### Carbon tax

A carbon tax is a tax on emissions. Without a tax or some other price on
emission, people do not consider the full consequences of their actions.
They can emit CO_{2} without considering that this harms others.
Economists call this a market failure: the price of fossil fuel energy
does not represent the true price, unlike with most other products in the
economy. A a result, people use too much fossil fuel energy.

A carbon tax fixes this problem by enforcing people to consider the full costs of fossil fuel energy, including the harms that using fuel energy will cause due to climate change. A carbon tax is thought by many to be the most efficient method of controlling emissions.

There are two ways in the model to impose a carbon tax. The first is to choose a carbon tax explicitly through the simulated carbon tax option. The second is to choose the optimization option. If you choose optimization, the computer calculates an emissions path that maximizes the objective function and then determines the carbon tax that is necessary to achieve that path. more

If webDICE is run in optimization mode or with an imposed treaty, it computes the emissions control rate $\mu$ that gives the appropriate level of emissions reductions. To display the carbon tax it uses the tax that is implied by the emissions control rate via the equation: \[ \tau(t)=BC(t)\mu(t)^{\theta_{2}-1}, \] where $BC(t)$ cost of the backstop technology.

If the user sets the carbon tax explicitly, the model finds the implied emissions control rate, solving the above equation for $\mu$: \[ \mu(t)=\left(\frac{\tau(t)}{BC(t)}\right)^{1/\left(\theta-1\right)}. \]