The Cost of Energy

I was working on a project for school that looked at the benefits of solar hot water heating equipment and I ran into something odd. Solar hot water heating panels look like regular solar panels but they're usually solid black and water is pumped through them. They're fairly common to see because unlike solar panels that produce electricity (in many cases, lets not get into it) they actually pay for themselves. But there is an interesting oddity to them. They are generally meant to replace the quantity of natural gas needed for heating water, but natural gas is cheap. So even though they save a large amount of energy they do not in fact save that much money. Here is why:

Here I'm showing the three most commonly bought forms of energy: natural gas, electricity, and gasoline.

Natural gas is sold in therms.
1 therm = 100,000 BTU's (British thermal units)
Cost per 100,000 BTU's = $0.86 (in Chicago currently, it's usually about a dollar)

Electricity is sold in kilowatt hours (kWH - 1000 watts for one hour).
1 watt = 3.412 BTU's so a kWH is 3,412 BTU's.
Cost = 12 cents per 3,412 BTU's
Cost per 100,000 BTU's = $3.52

Gasoline is sold by the gallon.
1 gallon of gasoline = 125,000 BTU's
Cost = $4.50 (in Chicago currently)
Cost per 100,000 BTU's = $3.60

So natural gas is more than four times cheaper than other forms of energy per unit. This is why heating my apartment with electricity is stupid. It was cheap for the contractor to put in electric radiant heat washes near the windows but it's incredibly expensive for me to run. The price of electricity is almost double on the west coast ($.025/kWH) and the east coast ($0.20/kWH). Say what you will but nuclear energy makes energy relatively cheap for the Midwest.

When you change the cost of an input, in this case energy, it changes behavior - not really shocking. Doubling the price of electricity causes people to buy more solar panels because it becomes cost effective.

In Chicago it can get up to 100F in the summer - about 30 degrees warmer than we'd like. In the winter it can get to -10F - roughly 80 colder than we'd like. Thus, it takes more energy to heat our homes than it does to cool them. From an environmental/ecological point of view we should live in a warmer climate, but monetarily an 80F difference divided by 4 times cheaper energy because we're using natural gas and not electricity means it's actually cheaper to heat our homes in winter than it is to cool them in the summer with electricity. This is how the cost of something can create perverse incentives.

What is shocking is that no one has figured out how to arbitrage this situation. Why don't any cars run on natural gas or why don't people produce their own electricity from natural gas? The answer is of course in the up front costs of doing such things. Generating your own power is expensive an inefficient. Most generators are roughly 20%-40% efficient...