Question

1. If the marginal propensity to consume is 0.6, the marginal propensity to save is 0.4, and government spending increases by $2 billion at the same time taxes rise by $2 billion, equilibrium income will:

rise by $2 billion. is the answer, I just dont know what steps to undertake to get the answer nor know what equation to use.

2. In the nation of Economia, the economy is over heating and there is danger of inflation. The chief economist estimates that current income is $50 billion, the optimal level is $40 billion, and the multiplier is 4. If government wants to close the inflationary gap, it should reduce government spending by:

Answer is: $2.5 billion. I just dont know what steps to undertake to get the answer nor know what equation to use.

3. If consumption decreases from $600 billion to $575 billion and the marginal propensity to consume is 0.8, then equilibrium income will:

Answer: fall by $125 billion.(dont know how to arrive at that answer)

Answer 1

Multiplier is used to estimate the change in the level of income in an economy in response to injection or reduction in any of the macroeconomic variables. The formula for the multiplier is

Multiplier = 1/(1 – MPC)

MPC = Marginal Propensity to Consume

Part 1) The equilibrium condition is the following

Y = c(Y – t) + I + G

Y = Income

c = share of income spent on consumption

I = Investment

G = Government spending

t = Taxes

Now, it is given that both the tax and government spending has changed so,

ΔY = c’(ΔY – Δt) + ΔG

ΔY – c’ΔY = – c’Δt + ΔG

ΔY = (– c’Δt + ΔG)/(1 – c’)

Now, it is given that the government spending and taxes has increased by same amount of $2 billion. So, substituting ΔG = Δt

ΔY = (– c’ΔG + ΔG)/(1 – c’)

ΔY = ΔG[(1 – c’)/(1 – c’)]

So, ΔY = ΔG

So, the equilibrium income will rise by $2 billion. This happens because while the increase in government spending first directly increases the national income and then indirectly through multiplier effect, the tax increase has impact only when decline in disposable income reduces consumption expenditure.

Part 2) The inflationary gap = $10 billion

Multiplier = 4

Reduction in government spending = Inflationary gap ÷ multiplier

Reduction in government spending = 10 billion ÷ 4

Reduction in government spending = $2.5 billion

Part 3) Change in consumption = $600 billion – $575 billion = $25 billion

Marginal Propensity to Consume (MPC) = 0.8

Multiplier = 1/(1 – MPC)

Multiplier = 1/(1 – 0.8)

Multiplier = 5

Decline in Equilibrium Income = Change in Consumption × Multiplier

Decline in Equilibrium Income = 25 billion × 5

Decline in Equilibrium Income = $125 billion