Part A — AE components, MPC/MPS and the multiplier
This worksheet drills the core quantitative skills of the AE model: MPC and MPS, the multiplier, the multiplier process round by round, and applying ΔY = ΔAE × k.
Components and the consumption function
1. Write the aggregate expenditure equation and name each component.
2. Define the marginal propensity to consume and the marginal propensity to save, and state the relationship between them.
3. A household receives an extra $500 and spends $400 of it. Calculate its MPC and MPS.
Multiplier calculations
4. Calculate the multiplier for each MPC: (a) 0.5; (b) 0.8; (c) 0.9.
5. Government spending rises by $300m and the MPC is 0.8. Calculate the multiplier and the total change in equilibrium income. Show your working.
6. Complete the first four rounds of the multiplier process for a $1,000m injection with MPC = 0.7, then state the eventual total change in income.
| Round | Spending added ($m) |
|---|---|
| 1 (injection) | 1000 |
| 2 | |
| 3 | |
| 4 | |
| Eventual total |
Equilibrium and application
7. Explain how a build-up of unplanned inventories signals that planned aggregate expenditure is below output, and describe how the economy returns to equilibrium.
8. A mining downturn cuts business investment by $2 billion. With an MPC of 0.75, estimate the eventual effect on equilibrium income, and explain why the fall in income is larger than the fall in investment.