# 2.2 The Keynesian multiplier (HL)

Definition:

• The multiplier is a factor by which GDP changes following a change in an injection or leakage.

The formula for the multiplier:

1. Multiplier = 1 / (1 – MPC)
2. Multiplier = 1 / (MPS + MPT + MPM), where:
• MPC – Marginal Propensity to Consume
• MPS – Marginal Propensity to Save
• MPT – Marginal Propensity to Tax
• MPM – Marginal Propensity to Import

Essentially, both formulas are the same. Which one you will have to use depends on the information you have.

You have to know:

• how to calculate the effect on GDP resulting from a change in any of the Injections (Investment, Government spending, Exports)
• what kind of a change is required in a given injection to reach a certain level of GDP

Example:

Question: Current GDP is \$100 bn, MPS = 0.1, MPT = 0.2, MPM = 0.2. Government’s GDP target is \$150 bn. How much does government need to increase their spending by to reach the target? How will the budget be affected?

Solution:

1. What change of GDP we need to achieve: 150 – 100 = \$50 bn
2. Finding the multiplier: 1 / (0.1 + 0.2 + 0.2) = 2
3. 50 / 2 = \$25 bn is the value by which the government needs to increase their spending to reach the GDP target
4. Find how much more will the governments earn in tax as a result of \$50 bn increase in GDP: 50 * 0.2 = \$10 bn (general formula: total change in GDP multiplied by the MPT)
5. The government will spend \$25 bn and there will be \$10 bn increase in taxes collected. So effect on the budget: \$10 – \$25 = \$-15 bn

Also, I remember while preparing for the IB Economics exam there was one question in one of the maths papers. It asked to show the multiplier effect on a diagram (2 marks). This is how the diagram for 2 marks had to look like. Exactly like that. The second shift in the AD (AD2 -> AD3) had to be bigger than the first one (AD1 -> AD2). Anything different to this (more AD curves, the two shifts being the same size, etc.) would score you 1 mark. However, always consult your teacher on matters like this as it is possible that the question is worded differently. That might change what is given in the markscheme/what the examiner is expecting.