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### Economic model

webDICE uses an economic model in which labor and capital combine to produce output. The productivity of the economy determines how much output can be produced with a given amount of labor and capital. It is a measure of how skilled our workers are and how good the machines are that they use. The model treats the entire world as a single economic region and therefore does not include differences among countries or trade.

These three factors - labor, capital, and productivity - change over time in the model to produce a dynamic economy. The population is assumed to grow over time, increasing the supply of labor. Productivity grows over time but the growth rate slows down. Capital in a given time period is equal to the capital that was available in the last period reduced by wear and tear, plus savings in the last period. (see capital.)

Economic output is reduced by the harms from climate change (see Damages) and by an expenditures spend on reducing emissions (see abatement). What remains can be used by people to consume or to save for the future. more

Pre-climate change output $Y(t)$ depends on a (constant-returns-to-scale) Cobb-Douglas production function in technology, capital and labor, denoted by $A(t)$, $K(t)$, and $L(t)$ respectively. $Y(t)=A(t)K(t)^{\gamma}L(t)^{1-\gamma}$ The capital share, $\gamma$, is set to 30%. $A(t)$ and $L(t)$ evolve exogenously. Capital is determined within the model based on initial period capital, an assumed depreciation rate, and an assumed savings rate.

Final usable output $Q(t)$, is pre-damages output reduced by the fraction of harms from climate change, $\Omega(t)<1$, and by resources spent on abatement, $\Lambda(t)<1$. $Q(t)=\Omega(t)[1-\Lambda(t)]A(t)K(t)^{\gamma}L(t)^{1-\gamma}.$