7. Negative Externality Numerical Example
Based on Dr. Galal's slides + Exam data (MEC = $20 constant)
Problem Setup
A product sold in competitive market. No external benefit. External cost (MEC) = $20/unit constant.
Try filling in the table yourself first, then check!
Fill-the-Table Exercise
| Units | MPB | MPC | MEC | MSB=MPB | MSC=MPC+MEC |
|---|---|---|---|---|---|
| 10 | 80 | 20 | |||
| 20 | 70 | 30 | |||
| 30 | 60 | 40 | |||
| 40 | 50 | 50 | |||
| 50 | 40 | 60 | |||
| 60 | 30 | 70 |
Completed Table:
| Units | MPB | MPC | MEC | MSB=MPB | MSC=MPC+MEC |
|---|---|---|---|---|---|
| 10 | 80 | 20 | 20 | 80 | 40 |
| 20 | 70 | 30 | 20 | 70 | 50 |
| 30 | 60 | 40 | 20 | 60 | 60 |
| 40 | 50 | 50 | 20 | 50 | 70 |
| 50 | 40 | 60 | 20 | 40 | 80 |
| 60 | 30 | 70 | 20 | 30 | 90 |
Solution
- Market equilibrium: MPB = MPC at Q = 40, P = $50
- Efficient point: MSB = MSC at Q = 30, P = $60
- Corrective Tax = MEC = $20
- Consumer price after tax: $60 (price on demand at Q=30)
- Producer price after tax: $60 - $20 = $40 (or MPC at Q=30 = 40)
- DWL/Efficiency gains: \(\frac{1}{2} \times (40-30) \times (70-50) = \frac{1}{2} \times 10 \times 20 = 100\)
ERROR FLAG: Dr. Galal's Slides
Dr. Galal's answer states: "The probable efficient level of output @ E1@ Q = 40"
This is INCORRECT. Q=40 is the market equilibrium (where MPB=MPC=50), NOT the efficient point.
Correct Answer: The efficient level is Q=30 where MSB=MSC=60. Market equilibrium is Q=40 where MPB=MPC=50.
At Q=40: MSC(70) ≠ MSB(50). The efficiency condition is NOT satisfied.
At Q=30: MSC(60) = MSB(60). The efficiency condition IS satisfied.
At Q=40: MSC(70) ≠ MSB(50). The efficiency condition is NOT satisfied.
At Q=30: MSC(60) = MSB(60). The efficiency condition IS satisfied.