/(1-0.75) = -3

Question 4

How much does equilibrium income Y increase when both G and T are increased
by 100. What is the balanced budget multiplier?

(So Y = AE (1) and aggregate expenditure is AE = C + I + G (2). Consumption is given by the equation C = 400+ 0.75 (Y − T). (3). I=300, G=400 and T=400.)

Answer 4

New equilibrium with G = 400 and T = 400 gives:
Y=(200-0.75T+I+G)/(1-0.75)
Sub in vals:
Y=(200-0.75(400)+300+400)/(1-0.75)
Y=2400 thus income increases by 100
The balanced budget multiplier is:
ΔY/ΔG=(1/1-MPC) - (MPC/1-MPC)
ΔY/ΔG=1

Question 5

What is the balanced budget multiplier?

Answer 5

the sum of the government multiplier and tax multiplier

ΔY/ΔG=(1/1-MPC) - (MPC/1-MPC)

Question 6

What is the government multiplier?

Answer 6

ΔY/ΔG=1/1-MPC

Question 7

What is the tax multiplier?

Answer 7

ΔY/ΔG = MPC/1-MPC

Question 8

What is the equation for aggregate expenditure (AE)?

Answer 8

AE = C + I + G