Appendix Model Description1

The numerical results described in Figs. 1-5 are based on a simplified model of the links between climate change and the world economy that was developed by Howarth (1998). The model's empirical assumptions are derived from the previous work of Nordhaus (1994b), who provides a concise representation of climate dynamics and the technical determinants of economic growth. Nordhaus' analysis, however, focuses on an "optimal growth'' model in which decisions regarding consumption, investment, and greenhouse gas emissions are made by a hypothetical central planner to maximize a measure of long-term social welfare. Howarth's model, in contrast, makes use of an alternative specification in which routine economic decisions are made by individual households and businesses. In this model, the role of government is limited to the definition of environmental policies.

The model considers a market economy in which goods and services are produced using inputs of capital and labor. Economic output is divided between consumption and investment, and production is carried out by competitive firms that seek to maximize their profits given the prevailing prices of inputs and outputs. In the model, wages and salaries account for three-quarters of the value of economic output while capital accounts for the remainder. In addition, the model assumes that technological change augments the level of output at an initial rate of 1.4% per year. In line with standard demographic projections, the human population rises from its present level of about 6.0 billion persons to 10.5 billion in the long-run future. Population growth is concentrated in the next 100 years, during which four-fifths of the total increase occurs. The model assumes that the supply of labor is proportional to the total population. Individuals earn wage income by providing labor services to employers in the production sector.

Decisions regarding savings and investment are made by private individuals. A typical person lives for 70 years, investing part of the income she earns during her working years to provide for her retirement in old age. Savings are invested in capital goods at the prevailing interest rate, which reflects the incremental contribution that increased wealth makes to future economic activity. The model's assumptions about consumer preferences are chosen to match expected rates of economic growth.

The model assumes that greenhouse gas emissions - which include carbon dioxide, chlorofluorocarbons (CFCs), and CFC substitutes - increase in proportion to economic output. In the absence of emissions abatement policies, emissions in the year 2000 amount to some 0.37 kg of carbon equivalent per dollar of output. Due to technological innovations, the ratio of emissions per unit output falls at an initial rate of 0.55% per year. The model assumes that emissions abatement, although technologically feasible, is economically costly. A 50% reduction in greenhouse emissions requires a 0.93% reduction in economic output. Abatement costs rise to 6.86% of economic activity when emissions are fully controlled.

The model rests on a simple, but analytically tractable, representation of climate dynamics. Approximately two-thirds of greenhouse gas emissions go into the atmosphere, while the remaining third is absorbed by ecosystems and the surface waters of the oceans. Once in the atmosphere, a typical greenhouse gas molecule remains airborne for 120 years. Thus, anthropogenic emissions of greenhouse gases are removed from the atmosphere to the deep ocean at an effective rate of 0.833% per year. The model assumes that mean global temperature increases with the level of total greenhouse gas concentrations, measured in terms of carbon equivalent. A doubling of greenhouse gas concentrations relative to the pre-industrial norm (i.e., the prevailing conditions of the late 19th century) causes a net temperature increase of 2.91 °C. The climate impacts of methane and nitrous oxide (which are small in comparison with those caused by carbon dioxide, CFCs, and CFC substitutes) follow a fixed time path that is not affected by public policies.

A critical aspect of the model is regarding its assumptions about the damage imposed by climate change. Following Nordhaus (1994b), the model assumes that a 3.0°C temperature increase imposes environmental costs equivalent to a 1.33% reduction in economic output, while a 6.0°C temperature increase leads to a 5.32% output loss. The level of damage is proportional to the economic activity.

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