## The Multiplier

__The multiplier ratio, the multiplier effect and its effect on the economy__

- The multiplier ratio is a ratio between change in real income and the initial injection. It is also described as the number of times the change in income exceeds the injection which caused the autonomous change in the first place.

- The multiplier effect is just describing the phenomenon where an initial injection causes a larger change in income. The effect occurs because any injections would circulate around the economy more than once as described in the circular flow of income model. E.g. if we have a multiplier value of 5 then an injection of £1 million pounds leads to an overall increase in income of £5 million.
- The only way money leaves the circular flow of income is withdrawals, and therefore it is no surprise that the amount of withdrawals effects how large the multiplier ratio is.
- If there are few withdrawals, then the multiplier is large because any injection would circulate many times before leaving the system. If there are large withdrawals in the economy, then the injected money wouldn’t circulate the system many times i.e. there is a small multiplier, and only a small rise in income.

__Understanding of marginal propensities and their effects on the multiplier__

**Marginal propensity to consume (MPC)**

- The marginal propensity to consume is the
**proportion**of each**extra**pound (£) earned that is**spent**within the economy. - The formula used to derive the value of MPC is:

- The formula delta sign means ‘change in’, therefore MPC is equal to change in consumption divided by the change in income (income is written as Y).
- The
**higher**MPC is, the**larger**the multiplier, as proportionally more is being spent in the economy.

**Marginal propensity to save (MPS)**

- The marginal propensity to save is the
**proportion**of each**extra**pound earned that is**saved**. - The formula used to derive the value of MPS is:

- Therefore, MPS is the change in savings divided by the change in income.
- The
**higher**the value of MPS, the**smaller**the multiplier is because saving is a**withdrawal**of money from the economy.

**Marginal propensity to tax (MPT)**

- The marginal propensity to tax is the
**proportion**of each**extra**pound earned that is**paid as****taxes**. - The formula used to derive the value of MPT is:

- Therefore, MPT is the change in tax divided by the change in income.
- The
**higher**the value of MPT, the**smaller**the multiplier is because taxation is a**withdrawal**of money from the economy. More tax means less disposable income per consumer which leads to less spending and so a smaller multiplier.

**Marginal propensity to import (MPM)**

- The marginal propensity to import is the
**proportion**of each**extra**pound earned that is**spent on imports**. - The formula used to derive the value of MPM is:

- Therefore, MPM is the change in imports divided by the change in income.
- The
**higher**the value of MPM, the**smaller**the multiplier is because importing goods removes money from the circular flow of income. More imports mean less is spent in the economy before it leaves, resulting in a smaller multiplier.

__Calculations of the multiplier__

- The value of the multiplier itself is derived in a couple of different ways using marginal propensities.
- Before that, we need to understand what the term MPW means. It is the marginal propensity to withdraw and the formula for calculating it is:

*MPW = MPS + MPT + MPM*

- Extra income either has to be spent or withdrawn – hence the formula:
*MPC + MPW = 1*

- The multiplier can be worked out using MPW:

- It can also be worked out using MPC.
- As
*MPC + MPW = 1*,*MPW = 1 – MPC.* - As a result, the multiplier formula can also be:

__The significance of the multiplier for shifts in AD__

- If the multiplier increases the national income by more than the initial injection, it also does the same to national output and therefore must affect AD greater than initially intended.
- This is exactly the case. If the multiplier is large then the AD curve shifts outwards further. This is acceptable when there is a large spare capacity in the economy, as we can have rapid economic growth (AD to AD₁) without much of a rise in price levels (roughly stays at P) and so minimal inflation.

- However, when the multiplier effect causes a larger shift than expected past the bottleneck stage on the LRAS curve, there is going to be inflationary problems. An injection by the government may have only been expected to shift AD₁ to AD₂ but may actually shift it to AD₃. A massive problem of this shift would be that price levels increase from P to P₃ instead of P₂ which could cause inflation to exceed the targeted level (2% in the UK). If it causes hyperinflation the effects could be devastating, so the government must take it into account when intervening (e.g. via demand side policies).