# The Multiplier

In my article on Government Spending, I mentioned how the multiplier effect could take place – here, we will look more in-depth into how to calculate this multiplier and what affects it

The Multiplier is essentially an economic factor multiplied by the initial injection into the economy to find the increase in real GDP caused. An example of the multiplier effect is when the government increases funding for the NHS. This is an increase in G, which increases AD and leads to an increase in output. With more funding, more workers can be hired and employees can be paid more – with this increased income, people spend more, increasing C. This further increases AD and thus output. If consumers are spending more, firms gain more profit which can be used to buy more capital and other factors of production, increasing I and AD, and therefore accelerating output growth. This shows how the initial injection can have a greater effect on GDP, and this is due to the Multiplier.

• MPC – Marginal Propensity to Consume
• MPW – Marginal Propensity to Withdraw
• MPS – Marginal Propensity to Save
• MPT – Marginal Propensity to Tax
• MPI – Marginal Propensity to Import

The Marginal Propensity to x (x being an action e.g. consume) is basically how much of any additional income gained will be spent on x, and is a value between 0 and 1. For example, if someone had an MPS of 0.1, this means that for every £1 of additional income, they would save 10p.

MPW = 1 – MPC

MPW = MPS + MPT + MPI

Multiplier = 1/(1 – MPC) OR Multiplier = 1/MPW OR Multiplier = 1/(MPS + MPT + MPI)

Example Question

A consumer in the UK is likely to spend £30 of every £50 they receive in additional income, save £10, buy imports of £3 and pay tax of £7. If the government increased spending by £83 billion, what would be the corresponding increase in real GDP?

Firstly, calculate the MPC / MPW

MPC = 30 / 50 = 0.6

MPW = MPS + MPT + MPI = (10 / 50) + (7 / 50) + (3 / 50) = 0.4

Plug these values into the multiplier equation

Multiplier = 1 / (1 – 0.6) or 1 / (0.4) = 2.5

Now that we have the multiplier, simply multiply the initial injection by this value

83 X 2.5 = £207.5 billion

Therefore, real GDP will increase by £207.5 billion