# Multiplier and equilibrium output calculation problem?

Hello, I have some problem by solving the following question. Please help me. Thank you in advance.

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

ANSWER:

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 )

More Questions and Answers:

How much money does an average person make in africa?
Consumer awarness and its need? (pls i need this ans as quick as possible)?
Why is unexpected inflation considered to be an economic problem? How can the monetary authorities assure the?
Perfect Competition?
What does it mean to live in a Capitalistic system? what are some of the negative sides?
The importance of evirnomental protection?
What is the economics defition of union wage premium?
Simple economics question: calculate GDP. Pls help?
How Keynesianâ€™s multiplier can be calculated algebraically?
Where can iget economics question and answer?

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.)

**Answer:**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

ANSWER:

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 )

The answers post by the user, for information only, FunQA.com does not guarantee the right.

More Questions and Answers: