where a 1 is the marginal energy consumption of a server, a 2 refers to the server's basic energy consumption generated by some non-workload-related components, e.g., power supply unit and storage devices etc. [44].
The marginal fuel consumption for power (beta _{g}^{el}) and heat (beta _{g}^{th}) production, the power generation upper (p_{g}^{mathrm {max}}) and lower (p_{g}^{mathrm {min}}) limits, the heat generation upper limit (q_{g}^{mathrm {max}}) and the power-to-heat ratio (alpha _{g}) are technical parameters of the units.
This is likely to have an adverse effect on our initial financial performance, though marginal as consumption levels may decrease slightly.
Equation (5) represents the standard optimal consumption-leisure choice: the marginal utility of consumption times the foregone consumption units as a result of one additional unit of leisure, the latter being (theta ^iw_t left( {1-tau _1^i-n_t^i times frac{partial tau _1^i }{partial n_t^i }}right) ), must equal the marginal utility of leisure.
There are no non-concavities due to borrowing constraints in our model because the only borrowing constraint is generated by the no-bankruptcy condition, which is in effect enforced by having infinite marginal utility of consumption at zero consumption.
Furthermore, due to the linearity of marginal utility of consumption, the SDF can be represented through aggregate consumption and aggregate bliss point consumption: begin{aligned} m_{i}=frac{c_i^b - c_{i1}}{c_i^b - c_{i0}}=frac{c^b - c_{1}}{c^b - c_{0}}, end{aligned} (84 for (i=1,2).
If the marginal utility of consumption today is positively correlated with historical consumption, then the period in which people were given financial incentives to go to the gym could also induce them to go to the gym more often in the future, leading to habit formation (Charness and Gneezy 2009).
The non-concavity arises because of changes in labour market status in future periods: the slope of the value function is given by the marginal utility of consumption, but this is not monotonic in the asset stock because consumption can decline as assets increase and expected labour market status in future periods changes.
Tax progressivity is motivated by a belief that the urgency of spending needs declines as the level of spending increases (economists call this the declining marginal utility of consumption), so that wealthy people can afford to pay a higher fraction of their resources in taxes.
