The Encyclopedia of Economic Principals

Chapter 83

Pollution, Climate Policy, Leakage, and Regulatory Instruments

Where plants go, how emissions move with growth, and which instrument to use.

Four of the chapter's worked examples, made interactive: a pollution-haven location choice, the environmental Kuznets curve split into its parts, the green paradox, and prices versus quantities. Change one value at a time and watch the figure, the numbers and the hand calculation respond.

Every example here is a constructed teaching example: it uses the hypothetical numbers of the chapter's worked examples, plus a few values added for comparison and labelled as such in each panel. Nothing here measures a real market, firm or household.

Demonstration 1 of 4

Pollution haven location choice

When does a looser environmental rule plus cheaper trade pull a plant abroad?

A plant goes where total delivered cost is lowest. A regulatory gap alone may not be enough when trade costs are high; cutting trade friction can tip the balance. Equal enforcement removes the reason to move.

Equation, written in LaTeX: K_S=14.7+0.3+0.5=15.5\text{ million dollars},

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K is a location's annual delivered cost in $ million: ordinary cost (labor, inputs, facility), environmental compliance cost and delivery cost to the market. North's ordinary cost is 14.0 and environmental cost 1.8; South's ordinary cost is 14.7.

Predict first. If South enforced half the gap (environmental cost 1.05), would the plant still move after the agreement?

Your prediction

Choose an example

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Figure: Pollution haven location choice. Stacked bars of ordinary, environmental and delivery cost: North 15.80 million, South 15.50 million with delivery 0.50 and environmental cost 0.30.
South delivery cost ($ million): 0.5, South environmental cost ($ million): 0.3
Constructed example: the chapter's hypothetical component maker (North 14.0 and 1.8, South 14.7 and 0.3, delivery 1.2 and 0.5, equal enforcement 1.8); delivery 0.85 and South environmental cost 1.05 are added for comparison.

Calculated values

North total ($ million)
15.80
South total ($ million)
15.50
Location
South
Gap South minus North
-0.30

North costs 14.0 + 1.8 = 15.80 million. South costs 14.7 + 0.30 + 0.50 = 15.50 million. South is cheaper by 0.30 million, so the plant moves. South's ordinary cost is 0.7 million higher, so any move rests on its environmental-cost advantage of 1.50 million and the delivery cost.

Worked steps

  1. North = 14.0 + 1.8 = 15.80
  2. South = 14.7 + 0.30 + 0.50 = 15.50
  3. South - North = 15.50 - 15.80 = -0.30

Use the idea

List every cost component by site, including compliance and delivery, before attributing a relocation to environmental rules.

Where the conclusion applies

One plant, fixed costs at each site and a single market. Cleaner technology, which shrinks the environmental gap, also removes the incentive to move.

Check your understanding: At delivery 0.5 and South environmental cost 1.05, what is South's total?
14.7 + 1.05 + 0.5 = 16.25, above 15.8, so the plant stays North.

Chapter 83 source: section "Pollution-haven hypothesis".

Demonstration 2 of 4

Environmental Kuznets curve decomposition

Does growth itself clean the air, or do composition and technique do the work?

Emissions are scale times composition times technique. Growth raises scale; a falling dirty share and cleaner techniques can more than offset it. With the original techniques only the full shift to share 0.25 bends the curve, and barely (203.5 against 217.7).

Equation, written in LaTeX: E_L=80[0.45(2.5)+0.55(0.4)]=107.6.

Equation, written in LaTeX: E_M=140[0.55(2.5)+0.45(0.4)]=217.7.

Equation, written in LaTeX: E_H=220[0.25(0.7)+0.75(0.2)]=71.5.

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E is emissions: output times the share-weighted emission intensity of the dirty industry and the other sector. Output is 80, 140 and 220 at low, middle and high income.

Predict first. With cleaner technique but no shift away from industry (share 0.45), do emissions still fall from the middle stage?

Your prediction

Choose an example

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Figure: Environmental Kuznets curve decomposition. Emissions against output at three income stages: 107.6 at 80, 217.7 at 140 and 71.5 at 220, with high-income dirty share 0.25 and cleaner techniques (0.7 and 0.2).
High-income dirty share: 0.25, High-income technique: Cleaner (0.7, 0.2)
Constructed example: the chapter's hypothetical economy (outputs 80, 140, 220, shares 0.45, 0.55, 0.25, intensities 2.5 and 0.4, then 0.7 and 0.2); high-income shares 0.45 and 0.55 are added.

Calculated values

E_L
107.6
E_M
217.7
E_H
71.5
Shape
inverted U

At high income with dirty share 0.25 and cleaner techniques (0.7 and 0.2), E_H = 220 x (0.25 x 0.7 + 0.75 x 0.2) = 220 x 0.325 = 71.5. Emissions fall from 217.7 to 71.5, so the path is an inverted U. Income alone does not turn the curve; composition and technique do.

Worked steps

  1. E_L = 80[0.45(2.5) + 0.55(0.4)] = 107.6
  2. E_M = 140[0.55(2.5) + 0.45(0.4)] = 217.7
  3. E_H = 220[0.25(0.7) + 0.75(0.2)] = 71.5

Use the idea

Before reading an inverted U as a law of growth, split the change in emissions into scale, composition and technique.

Where the conclusion applies

Two sectors with fixed intensities at each stage and territorial emissions. If dirty industry simply moves abroad, consumption-based emissions can stay high.

