The payment must match the missing incentive.
A corrective tax can make a decision maker face a marginal external cost; a subsidy can reward a marginal external benefit. In the simple competitive model, a tax equal to MEC at the social optimum or a subsidy equal to MEB there can align private incentives with that output. This result depends on the measured gap, policy base, enforcement and other assumptions; any positive tax or subsidy is not automatically corrective.
- Tax
- A tax charges the decision maker for the activity. In the simple model, a per-unit tax equal to MEC at the optimum adds the missing external cost to the private incentive and reduces output towards that optimum.
- Subsidy
- A producer subsidy is a government payment that lowers the producer's net cost per unit. A subsidy equal to MEB at the optimum can reward the missing external benefit and encourage the worthwhile extra output.
- Getting the rate right
- Too little correction leaves part of the original problem. Too much can push output past the optimum, losing benefits worth more than the costs saved or adding units worth less than their cost.
What can prevent the textbook correction?
Measurement
MEC and MEB may vary by output, location and person. The relevant corrective rate is the marginal gap at the optimum, not total external damage divided by any convenient quantity.
Tax base
The tax base is what the charge applies to, such as each unit of output or each tonne of emissions. Taxing output targets pollution accurately only if their relationship is known; an emissions charge can respond more directly when firms can change how they produce.
Responses
Alternative products, production capacity, time and whether people follow the rules affect the quantity response. A financial payment alone need not correct misinformation.
Budget and welfare
A subsidy payment transfers money from government to recipients; it is not itself a measure of resources used or net social benefit. Government still needs funding. Count real administration resources and any costs of raising or diverting funds when evaluating the actual policy.
| Tax per unit | Resulting Q | Remaining allocation loss |
|---|---|---|
| 0 | 80 | 40 |
| 2 | 70 | 10 |
| 4 | 60 | 0 |
| 8 | 40 | 40 |
Worked example: A correctly sized tax and an excessive one
Use MPB = 20 - 0.1 Q, MPC = 4 + 0.1 Q and MEC = $4. The unregulated quantity is 80 and social optimum is 60.
- A $4 tax on each unit raises the private supply price to MPC + 4, giving Q = 60. For any tax t, set 20 - 0.1Q = 4 + 0.1Q + t. Then 16 - t = 0.2Q, so Q = 80 - 5t.
- The tax changes the private incentive; it does not physically erase the external damage from each remaining unit.
- At a $2 tax, Q = 70. The remaining quantity gap is 70 - 60 = 10, and MSC - MSB at 70 is $2. Remaining DWL is 0.5 x 10 x 2 = $10.
- An $8 tax instead gives Q = 80 - 5(8) = 40, below the optimum. Between 40 and 60, benefits exceed social costs. The gap is $4 at 40, so the new loss is 0.5 x 20 x 4 = $40.
- For a separate positive externality of $4, a $4 producer subsidy moves output from 80 to 100. Its budget cost is $400, while the modelled welfare improvement is $40.
Watch out for this
A larger corrective tax always produces a larger welfare gain.
Reducing harmful activity beyond its social optimum can forgo benefits greater than the costs saved. Calibrate the policy to the relevant margin.
Check your understanding
If MEC at the social optimum is $3, which is the best starting rate in the stated simple corrective-tax model?
- Always zero because taxes reduce trade.
- $3 per unit, subject to measurement and implementation assumptions.
- Any rate above $3, because more reduction is always better.