The Atmosphere

Every thread of this volume gathers in the atmosphere. The carbon dioxide released from a chimney or a tailpipe joins a stock shared across borders, and part of the resulting disturbance persists beyond the lives of those who made the bargain that released it. The sale of the fuel is concluded; its consequences continue. The physical process gives the externality its reach. Carbon moves among the atmosphere, oceans and land on different timescales, so an emission has no single expiry date after which its effects can simply be struck from the account. A 2013 comparison of carbon-cycle models led by Fortunat Joos found a rapid initial decline in an added atmospheric pulse followed by a persistent tail extending through the study’s thousand-year horizon. The common atmosphere also gives the harm a geography different from the transaction. The people exposed to a changing climate need not be the people who purchased the energy, and the burdens need not be equal among those exposed. Global reach, persistence and unequal exposure enter the same account.¹

The social cost of carbon asks what one additional unit of emissions adds to that account. It follows the increment through the carbon cycle and climate into future losses, then expresses their value in units that can be compared with a cost borne now. This is a marginal, counterfactual calculation: compare two otherwise specified paths, one with the added emission and one without it. An integrated assessment model makes the links explicit, along with choices about adaptation, production, consumption and welfare. In their 2014 model, Mikhail Golosov, John Hassler, Per Krusell and Aleh Tsyvinski derived a particularly transparent expression: with logarithmic utility, a specified proportional damage structure, a linear carbon response and a constant saving rate, the optimal tax relative to current output depends on discounting, expected damage parameters and carbon persistence. Longer persistence matters because more future losses enter the sum; larger marginal damages matter because each date contributes more. The simplicity belongs to the model’s assumptions. It clarifies the channels through which a price is constructed, while leaving the magnitude to the evidence and the valuation placed upon it.²

Discounting determines how a later consequence enters today’s comparison. Suppose, solely to isolate that operation, an additional emission causes a certain loss of 100 units of real consumption fifty years from now and no other loss. At a constant annual discount rate of one percent its present value is about 60.80; at three percent it is about 22.81. The physical loss is identical. The valuation differs because the later units receive different weights. The discount rate used for consumption can itself reflect several judgments: the weight attached to later welfare, the expected growth of consumption, and how the value of an additional unit changes with the circumstances of its recipient. Uncertainty adds the question of which future states contain the loss. A hundred units lost when people have little may carry a different welfare cost from a hundred lost amid abundance. A financial return offers information about intertemporal exchange under particular risks and opportunities; applying it to a global harm requires identifying the comparable claim. The choice cannot be settled by the date alone, and the carbon price also remains sensitive to the physical response, the damage relation and who bears the damage.³

A carbon price carries this valuation into the choice of how much to emit. If an extra unit imposes a valued harm of fifty and can be avoided for thirty, avoiding it creates a net gain of twenty under that calculation. Avoiding an otherwise identical unit at a cost of seventy would cost more than the harm it prevents. A uniform charge of fifty makes these different abatement opportunities face the same marginal test. This is the familiar Pigovian condition, applied to a consequence spread through time. Its first-best implementation assumes that the other relevant margins and the policy’s coverage are properly accounted for. A tax receipt transfers purchasing power; the avoided emissions supply the environmental gain. An emissions cap instead fixes the covered quantity for the relevant period and lets the permit price adjust. Its atmospheric consequences still depend on emissions outside the cap and on the path before and after that period. The instruments organize a choice; their distributional effects also depend on how revenues or permits are assigned and what alternatives households and producers can use.⁴

The national incentive can remain smaller than the global gain even when every calculation is agreed. Consider two countries, each choosing a nonnegative amount of abatement. Suppose each country receives four units of benefit for every unit abated by either country, while bearing a domestic cost equal to half the square of its own abatement. Acting separately, each chooses four: its marginal domestic benefit is four and its marginal cost reaches four there. If they choose to maximize their combined benefit less cost, each abates eight, because every unit benefits both countries. At four each, each country gains twenty-four after costs; at eight each, each gains thirty-two. Yet a country that cuts its own abatement back to four while the other stays at eight gains forty. The cooperative result improves both countries’ positions and still invites defection. The figures are an illustration of the incentive, with equal benefits and costs and no other interactions. If a country’s abatement benefited only itself, the omitted benefit would disappear and this reason for the two choices to diverge would disappear with it.⁵

Cooperation therefore needs an arrangement that can sustain participation as well as identify a desirable total. Nordhaus’s 2015 climate-club proposal joined a common carbon-price target to trade penalties on nonparticipants. The penalty changed the payoff from remaining outside, allowing the model to support more participation at some target prices. Its assumptions included a framework permitting the specified penalties and excluding retaliation; its success varied with the cost of abatement and the chosen target. The proposal makes the participation problem concrete. A promise is more durable when the parties have reasons to keep it, and a common target still leaves the division of costs to be worked out. Monitoring emissions, comparing performance and maintaining the agreed consequences all require institutions. The same burden can weigh differently on a wealthy country and a poor one; a uniform marginal signal can coexist with transfers that change who pays. The global gain supplies a reason to coordinate, while the terms of coordination determine whether the agreement can endure.

The atmosphere brings the volume to the edge of the bargaining table. The damage can reach people who have no claim within the original transaction, and future people cannot appear to negotiate the terms on which their world is altered. A present institution must give their interests a place in the decision. The price can record the value assigned to an additional emission; it acquires practical force through rules that measure, collect, enforce and revise. Better knowledge can change that value, and a durable arrangement must permit learning without making every commitment vanish at the next disagreement. The shared stock thus gathers the volume’s questions about measurement, rights, incentives and authority into a single case. The companion inquiry in The Commons takes up the institution capable of governing what many use together. Here the chimney’s account closes only when it has made room for consequences beyond the owner’s boundary and beyond the owner’s lifetime.