8. Positive Externality Numerical Example
Based on Dr. Galal's slides (MEB = $20 constant)
Problem Setup
A product sold in competitive market. No external cost. External benefit (MEB) = $20/unit constant.
Try filling in the table yourself first, then check!
Fill-the-Table Exercise
| Units | MPB | MPC | MEB | MSB=MPB+MEB | MSC=MPC |
|---|---|---|---|---|---|
| 10 | 80 | 20 | |||
| 20 | 70 | 30 | |||
| 30 | 60 | 40 | |||
| 40 | 50 | 50 | |||
| 50 | 40 | 60 | |||
| 60 | 30 | 70 |
Completed Table:
| Units | MPB | MPC | MEB | MSB=MPB+MEB | MSC=MPC |
|---|---|---|---|---|---|
| 10 | 80 | 20 | 20 | 100 | 20 |
| 20 | 70 | 30 | 20 | 90 | 30 |
| 30 | 60 | 40 | 20 | 80 | 40 |
| 40 | 50 | 50 | 20 | 70 | 50 |
| 50 | 40 | 60 | 20 | 60 | 60 |
| 60 | 30 | 70 | 20 | 50 | 70 |
Solution
- Market equilibrium: MPB = MPC at Q = 40, P = $50
- Efficient point: MSB = MSC at Q = 50, P = $60
- Corrective Subsidy = MEB = $20
- Producer price after subsidy: $60 (price on MSC/MPC at Q=50)
- Consumer price after subsidy: $60 - $20 = $40 (= MPB at Q=50)
- Efficiency gains: \(\frac{1}{2} \times (50-40) \times (70-50) = \frac{1}{2} \times 10 \times 20 = 100\)
ERROR FLAG: Dr. Galal's Slides - Positive Externality
Dr. Galal's answers state: "Producer price before subsidy @ E1@ P = 60 @ Q = 30" (claiming equilibrium at Q=30)
This is INCONSISTENT with the table data.
Correct Answer: Market equilibrium is where MPB = MPC.
At Q=30: MPB=60, MPC=40. NOT equal (60 ≠ 40).
At Q=40: MPB=50, MPC=50. EQUAL! This is the market equilibrium.
Efficient: Q=50 where MSB=MSC=60. Galal says Q=40, which is also incorrect.
At Q=30: MPB=60, MPC=40. NOT equal (60 ≠ 40).
At Q=40: MPB=50, MPC=50. EQUAL! This is the market equilibrium.
Efficient: Q=50 where MSB=MSC=60. Galal says Q=40, which is also incorrect.