In the aggregate demand model in equilibrium GDP Y C IX ope

In the aggregate demand model in equilibrium, GDP (Y) = C +I+X (open economy). Where C+ consumption schedule+100+.75Y (consumption is a function of income). Where I+ planned investment+20 and X + net exports+40. Both are independent of GDP (Y). Use the information provided to complete the following: Calculate the equilibrium level of income or real GDP for this economy. What happens to equilibrium Y if Ig changes to 15? What does this outcome reveal about the size of the multiplier?

Solution

In equilibrium Y = AD = C(Consumption Expenditure) + I(Planned Investment) + X(Net Exports),

that is Y = C + I + X

Y = 100 + 0.75Y + 20 + 40

Y – 0.75Y = 100 + 20 + 40 (Solving using simple algebra)

0.25Y = 160

Y = 640

Now if I or Planned investment falls to 15

equilibrium

Y = AD,

that is Y = C + I + X

Y = 100 + 0.75Y + 15 + 40

Y – 0.75Y = 100 + 15 + 40

0.25Y = 155

Y = 620

The multiplier in cases with I=20 and I= 15 is same.

Multiplier is given as 1/1-c, where c is MPC which would be in both cases 1/1-0.75 = 4