Question

Suppose an economy is described by following aggregate expenditure (AE) model:

C = 40 + 0.75YD    

I = 60

C is consumption (0.75 is the marginal propensity to consume)

 YD is disposable income, 

 I is investment spending.

• (a)  Derive an expression for AE as a function of Y. Calculate the equilibrium level of Y and illustrate in a diagram with AE on the vertical and Y on the horizontal axis.
• (b)  Calculate the level of consumption. Express the components of aggregate expenditure (C, and I) as percentages of GDP (to one decimal place). Derive the saving function and solve for the equilibrium level of saving.

Answer 1

(a) An expression for AE as a function of Y.

The equilibrium level of Y

AE = C+I + G

AE = 40 + 0.75Y + 60

AE = 100+0.75Y : expression for AE as function of Y

at equilibrium, Y = AE

Y = 100+0.75Y

0.25Y = 100

Y = 400

Equilibrium level of income = $400

(b) The level of consumption

Consumption $C = 40 + 0.75 \times 400 = 340$

Share of C in $GDP = \frac{340}{400} \times100 = 85 \%$

Share of I in $GDP = \frac{60}{400} \times100 = 15 \%$

Savings function $S = -\bar{C} + (1-MPC) \times Y$

S = -40 + 0.25Y

at Y = 400

$S = -40 + 0.25 \times 400 = 60$