Question

Consider a hypothetical closed economy in which households spend $0.60 of each additional dollar they earn and save the remaining $0.40.

The marginal propensity to consume (MPC) for this economy is   , and the spending multiplier for this economy is   .

Suppose the government in this economy decides to increase government purchases by $400 billion. The increase in government purchases will lead to an increase in income, generating an initial change in consumption equal to _________   . This increases income yet again, causing a second change in consumption equal to _______   . The total change in demand resulting from the initial change in government spending is _______.

Answer 1

$$ \begin{aligned} \text { Marginal propensity to consume } &=\frac{\text { Change in consumption }}{\text { Change in income }} \\ &=\frac{0.60}{1} \\ &=\$ 0.60 \end{aligned} $$

Calculate spending or expenditure multiplier:

$$ \begin{aligned} \text { Spending multiplier } &=\frac{1}{1-M P C} \\ &=\frac{1}{1-0.60} \\ &=\frac{1}{0.40} \\ &=\$ 2.5 \end{aligned} $$

The marginal propensity to consume for this economy is \(\$ 0.60\), and the spending multiplier is \(\$ 2.5\)

Suppose the government decides to increase government purchases by \(\$ 400\) billion. As there is an increase in government purchases there will be an increase in income.

An initial change in consumption is equal to \(\$ 400 \times 0.60=\$ 240\)

An increase in income again causes a second change in consumption equal to \(\$ 240 \times 0.60=\$ 144\)

Calculate the change in demand:

Change in demand= Government purchases \(\times\) multiplier

$$ \begin{array}{l} =\$ 400 \times 2.5 \\ =\$ 1,000 \end{array} $$

Therefore, the total change in demand resulting from the initial change in government spending is \(\$ 1,000\)

Answer 2

We know that MPC = change in Consumption / Change in Income = $\Delta C/\Delta Y$

MPC = As with every additional increase in income, consumption increases by 0.60.

$\Delta C/\Delta Y$ = 0.60 / 1

MPC = 0.60.

And Spending or Expenditure Multiplier = 1 / (1-MPC)

Spending Multiplier = 1 / (1-0.6) = 1/0.4 = 2.5.

If the government increases its expenditure by $400 billion, there would be increase in income. It will initiate change in consumption that would be equal to Marginal Propensity to consume. That is consumption will increase by MPC.

with 1 dollar increased, Consumption increased by 0.60

Hence with $400 billion increase, Consumption will increase by 0.60*400 billion = $240 billion.

This increases income yet, causing a change in consumption at second times equal $240 billion * 0.6 = $144 billion.

And the process continues, Thus the total change in income by this increment in government spending equals as:

Change in Demand = Multiplier*change in G

Change in Demand= $400 billion * 2.5 = $1000 billion.

The graph before change in G is already given in the question.

The graph After change in G is as follows: