Answer to Question #224795 in Macroeconomics for beezee

Question

Here we investigate a particular example of the model studied in Sections 10-2 and 10-3 with no government. Suppose the consumption function is given by C 5 100 1 .8 Y , whereas investment is given by I 5 50.

a. What is the equilibrium level of income in this case?

b. What is the level of saving in equilibrium?

c. If, for some reason, output is at the level of 800, what will the level of involuntary inventory accumulation be?

d. If I rises to 100 (we discuss what determines I in later chapters), what will the effect be on the equilibrium income? e. What is the value of the multiplier, a, here?

f. Draw a diagram indicating the equilibria in both parts a and d

Answer 1

Solution:

a.). The equilibrium level of income:

At equilibrium: Y = AE

AE = C + I, since there is no government sector.

C = 100 + 0.8Y

I = 50

AE = 100 + 0.8Y + 50 = 150 + 0.8Y

Y = AE

Y = 150 + 0.8Y

Y – 0.8Y = 150

0.2Y = 150

Y = 750

 

b.). Level of saving in equilibrium:

Y = C + S

S = Y – C

S = Y – (100 + 0.8Y) = -100 + 0.2Y

Y = 750

S = -100 + 0.2(750) = -100 + 150 = 50

The level of saving in equilibrium = 50

 

c.). The level of involuntary inventory accumulation:

Involuntary inventory accumulation = Y – AE = 800 – (150 + 0.8(800)) = 800 – 790 = 10

The level of involuntary inventory accumulation = 10

 

d.). Effect on the equilibrium when I is increased to 100:

Y = C + I

Y = 100 + 0.8Y + 100 = 200 + 0.8Y

Y – 0.8Y = 200

0.2Y = 200

Y = 1000

When Investment (I) is increased to 100, the equilibrium income will also increase by 250 from 750 to 1000.

 

e.). The value of the multiplier:

Multiplier = $\frac{1}{1 - MPC}$

MPC = 0.8

$\frac{1}{1 - 0.8} = \frac{1}{0.2} = 5$

The value of the multiplier = 5

 

f.). Equilibrium national income diagram is as below: