Question

3. Consider an economy characterized by the following equations

AE = 10 + 0.75Y - 0.5P

AS: Y = 10 + P

where Y is national income, AE is desired aggregate expenditure, P is the price level, AS is the aggregate supply. National income is in billions of dollars.

a) What is the equation for the aggregate demand (AD)? Solve for equilibrium P and Y. Illustrate the equilibrium in a diagram with P on the vertical axis and Y on the horizontal axis.

i) Now suppose, all else equal, exports increase by $1.5 billion. What is the new aggregate demand? Solve for the new equilibrium P and Y.

ii) What is the multiplier for this economy when prices are allowed to change?(1 mark)

Answer 1

(a)

(1) Equation of AD curve: Y = AE

Y = 10 + 0.75Y - 0.5P

(1 - 0.75)Y = 10 - 0.5P

0.25Y = 10 - 0.5P

Y = 40 - 2P

(2) In equilibrium, AD = AS

40 - 2P = 10 + P

3P = 30

P = 10

Y = 10 + 10 = 20

(3) In following graph, AD & AS are the AD-AS curves intersecting at point A with price level P0 (= 10) and output Y0 (= 20).

From AD curve,

When Y = 0, P = 40/2 = 20 (Vertical intercept) and when P = 0, Y = 40 (Horizontal intercept).

From AS curve,

When P = 0, Y = 10 (Horizontal intercept).

(i)

(1) When NX rises by 1.5 (billion),

Aggregate demand: Y = 10 + 0.75Y - 0.5P + 1.5

(1 - 0.75)Y = 11.5 - 0.5P

0.25Y = 11.5 - 0.5P

Y = 46 - 2P

(2) Equating new AD and AS,

46 - 2P = P + 10

3P = 36

P = 12

Y = 12 + 10 = 22

(ii)

Multiplier = Change in Y / Change in NX = (22 - 20) / 1.5 = 2 / 1.5 = 4/3 = 1.33