### Capital

Capital — machines, land, patents, and so forth — is used to produce economic output. The model starts with a specified level of capital based on the current economy. This capital depreciates due to wear and tear and obsolescence but in each period, the people in the model save a portion of their output, adding to existing capital. Therefore, the capital available in a given period is the capital from previous time-periods, reduced by depreciation, plus savings. more

The amount of capital available for use in a given time period, $K(t),$ is the sum of depreciated capital from the prior period, $(1-\delta_{K})K(t-1),$ and the amount saved, $I(t)$: \[ K(t)=I(t)+(1-\delta_{K})K(t-1), \]

The model sets the default depreciation rate, $\delta_{K},$ to 10%; users can choose to adjust this parameter between 8% and 20%.

Total savings, $I(t),$ is a fixed fraction of output, $Q(t),$ determined by the savings rate, $s$. \[ I(t)=s\times Q(t) \]

Output, $Q(t),$ is split between consumption, $C(t),$ and savings, $I(t).$ \[ Q(t)=C(t)+I(t) \]

The model sets the default savings rate, $s,$ to 22% of output. Some versions of DICE solve for the optimal savings rate. webDICE does not support optimization of the savings rate because Nordhaus reports that the optimal savings rate is relatively insensitive to assumptions and optimization would slow down the model significantly. Instead of optimization, webDICE allows users to choose a savings rate between 15% and 25%.