In the above question, calculate the effect on output of a 10 per cent increase in transfers, and a 10 per cent increase in lump-sum taxes. Compare the effects of the two.
Step 1: Identify the given values from Question 6
- Marginal propensity to consume (c) = 0.80
- Transfers (TR) = 100
- Lump-sum tax (T) = 30 (from part c)
Step 2: Calculate the effect of 10% increase in transfers
- ΔTR = = 10
- Transfer multiplier = c/(1-c) = 0.80/(1-0.80) = 0.80/0.20 = 4
- ΔY = = 40
Step 3: Calculate the effect of 10% increase in lump-sum taxes
- ΔT = = 3
- Tax multiplier = -c/(1-c) = -0.80/(1-0.80) = -0.80/0.20 = -4
- ΔY = - = -12
Step 4: Compare the effects
- Both multipliers have the same absolute value (4)
- Transfer increase raises output by 40
- Tax increase reduces output by 12
- The effects are opposite in direction
- The magnitude differs because the base values differ (100 vs 30)
Explanation
The question requires calculating the effect of a 10% increase in transfers and a 10% increase in lump-sum taxes on output. From Question 6, c = 0.80, TR = 100, and T = 30 (from part c). The transfer multiplier is c/(1-c) = 4, and the tax multiplier is -c/(1-c) = -4. Both have the same absolute value but opposite signs. A 10% increase in transfers (ΔTR = 10) raises output by 40, while a 10% increase in taxes (ΔT = 3) reduces output by 12. The effects are opposite in direction, and the magnitude differs because the base values differ.
Solution Steps
Step 1: Identify the given values from Question 6 - c = 0.80, TR = 100, T = 30
Step 2: Calculate the effect of 10% increase in transfers - ΔTR = 10, multiplier = 4, ΔY = 40
Step 3: Calculate the effect of 10% increase in lump-sum taxes - ΔT = 3, multiplier = -4, ΔY = -12
Step 4: Compare the effects - opposite direction, same absolute multiplier, different magnitude due to different base values