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### Abatement costs

Reducing emissions will cost money. These costs are called abatement costs. If you run the model under the default, business as usual mode, these are zero as emissions are allowed to go uncontrolled. If instead you impose a climate policy, either by setting a tax or a treaty or by allowing the computer to optimize, these costs will be positive.

The model specifies abatement costs as a fraction of the total output: this is the portion of GDP that we spend replacing fossil fuel energy with clean energy. The amount is determined by the cost of clean energy (called the backstop technology link), the extent of emissions reduction (link to emissions control rate) and how many countries or industries participate (link to the participation rate). In general, abatement costs increase with the extent of the reductions, go down the more countries and industries that participate in reductions, and go down as the costs of clean energy go down. You cannot change abatement costs directly. Instead, you can change each of these three components that make up abatement costs. more

The abatement cost, $$\Lambda(t),$$ is the fraction of output spent on limiting emissions based on the specifications of a given climate policy. There are three components to abatement costs: the emissions control rate, $\mu(t)$, the participation fraction, $\varphi(t)$, and the cost of replacing all fossil fuels with carbon-free energy (the backstop technology), $\theta_{1}(t)$. Abatement costs are the product of these three components:

$\Lambda(t)=\theta_{1}(t)\varphi(t)^{1-\theta_{2}}\mu(t)^{\theta_{2}}.$