# Multiplier and equilibrium output calculation problem?

Given parameters:
Consumption (C) = 10 + 0,5Y
Investments (I) = 10
Exports (X) = 20
Imports (M) = 5 + 0,1Y
Government spending (G) = 10
Taxes (T) = 0.4Y

a) How to calculate the multiplier?
b) What is the equilibrium output?
c) What is the new equilibrium output if the investments are increased to 15? (By using the multiplier.)

I answered a similar question not long ago, I recommend you search previous answers before asking a question.

For you convenience, I will copy the problem and answer below:

QUESTION:

The following information is given for a hypothetical economy:
C = 400 + .8 Y
I = 100 + .2 Y
G = 200
X = 400
M = 100 + .1 Y

Where:
C = Consumption
I = Investment
G = Government Spending
X = Exports
M = Imports
Y = GDP

Calculate:

(1) The Income Multiplier
(2) Equilibrium GDP

Autonomous consumption increases by \$100. Calculate:

(3) Aggregate Change in GDP

I'm not quite sure what they mean by "Income mulitplier", but given that a multiplier is the total impact an increase in something will have on aggregate demand, the answers can be easily determined by using the definition of GDP.

GDP = C + I + G + (X - M)

Then make the necessary subsitutions:

Y = (400 + 0.8 Y) + (100 + 0.2Y) + 200 + (400 - (100 + 0.1Y))
Y = 1000 + 0.9 Y

Note the coefficient for Y in the consumption equation C = 400 + 0.8 Y. A rise in income Y will produce a rise in consumption C. That is the defintion of the MPC (marginal propensity to consume). The multiplier can be easily calculated using the defintion M = 1/ (1- MPC)

M = 1/ (1-0.8)
M = 5

This is the answer to part 1) Income multiplier.

Now solve for Y:
0.1 Y = 1000
Y = 10000

This is the answer to 2) Equilibrium GDP.

Since the multiplier is already known, part 3 is simple.

Change in GDP = Multiplier * change in consumption
Change in GDP = 5 * 100 = 500

This is the answer to part 3).
a), K= 1/ [1- {b(1-t)-m}]
= 1/ [1- {0.5(1-0.4)-0.1}]
= 1/ 1-0.2
= 1.25

b)
Y=AE=10+10+20+10-5+ 0.2Y
=45+0.2Y
equil.=45/0.8
=56.25

c) Y= 60+0.2Y
new equil = 60/0.8
=75

Therefore, an increase of (I) by 15 results in Y increasing by 18.75. ( 18.75/ 15= K=1.25 )

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