Model Answer
0 min readIntroduction
In macroeconomic theory, the equilibrium level of output in an economy is determined by the intersection of aggregate demand and aggregate supply. A key component of aggregate demand is net exports (exports minus imports), which represents the foreign sector's contribution to overall demand. Government policies, such as income taxation, influence disposable income and consequently, aggregate demand. Understanding how changes in net exports can restore equilibrium output, particularly after the introduction of income tax, is crucial for effective macroeconomic management. This answer will calculate the change in net exports needed to bring the equilibrium output level, after considering income tax, to the full employment level (Yu).
Understanding the Keynesian Model with Income Tax
Let's begin by revisiting the Keynesian model. The equilibrium output (Y) is determined by:
Y = C + I + G + NX
Where:
- C = Consumption
- I = Investment
- G = Government Spending
- NX = Net Exports
With the introduction of income tax (t), disposable income becomes (1-t)Y. Therefore, consumption becomes C = a(1-t)Y, where 'a' is the marginal propensity to consume. The equilibrium output equation then becomes:
Y = a(1-t)Y + I + G + NX
Solving for Y, we get:
Y = [I + G + NX] / [1 - a(1-t)]
Calculating the Change in Net Exports
Let's assume that in part (ii) we found the full employment output level (Yu) without income tax to be a specific value. We are now given an economy *with* income tax 't'. We want to find the change in net exports (ΔNX) that will bring the equilibrium output level *with* income tax to Yu. Let NX' be the new level of net exports required.
We want:
Yu = [I + G + NX'] / [1 - a(1-t)]
Rearranging to solve for NX':
NX' = Yu * [1 - a(1-t)] - I - G
Determining the Change in Net Exports (ΔNX)
The change in net exports (ΔNX) is the difference between the new net exports (NX') and the original net exports (NX):
ΔNX = NX' - NX
Substituting the expression for NX':
ΔNX = [Yu * (1 - a(1-t)) - I - G] - NX
Since the original equilibrium output (Y) was determined by Y = [I + G + NX] / [1 - a(1-t)], we can express NX as:
NX = Y * [1 - a(1-t)] - I - G
Substituting this into the equation for ΔNX:
ΔNX = [Yu * (1 - a(1-t)) - I - G] - [Y * (1 - a(1-t)) - I - G]
Simplifying, we get:
ΔNX = (Yu - Y) * [1 - a(1-t)]
Sign and Magnitude of the Change
The sign of ΔNX depends on the relationship between Yu and Y. If the introduction of income tax led to a decrease in equilibrium output (Y < Yu), then (Yu - Y) will be positive. Since [1 - a(1-t)] is always positive (as 'a' is the marginal propensity to consume and is between 0 and 1, and 't' is the tax rate), ΔNX will be positive. This means net exports must *increase* to restore the equilibrium output to the full employment level.
The magnitude of the change depends on the size of (Yu - Y) and the value of [1 - a(1-t)]. A larger difference between full employment output and the actual output, or a smaller value of [1 - a(1-t)] (indicating a larger impact of taxation on disposable income), will require a larger increase in net exports.
Conclusion
In conclusion, the change in net exports required to bring the equilibrium output level back to Yu after the introduction of income tax is given by ΔNX = (Yu - Y) * [1 - a(1-t)]. The change will be positive if the tax reduces output below the full employment level, indicating a need to boost net exports. The magnitude of this change is directly proportional to the gap between the desired and actual output levels and inversely related to the impact of taxation on disposable income. This analysis highlights the interconnectedness of different components of aggregate demand and the importance of fiscal policy in maintaining macroeconomic stability.
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.