Electricity Utility over Time

Electricity will normally be consumed when it is needed, at . However, if the price is very high at , or the electrical system risks blackouts, consumers need to delay their consumption, to take advantage of the lower price before the peak occurs. The utility from consuming it at or at is lower. The following four synchronous dynamic graphs show: the utility over time for any KWh (upper left); the fixed-time utility (lower left); the time, KWh total curves (lower right) and the three-dimensional utility function (upper right), where is a general price level. Initially, the - and KWh-parameters show a normal consumer, with the following utility
 function:
,
with , an electricity price given by , some income and some fixed level for .

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