Question

Consider two economies. In economy A:  autonomous consumption equals 700, the marginal propensity to consume equals 0.80, taxes are fixed at 50, investment is 100, government spending is 100, and net exports are 40.

In economy B: autonomous consumption equals 1000, the marginal propensity to consume equals 0.8, taxes are proportional to income such that consumers pay 25% of their income as taxes, investment is 250, government purchases are 150, and net exports are 400.

Question 1: What is the planned aggregate expenditure (PAE) in each economy?

Question 2:What is the short-run equilibrium output in each economy?

Question 3: In which economy is the spending multiplier higher?

Question 4:Suppose autonomous consumption fall by 500 in each economy. Which economy will see a higher drop in GDP? Compute the equilibrium output in each economy.

Answer 1

1. For economy A : PAE = C + I + G + NX

C = Autonomous consumption + MPC (Y-T)

C = 700 + 0.80 (Y- 50)

C = 660 + 0.80Y

PAE = 660 + 0.80Y + 100+ 100+ 40

PAE = 900 + 0.80Y

For ecoonomy B : PAE = C+I+G+NX

C = Autonomous consumption + MPC ( Y-tY)

C = 1000 + 0.80 (Y - 0.25Y)

= 1000 + 0.80(0.75Y)

= 1000 +0.6Y

PAE = 1000+ 0.6Y + 250 + 150+ 400

PAE = 1800 +0.6Y

2. Short run equilibrium occurs when PAE = Y

For economy A : Y = 900+0.80 Y

0.20Y = 900

Y = 4500 (Equilibrium output of economy A)

For economy B : Y = 1800+ 0.6Y

0.4 Y = 1800

Y = 4500 (Equilibrium output of economy B)

3. Spending multiplier in economy A = 1/1-MPC = 1/1-0.80= 1/0.2 = 5

Spending multiplier in economy B = 1/1-0.60 = 2.5

Multiplier is higher in economy A.

4. Suppose autonomous consumption fall by 500 in each economy. Then , for economy A : GDP will decrease by (5)(500)= 2500 , so the equilibrium in economy A = 4500-2500= 2000.

And for economy B , GDP will decrease by (2.5)(500)= 1250 , so the equilibrium in economy B = 4500-1250= 3250.

The higher drop in GDP is in economy A.