Model Answer
0 min readIntroduction
The determination of equilibrium income is a cornerstone of macroeconomic analysis. The Keynesian theory posits that the level of output and income in an economy is determined by the aggregate demand. This demand, in turn, is influenced by consumption, investment, government spending, and net exports. The introduction of income tax significantly alters the disposable income available to households, thereby impacting consumption and ultimately, the equilibrium level of output. This answer will analyze the equilibrium levels of output in the presence and absence of income tax, demonstrating the multiplier effect and the impact of fiscal policy.
Keynesian Model Without Income Tax
In a simple Keynesian model, aggregate expenditure (AE) is the sum of consumption expenditure (C) and investment expenditure (I). Consumption is a function of income, represented as C = a + bY, where 'a' is autonomous consumption and 'b' is the marginal propensity to consume (MPC). Investment is assumed to be autonomous. Therefore, AE = a + bY + I.
Equilibrium occurs when AE = Y, where Y is the national income. Substituting the AE equation, we get: Y = a + bY + I. Solving for Y, we obtain the equilibrium income (Yo):
Yo = (a + I) / (1 - b)
This equation shows that the equilibrium income is determined by autonomous spending (a + I) and the multiplier (1 / (1 - b)).
Keynesian Model With Income Tax
When income tax is introduced, disposable income (Yd) becomes Y - T, where T is the tax amount. Consumption now depends on disposable income, so C = a + bYd = a + b(Y - T). Aggregate expenditure becomes AE = a + b(Y - T) + I.
Equilibrium occurs when AE = Y. Substituting the AE equation, we get: Y = a + b(Y - T) + I. Solving for Y, we obtain the equilibrium income (Yu):
Y = a + bY - bT + I
Y - bY = a - bT + I
Yu = (a - bT + I) / (1 - b)
This equation shows that the equilibrium income is now affected by the tax amount (T). The introduction of income tax reduces the disposable income and consequently, the equilibrium income.
Comparative Analysis
Comparing the two equilibrium income levels, we can see the impact of income tax:
- Yo = (a + I) / (1 - b)
- Yu = (a - bT + I) / (1 - b)
The difference between the two is:
Yo - Yu = (bT) / (1 - b)
This shows that the reduction in equilibrium income due to income tax is equal to the tax amount multiplied by the multiplier. The higher the MPC (b), the larger the reduction in equilibrium income.
The following table summarizes the key differences:
| Feature | Without Income Tax | With Income Tax |
|---|---|---|
| Consumption Function | C = a + bY | C = a + b(Y - T) |
| Aggregate Expenditure | AE = a + bY + I | AE = a + b(Y - T) + I |
| Equilibrium Income | Yo = (a + I) / (1 - b) | Yu = (a - bT + I) / (1 - b) |
| Impact of Tax | Not Applicable | Reduces equilibrium income |
The introduction of income tax acts as a contractionary fiscal policy, reducing aggregate demand and lowering the equilibrium level of output. The magnitude of this reduction depends on the size of the tax and the value of the MPC.
Conclusion
In conclusion, the presence of income tax significantly alters the equilibrium level of output in the Keynesian model. Without tax, equilibrium income (Yo) is determined solely by autonomous spending and the multiplier. However, with income tax, equilibrium income (Yu) is reduced due to the decrease in disposable income and subsequent reduction in consumption. The extent of this reduction is directly proportional to the tax rate and the marginal propensity to consume. Understanding this relationship is crucial for policymakers when designing fiscal policies to stabilize the economy.
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.