Public Finance Review — Using Every Tool on a Single Carbon Tax

Public Finance Review — Following One Policy All the Way Through

The previous nine chapters introduced tools one at a time. Real policy questions require all of them, in order. Using a carbon tax as the example, this chapter asks in turn: “Why intervene → who bears it → how much does it distort → where does the revenue go → is it worth it?” The numbers are assumptions chosen to show the structure.

1. Why intervene? (Chapter 1)

Greenhouse gas emissions are a textbook negative externality. The damage is spread across the whole world and future generations, and there are far too many victims for Coasean bargaining. As Chapter 1 concluded, the benchmark is a Pigouvian tax equal to the marginal external cost.

Assume the marginal damage from a tonne of carbon (the social cost of carbon) is 50,000 won. Burning a litre of petrol emits about 2.3 kg of carbon dioxide, so the tax per litre is $0.0023\times 50{,}000\approx 115$ won.

2. Who bears it? (Chapter 2)

In a small open economy like Korea, the supply of crude oil is almost perfectly elastic at the world price. In the Chapter 2 formula, when supply elasticity is very large, the consumer share $\varepsilon_s/(\varepsilon_s+|\varepsilon_d|)$ approaches 1. Most of the 115 won per litre shows up in consumer prices.

By income group, energy spending is a larger share of annual income for low-income households, so looking at the tax alone it is regressive. If a low-income household pays 200,000 won a year and a high-income household 600,000 won, the high-income household pays more in absolute terms but the low-income household pays more relative to income.

3. How much does it distort? (Chapters 2 and 5)

Assume a short-run price elasticity of petrol demand of $-0.2$ . Adding 115 won (about 6.8%) to a price of 1,700 won reduces consumption by about 1.4%. That reduction is the very purpose of a corrective tax. By the logic of Chapter 1, the trades eliminated by the corrective tax were ones whose social cost exceeded their benefit, so if the tax rate equals marginal damage, the reduction is a welfare gain, not an excess burden.

Excess burden arises elsewhere. Through the tax interaction effect of Chapter 5, higher energy prices lower real wages and slightly distort labour supply. And if transport, industry and households face different rates, the cost of cutting the same tonne differs by sector, and the inefficiency of not making the cheapest cuts first appears. A carbon tax is most efficient with the same rate on every source of emissions.

4. Where does the revenue go? (Chapters 3, 4 and 6)

If 500 million of 600 million tonnes of annual emissions are taxed, a rate of 50,000 won a tonne raises 25 trillion won. The character of the policy depends on how the money is used.

Uses of carbon tax revenue
Use	Efficiency	Distribution	Related chapters
Equal per-person rebate (carbon dividend)	No distortion	Lower income groups can be net gainers	Chapter 3
Cuts in income tax and social insurance contributions	Lower excess burden of other taxes (second dividend)	Benefits working households	Chapters 4 and 5
Deficit reduction	Lower future taxes	Transfer across generations	Chapter 6
Green investment spending	Depends on projects' NPV	Varies by project	Chapter 9

Let us work out an equal rebate. Dividing 25 trillion won among 50 million people gives 500,000 won per person a year. If the low-income household in the previous section (paying 200,000 won) has two members, it receives 1 million won, a net gain of 800,000 won; a two-person high-income household (paying 600,000 won) gains 400,000 won net. High-emitting households whose burden exceeds the per-person rebate bear a net cost. Because the scheme distributes even the tax paid by firms to households, most households are net gainers in this example; the actual distribution depends on each household’s direct and indirect emissions. Even if the tax itself is regressive, the policy combining tax and rebate can be progressive. As Chapter 3 taught, distribution is corrected most cheaply on the spending side.

5. Is it worth it? (Chapter 9)

In a cost-benefit framework, the benefit is abatement times the social cost of carbon, and the costs are the resources used in abatement (more expensive energy and equipment) plus the excess burden from tax interaction. Because the benefits appear over decades, the choice of discount rate in Chapter 9 heavily influences the conclusion. Estimates of the social cost of carbon themselves vary several-fold with the discount rate.

As the principles of Chapter 7 imply, the role of local government is limited. Because the benefits leak to the whole planet, a regional carbon tax tends to be set too low, and if only one region taxes, emissions move to other regions (carbon leakage). Border carbon adjustment applies the same logic at the national level.

6. Summary of key formulas

Key formulas of Public Finance Chapters 1–9
Chapter	Formula	Meaning
1	ΣMB_i = MC	Efficiency condition for public goods (Samuelson)
1	t = MEC(Q)	Pigouvian tax
2	ΔP_d/t = ε_s/(ε_s+\|ε_d\|)	Consumers' share of the burden
2	DWL ≈ ½ t² · [ε_s\|ε_d\|/(ε_s+\|ε_d\|)] · Q/P	Excess burden is proportional to the square of the tax rate
2	t_i/P_i ∝ 1/\|ε_i\|	Ramsey inverse-elasticity rule
3	B = G − τE	Linear benefit, ending at G/τ
4	t* = 1/(1+e)	Revenue-maximizing tax rate
4	t_c + (1−t_c)t_d	Combined tax rate on dividend income
6	1/(1−c(1−τ)+m)	Spending multiplier with leakages
6	Δb ≈ (r−g)b − s	Debt-ratio dynamics
7	p = 1/(1+m)	Local price created by a matching grant
8	Contribution rate = dependency ratio × replacement rate	Balance of a pay-as-you-go pension
9	NPV = Σ(B_t−C_t)/(1+ρ)^t	Cost-benefit analysis

Series contents

References

Jonathan Gruber, Public Finance and Public Policy
Harvey Rosen and Ted Gayer, Public Finance
Institute for Fiscal Studies, Tax by Design: The Mirrlees Review (2011), ch. 13
William Nordhaus, The Climate Casino (2013)