The Multiplier, Growth and Money and Banking: Question 2

Worked solution

Part (a): Finding the marginal propensity to consume

Out of every additional $1 of national income, the whole $1 is either consumed, saved, taxed away, or spent on imports, so:

$MPC + MPS + MRT + MPM = 1$

Substituting the given values:

$MPC = 1 - MPS - MRT - MPM = 1 - 0.2 - 0.1 - 0.1 = 0.6$

So $MPC = \boxed{0.6}$, households consume $0.60 of every additional $1 of income domestically.

Part (b): Calculating the multiplier

In an open economy with a government sector, the multiplier is the reciprocal of the sum of all the marginal leakages (withdrawals) from the circular flow of income. Here, saving, tax and imports:

$k = \frac{1}{MPS+MRT+MPM} = \frac{1}{0.2+0.1+0.1} = \frac{1}{0.4} = 2.5$

So the multiplier for Astera is $k = \boxed{2.5}$.

Part (c): Change in equilibrium national income

A change in a component of Aggregate Demand (here, an injection of government spending of $40 million, so $\Delta J = 40$) leads to a change in equilibrium national income of:

$\Delta Y = k \times \Delta J = 2.5 \times 40 = 100$

So equilibrium national income rises by $100 million. The initial $40 million of extra spending becomes income for construction firms and public-sector suppliers, part of which is re-spent by their employees and owners, and so on, so the eventual rise in national income ($100 million) is larger than the initial injection ($40 million).

Part (d): Why a higher MPM reduces the multiplier

The multiplier process works because an initial injection of spending becomes someone else’s income, part of which is spent again in the domestic economy, becoming further income, and so on. Only spending that stays inside the domestic circular flow, via consumption, keeps this chain going; saving, tax and import spending are all withdrawals (leakages) that remove part of each round of extra income from further domestic respending.

If Astera’s $MPM$ rises, then a bigger share of every extra dollar of income leaks abroad on imports at each round, leaving a smaller share to be re-spent domestically as consumption. Each successive round of the multiplier process therefore adds less to domestic income than before, so the whole chain reaction dies out more quickly and the total (eventual) rise in national income from a given injection is smaller.

This is confirmed directly by the formula: since $k = \dfrac{1}{MPS+MRT+MPM}$, a rise in $MPM$ increases the denominator, which reduces the value of $k$.

Final answers

• (a) $MPC =$ 0.6
• (b) $k =$ 2.5
• (c) $\Delta Y =$ $100 million
• (d) A higher $MPM$ is a bigger leakage from the circular flow at each round of respending, so less of each extra dollar of income continues to be re-spent domestically, and $k = \dfrac{1}{MPS+MRT+MPM}$ falls as $MPM$ rises