Check your understanding: At share 0.45 with cleaner technique, what is E_H?
220[0.45(0.7) + 0.55(0.2)] = 220(0.315 + 0.11) = 93.5, still below 217.7.

Chapter 83 source: section "Environmental Kuznets curve".

Demonstration 3 of 4

Green paradox and announced charges

Does announcing a future charge on fossil producers pull extraction forward?

A resource owner compares net prices across dates. A charge expected later lowers the value of leaving the resource in the ground, so sales move forward until net prices match again. The same charge in both periods cancels out.

Equation, written in LaTeX: p_t=100-q_t

Equation, written in LaTeX: q_0+q_1=100

Equation, written in LaTeX: 100-q_0=q_0-20,

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q0 and q1 are units extracted in periods 0 and 1 from a stock of 100, with no extraction cost and zero interest. Inverse demand is p = 100 - q in each period. t0 and t1 are per-unit charges on the producer.

Predict first. Does a heavier future charge of 30 pull more extraction forward than 20?

Your prediction

Choose an example

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Figure: Green paradox and announced charges. Bars of extraction: 60 in period 0 and 40 in period 1, with charges 0 and 20; a dashed line marks 50, the no-policy split.
Period 1 charge: 20, Period 0 charge: 0
Constructed example: the chapter's hypothetical owner (stock 100, demand p = 100 - q, charge 20 in period 1 or in both); charges of 10 and 30 are added for comparison.

Calculated values

q0
60
q1
40
p0
40
p1
60
Net price each period
40
Units moved to period 0
10

The owner sells where net prices match: 100 - q0 - 0 = q0 - 20, so q0 = (100 + 20 - 0) / 2 = 60 and q1 = 40. Compared with 50 and 50, 10 units move into period 0 before the heavier later charge. Total extraction stays 100.

Worked steps

  1. Net prices equal: 100 - q0 - 0 = q0 - 20
  2. q0 = (100 + 20 - 0) / 2 = 60
  3. q1 = 100 - 60 = 40
  4. p0 = 100 - 60 = 40; p1 = 100 - 40 = 60

Use the idea

When a climate policy is announced ahead of time, model the producer's timing choice before counting emissions savings.

Where the conclusion applies

A fixed stock that is all sold, zero cost and interest, and a credible announcement. If later demand were low enough to strand reserves, the total could change too.

Check your understanding: With a period 1 charge of 30 and none in period 0, what are q0 and q1?
100 - q0 = q0 - 30, so q0 = 65 and q1 = 35; prices 35 and 65, net 35 each.

Chapter 83 source: section "Green paradox".

Demonstration 4 of 4

Prices versus quantities

With uncertain abatement cost, should the regulator set a tax or a cap?

A tax fixes the marginal incentive and lets abatement adjust to the cost shock; a cap fixes abatement. If damages change little with quantity (flat benefit), letting quantity move costs little and the tax wins. If damages rise steeply, holding quantity matters more and the cap wins.

Equation, written in LaTeX: L_Q(\varepsilon)=\frac{\varepsilon^2}{2(b+c)}.

Equation, written in LaTeX: L_P(\varepsilon)=\frac{\varepsilon^2b^2}{2c^2(b+c)}.

Equation, written in LaTeX: L_Q=\frac{12^2}{2(2+6)}=9.

Equation, written in LaTeX: L_P=\frac{12^2(2^2)}{2(6^2)(2+6)}=1.

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b is the slope magnitude of marginal environmental benefit and c the slope of marginal abatement cost. The cost shock is 12 or -12 with probability one half each. L_Q and L_P are the welfare losses of a fixed cap and a fixed tax relative to the best response to the shock.

Predict first. When the two slopes are equal, which instrument wins?

Your prediction

Choose an example

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Figure: Prices versus quantities. Left: marginal benefit with slope -2 and marginal cost with slope 6, shifted up by 12; the cap holds abatement at the target, the tax lets it fall to -2.00. Right: losses 1.0 for the tax and 9.0 for the cap.
Marginal-benefit slope b: 2, Marginal-cost slope c: 6
Constructed example: the chapter's hypothetical regulator (shock 12, slopes b = 2, c = 6 and b = 12, c = 3); b = 6 is added for comparison.

Calculated values

L_Q (cap)
9.0
L_P (tax)
1.0
L_P / L_Q = (b/c)^2
0.111
Preferred instrument
Price (tax)

With shock 12, L_Q = 144 / (2 x 8) = 9.0 and L_P = 144 x 4 / (2 x 36 x 8) = 1.0. Price (tax) wins: marginal benefit is flatter than marginal cost (b < c), so letting quantity move is cheaper.

Worked steps

  1. L_Q = 144 / (2 x (2 + 6)) = 144 / 16 = 9.0
  2. L_P = 144 x 4 / (2 x 36 x 8) = 576 / 576 = 1.0
  3. L_P / L_Q = (2/6)^2 = 0.111

Use the idea

Estimate the two slopes around the target: when marginal benefit is flatter than marginal cost, favor a price; when steeper, favor a quantity.

Where the conclusion applies

Linear marginal curves near the target, an additive cost shock and policy set before the shock is known. Hybrids such as price ceilings move between the two cases.

Check your understanding: At b = 6 and c = 6, what are L_Q and L_P?
L_Q = 144 / (2 x 12) = 6; L_P = 144 x 36 / (2 x 36 x 12) = 6; a tie, since L_P / L_Q = (b/c)^2 = 1.

Chapter 83 source: section "Weitzman prices-versus-quantities result".