Model Answer
0 min readIntroduction
The Investment-Savings (IS) schedule represents the combinations of interest rates and levels of national income where the goods market is in equilibrium. Its slope indicates the sensitivity of investment to changes in the interest rate, and is inversely related to the size of the multiplier. Fiscal policy, particularly changes in taxation, significantly influences the multiplier and, therefore, the slope of the IS curve. The question posits a relationship between changes in proportional and lump-sum taxes and the IS curve’s slope, which requires a detailed examination of their respective impacts on aggregate demand.
Understanding the IS Curve and the Multiplier
The IS curve is downward sloping because a lower interest rate encourages investment, leading to higher aggregate demand and thus, a higher level of equilibrium income. The slope of the IS curve is determined by the marginal propensity to invest (MPI) and the marginal propensity to save (MPS). A larger MPI relative to MPS results in a flatter IS curve, indicating a greater responsiveness of income to interest rate changes. This responsiveness is directly linked to the size of the multiplier.
Proportional vs. Lump-Sum Taxes
Proportional tax is a tax levied at a constant rate on income, meaning the tax amount increases with income. Lump-sum tax, on the other hand, is a fixed amount of tax levied irrespective of income. The key difference lies in their impact on disposable income and, consequently, on aggregate demand.
Impact on the Multiplier
The multiplier (k) is calculated as 1/(1-MPC), where MPC is the marginal propensity to consume. Taxes reduce disposable income and, therefore, consumption.
- Proportional Tax: A reduction in the proportional tax rate increases disposable income by a larger percentage at higher income levels. This boosts consumption and increases the MPC, leading to a higher multiplier. A higher multiplier makes the IS curve flatter (steeper slope).
- Lump-Sum Tax: A reduction in a lump-sum tax increases disposable income by a fixed amount, regardless of income level. This leads to a parallel upward shift of the IS curve, but does *not* change the slope of the IS curve. The MPC is unaffected, and therefore, the multiplier remains constant.
Mathematical Representation
Let's consider a simple Keynesian model:
Y = C + I + G
C = a + b(Y - T)
Where:
- Y = National Income
- C = Consumption
- I = Investment
- G = Government Spending
- T = Taxes
- a = Autonomous Consumption
- b = MPC
If T is a proportional tax (T = tY), reducing 't' increases the MPC and thus the multiplier. If T is a lump-sum tax, reducing it simply shifts the consumption function upwards without altering the MPC.
The Statement: True or False?
The statement "The slope of the IS schedule will become steeper if the government reduces the rate of proportional tax but will not change at all if the government reduces the level of a lump sum tax" is TRUE. As explained above, a reduction in the proportional tax rate increases the multiplier, making the IS curve flatter (steeper slope). Conversely, a reduction in a lump-sum tax only shifts the IS curve without altering its slope.
Conclusion
In conclusion, the impact of fiscal policy on the IS curve’s slope hinges on the type of tax altered. Reducing proportional taxes influences the multiplier, leading to a flatter IS curve, while reducing lump-sum taxes merely shifts the curve without affecting its slope. Understanding this distinction is crucial for effective macroeconomic policy design, as it determines the responsiveness of output to changes in monetary policy and overall economic conditions.
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.