How much is "a little bit" of electricity worth?

Graphed on log-log due to the scale.

The market for many commodities demonstrate the law of diminishing returns.  An infinite supply does not necessarily create in infinite market.

As a "prepper" I am more interested in the skinny side of the market than the fat side.  What might customers pay for commodities that are in short supply?  This is a difficult topic to treat in a rigorous, academic way but I want to take a swing at the pinata using a more causal type of analysis.

Consider electricity

Consumers will cheerfully pay $35 for a watch with 10 year battery life.  The battery nominally holds 0.5W-hours of power.  That suggests that people are willing to pay $35 for the functionality enabled by half a Watt-hour.  In terms of $/kW-hr, that is $7000 per kW-hr vs. a national average somewhere around $0.12

Now consider smart phones.  I know a family who spends more on their wireless bill than they do for their house payment.  Let's say they are spending $900/month for five smartphones.  Further, let's assume they fully recharge their batteries (3.7v, 1650mAh) every day.  Between the five of them their phones are consuming 0.9 kW-hrs/month.  They are willing to pay $900 for the functionality (or value) created by 0.9kW-hrs.  That works out to $1000/kW-hr

Finally consider CPAP machines.  CPAP machines are low-power air compressors that assist folks with sleep apnea get a good nights sleep.  For the sake of argument, let's say 1/3 of the users are totally dysfunctional when their CPAP machine is in-op.  A quick survey suggests that they would gladly pay $100/month to get a good night's sleep.  A search of the internet suggests that CPAP machines draw anywhere between 10 and 60 Watts.  Let's take the average, 35 Watts, times eight hours a night times 30 nights.  That is $100/7.2 kW-hours or about $14 /kW-hour (100 times the national average).

This would be much higher if both Bill Gates and Warren Buffet used CPAP machines and they were fighting over the last 35 Watts in the United States...but you see how increasing scarcity weeds out the lower value-added applications and the fair market value of electricity goes up.

Markets
It is an article of faith among libertarians that "markets don't fail."

Markets are information clearinghouses.  They can be efficient or they can be inefficient.  They are more likely to be efficient when there are large numbers of buyers-and-sellers at a given price point.

The market for energy is NOT broken.  Energy is not scarce.  Therefore, information about the value of energy at very low volumes IS hard to come by.  That is why we have to engage in these kinds of mental exercises.

The value of these mental exercises is that it gives us some basis for buying "insurance".  Suppose that you use a CPAP machine and are concerned about the fragility of the power grid.  What is a reasonable amount of money to pay for 35 Watts of solar power?  If you figure a good nights sleep is worth $100 a month than you might think that $1000 for the panels and batteries is a bargain.