Model Answer
0 min readIntroduction
The Keynesian model, developed by John Maynard Keynes, revolutionized macroeconomic thought by emphasizing the role of aggregate demand in determining output and employment. A central concept within this framework is the multiplier effect, which posits that an initial change in autonomous spending (like investment or government expenditure) leads to a larger change in national income. The magnitude of this effect is captured by the multiplier. Traditionally, the multiplier is calculated based on the marginal propensity to consume (MPC). However, in a more realistic scenario, both consumption and investment depend on income, necessitating a modified calculation of the multiplier. This answer will explore how the multiplier is affected when both consumption and investment are functions of income.
The Simple Keynesian Multiplier: A Foundation
The basic Keynesian multiplier (k) is defined as the ratio of the change in national income (ΔY) to the change in autonomous expenditure (ΔA). It is calculated as:
k = 1 / (1 - MPC)
Where MPC represents the marginal propensity to consume – the fraction of an additional unit of income that is spent on consumption. This formula assumes that investment (I) is autonomous, meaning it doesn’t change with income.
Consumption and Investment as Functions of Income
In reality, investment is also influenced by income and economic conditions. Let's denote the marginal propensity to invest (MPI) as the fraction of an additional unit of income that is invested. When both consumption and investment are functions of income, the aggregate expenditure (AE) equation becomes:
AE = C + I + G
Where:
- C = a + bY (Consumption function, 'a' is autonomous consumption, 'b' is MPC)
- I = c + dY (Investment function, 'c' is autonomous investment, 'd' is MPI)
- G = Government expenditure (assumed autonomous for simplicity)
Therefore, AE = (a + c + G) + (b + d)Y
Deriving the Multiplier with Both Consumption and Investment
To find the multiplier in this scenario, we need to determine the change in income (ΔY) resulting from a change in autonomous expenditure (ΔA). ΔA would include changes in autonomous consumption (a) and autonomous investment (c) and government expenditure (G). The equilibrium condition is Y = AE, so:
Y = (a + c + G) + (b + d)Y
Solving for Y, we get:
Y = (a + c + G) / (1 - (b + d))
The multiplier (k) is then:
k = 1 / (1 - (MPC + MPI)) or k = 1 / (1 - (b + d))
Impact on the Multiplier
The inclusion of the marginal propensity to invest (MPI) in the denominator significantly affects the multiplier. Here's how:
- Reduced Multiplier Value: Since (b + d) will always be greater than 'b' (MPC), the denominator (1 - (b + d)) will be smaller than (1 - b). This results in a lower multiplier value compared to the simple Keynesian model where investment is assumed autonomous.
- Importance of Investment: The multiplier’s size is now dependent on both the MPC and MPI. A higher MPI will further reduce the multiplier, indicating that a larger portion of increased income is saved or used for imports rather than being re-spent within the economy.
- Real-World Relevance: This modified multiplier is more realistic as it acknowledges that investment decisions are not entirely independent of income levels. For example, as income rises, firms may invest in new capital goods to expand production.
Example
Consider a scenario where MPC = 0.8 and MPI = 0.2.
- Simple Keynesian Multiplier: k = 1 / (1 - 0.8) = 5
- Multiplier with both C & I: k = 1 / (1 - (0.8 + 0.2)) = 1 / (1 - 1) = Undefined
This example highlights that if MPC + MPI = 1, the multiplier becomes undefined, indicating that all additional income is either consumed or invested, leading to infinite expansion. In practice, this is unlikely due to factors like imports and taxes.
| Scenario | MPC | MPI | Multiplier (k) |
|---|---|---|---|
| Simple Keynesian | 0.8 | 0 | 5 |
| With Consumption & Investment | 0.8 | 0.2 | 10 |
| With Consumption & Investment | 0.7 | 0.3 | 3.33 |
Conclusion
In conclusion, when both consumption and investment are functions of income, the Keynesian multiplier is affected by the inclusion of the marginal propensity to invest (MPI). The multiplier becomes 1 / (1 - (MPC + MPI)), generally resulting in a larger multiplier than the simple model, but also making it more sensitive to changes in investment behavior. Understanding this nuanced relationship is crucial for effective macroeconomic policy formulation, as it highlights the interconnectedness of consumption and investment in driving economic growth. Furthermore, recognizing the limitations of the model, such as the assumption of autonomous government spending, is essential for a comprehensive analysis.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.