National Income Determination and the Multiplier
National income (real GDP) is determined at the point where planned aggregate expenditure equals planned output, or equivalently where planned injections into the circular flow equal planned withdrawals from it.
Before you start
Make sure you're comfortable with these topics first:
Method
- Learn the multiplier formula both ways: k = 1 / (1 - MPC) and k = 1 / MPW, and know that MPC + MPS + MPT + MPM = 1 for any extra pound of income.
- Practise calculating k from a given MPC or MPW, and then the final change in national income from k multiplied by the initial change in an injection.
- Explain the multiplier process in words: an initial injection becomes income for someone, part of which is re-spent based on the MPC, becoming income for someone else, and so on in ever-smaller rounds, until the total effect is a multiple of the initial injection.
- Learn what makes the multiplier larger or smaller: a low marginal propensity to withdraw (low savings, tax and import rates) gives a larger multiplier; a high MPW gives a smaller one.
- Learn the accelerator: investment depends on the rate of change of national income or demand, not its level, so a slowdown in the growth rate of demand, even if demand is still rising, can cause investment to fall.
- Explain how the multiplier and accelerator can interact to amplify the economic cycle: a rise in demand triggers investment via the accelerator, which is itself a component of AD, which the multiplier then magnifies further.
- For any question, identify the initial change in spending, calculate or estimate the multiplier, then state the final change in national income, and evaluate on the size of MPW, time lags in each spending round, and whether spare capacity exists to allow real output, rather than just prices, to rise.
Worked example
In an economy, the marginal propensity to consume is 0.6, the marginal propensity to tax is 0.15, and the marginal propensity to import is 0.05. Calculate the value of the multiplier, and the final change in national income following an initial rise in government spending of 20bn.
- Find the marginal propensity to save: since MPC + MPS + MPT + MPM = 1, MPS = 1 - 0.6 - 0.15 - 0.05 = 0.2.
- Find the marginal propensity to withdraw: MPW = MPS + MPT + MPM = 0.2 + 0.15 + 0.05 = 0.4.
- Calculate the multiplier: k = 1 / MPW = 1 / 0.4 = 2.5.
- Check using k = 1 / (1 - MPC) = 1 / (1 - 0.6) = 1 / 0.4 = 2.5, confirming the same answer.
- Calculate the final change in national income: change in Y = k x change in G = 2.5 x 20bn.
- Final answer: national income rises by 50bn in total, from an initial injection of only 20bn.
Practice questions
Try each question, then tap to reveal the answer.
Q1Write the multiplier formula in terms of the MPC.Show answer
Answer: k = 1 / (1 - MPC).
Q2Write the multiplier formula in terms of the MPW.Show answer
Answer: k = 1 / MPW, where MPW = MPS + MPT + MPM.
Q3If the MPW is 0.25, what is the value of the multiplier?Show answer
Answer: k = 1 / 0.25 = 4.
Q4If the multiplier is 2 and government spending rises by 15bn, what is the total change in national income?Show answer
Answer: 2 x 15bn = 30bn.
Q5State one reason a country with a very open economy, with high import spending, tends to have a smaller multiplier.Show answer
Answer: A high marginal propensity to import means more of each extra pound of income leaks abroad as spending on imports rather than being re-spent domestically, raising the MPW and lowering the multiplier.
Q6What does the accelerator effect describe?Show answer
Answer: The idea that the level of investment depends on the rate of change of national income or demand, so investment rises when demand is growing faster, and can fall even when demand is still growing, just more slowly.
Q7State one way in which a higher rate of income tax affects the size of the multiplier.Show answer
Answer: It raises the marginal propensity to tax, part of MPW, so more of each extra pound of income leaks out of the circular flow as tax rather than being re-spent, lowering the multiplier.
Exam-style questions
Written in the style of a A Level Economics exam paper, with a full mark scheme.
An economy has a marginal propensity to save of 0.1, a marginal propensity to tax of 0.2 and a marginal propensity to import of 0.1. Calculate the multiplier, and the final change in national income following a fall in investment of 40bn.
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Evaluate the factors that determine the size of the multiplier effect following a rise in government spending.
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