Question

Assume the following economy: Autonomous Consumption = £10,000; Marginal Propensity to Consume = 0.8; Business Investment = £30,000 A. Find the equilibrium size of income Y and the size of the Multiplier of Business Investment (hint: to find the Multiplier increase investment by 10,000) (5%) B. Assume now that a government sector is introduced, while business investment is still £30,000. Government spending injects £50,000 into the economy. However, in order to finance its expenditure the government levies an income tax at a rate of 25%. • Find the new equilibrium size of income and calculate the size of the Multiplier of Business Investment (hint: to find the Multiplier increase investment by 10,000) • Identify whether the government balance is balanced or not when I=30,000 and G=50,000

Answer 1

Autonomous Consumption(C*) = £10,000;

Marginal Propensity to Consume(b) = 0.8;

Business Investment(I) = £30,000

A)

For equilibrium level of Y:

Y= AD, Where AD= C*+cY+I

Y= 10000+0.8Y+30000

Y-0.8Y= 40000

0.2Y= 40000

Y= 40000/0.2= 200000 Equilibrium level of Y

Multiplier explains that by how much Income changes due to a unit change in I:

Multiplier= Change in Y/ Change in I

Assume investment to increase by 10000, then new I= 40000

Y= AD, Where AD= C*+cY+I

Y= 10000+0.8Y+40000

Y-0.8Y= 50000

0.2Y= 50000

Y*= 50000/0.2= 250000

Multiplier= 250000-200000 / 10000 = 50000/10000= 5

B)

Assume now that a government sector is introduced, while business investment is still £30,000. Government spending injects £50,000 into the economy. Government also levy 25% of income tax.

Here G= 50000 and t= 25%= 0.25

For equilibrium level of Y:

Y= AD, Where AD= C*+c(Y-tY)+I+G

Y= 10000+0.8(Y-0.25Y)+30000+50000

Y= 90000+0.8(0.75Y)

Y-0.8(0.75Y)= 90000

Y-0.6Y = 90000

0.4Y= 90000

Y**= 90000/0.4= 225000 New equilibrium level of Y

For multiplier:

Assume investment to increase by 10000, then new I= 40000

For equilibrium level of Y:

Y= AD, Where AD= C*+c(Y-tY)+I+G

Y= 10000+0.8(Y-0.25Y)+40000+50000

Y= 100000+0.8(0.75Y)

Y-0.8(0.75Y)= 100000

Y-0.6Y = 100000

0.4Y= 100000

Y= 100000/0.4= 250000

Multiplier= Change in Y/ Change in I= 25000/10000= 2.5

For Government balance to balance its revenue from income tax must be equals to its spending. So here

Government revenue from income tax= tY**= 0.25 x 225000= 56250

Government spending was 50000

Here Government revenue from income tax is more than the Government spending so Government balance is not balance it is in surplus.