Carbon Pricing: Tax vs Cap-and-Trade

Policy Instrument

Tax rate (price per ton CO₂) $60

Emissions cap (abatement target) 50%

Market Setup

Number of firms 28

Cost-curve steepness γ 1.6

Market Outcome

Firms abating

0 / 0

Tons abated

Clearing price

$0/t

Govt revenue

Market abatement cost (cheapest-first)

Cost of a uniform mandate, same tons

Savings from price mechanism

$0 (0%)

How it works

Each firm i has a marginal abatement cost MC_i — the $/ton price at which cutting one more ton of CO₂ becomes worth it to that firm. Sorted from cheapest to priciest, these costs trace a firm's marginal abatement cost curve (MACC), drawn here as bars sorted left→right by cost, with a translucent price plane at the current $/ton level.

Firm abates  ⟺  MC_i ≤ p
Tax:  government picks p directly (ideally p = SCC,
      the social cost of carbon / external damage per ton)
Cap:  government picks quantity Q; the market finds the
      price p* at which exactly the Q cheapest firms abate
      → p* = MC of the marginal (Q-th) firm
Weitzman equivalence: under certainty, a well-chosen tax and
a well-chosen cap implement the identical allocation.

Whichever way the price is set, letting every firm compare its own MC to the same price is cost-minimizing: it always sends abatement to the cheapest firms first. The "uniform mandate" comparison shows what the same tons of abatement would cost if every firm were instead required to cut the same share of its emissions, regardless of cost — with heterogeneous costs this ignores cheap opportunities and forces expensive ones, so its total bill is always ≥ the market outcome. That gap is the classic argument for price-based over command-and-control instruments.

Carbon Tax / Cap & Trade — switch which lever the policy sets directly; the other becomes an outcome.
Tax rate / Cap slider — moves the price (tax) or the target quantity (cap); bars flip from paying (amber) to abating (green) as their cost crosses the price plane.
Number of firms / steepness γ — reshape the market: more firms or a steeper γ spreads costs further, changing how much abatement a given price buys.

Firm abates (MC ≤ price) Firm pays tax / buys permit Carbon price plane

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