🏭 Efficient Pollution Abatement

Explore how marginal and total benefits/costs determine the socially optimal level of abatement

1
Set Cost & Benefit Parameters
2
Adjust Abatement Level X
3
Compare Total & Marginal Views
🎯 Abatement Level
Abatement (X) 50
📈 Benefit Function B(X)
Scale (a) 20
Curvature (b) 0.10
B(X) = aX - bX²
MB(X) = a - 2bX
📉 Cost Function C(X)
Curvature (c) 0.10
C(X) = cX²
MC(X) = 2cX
📊 Optimal Solution
Optimal X* 50
MB = MC at $10.00
Max NB $500
💡 Key Insight

Net Benefits are maximized where MB = MC. At X*, the slope of B(X) equals the slope of C(X), meaning NB = B - C is at its peak.

Below X*: MB > MC → net benefits increase with more abatement.
Above X*: MC > MB → net benefits increase with less abatement.

Total Benefits & Costs
B(X) - Total Benefit
C(X) - Total Cost
B(X)
$750
C(X)
$250
NB = B - C
$500
Marginal Benefits & Costs
MB(X) - Marginal Benefit
MC(X) - Marginal Cost
Net Benefits Area