For example, the cost-per-mile difference between a car getting 10 mpg and a car getting 20 mpg is greater than the difference between a 25 mpg car and a 50 mpg hybrid.
He tested his theory of misconception on college kids; not being asked, I decided to find out for myself.
| miles / gallon | 10 | 20 | 25 | 30 |
| gallons / mile | 0.1 | 0.05 | 0.04 | 0.03333 |
| cost ($) / mile | 0.4 | 0.2 | 0.16 | 0.13333 |
| % improve each 10 mpg | 0.0% | 50.0% | 20.0% | 33.3% |
| $ improve from 10 mpg | $0.00 | $0.20 | $0.24 | $0.27 |
| % improve from 10 mpg | 0.0% | 50.0% | 60.0% | 66.7% |
| $ improve from 25 mpg | -$0.24 | -$0.04 | $0.00 | $0.03 |
| % improve from 25 mpg | -150.0% | -25.0% | 0.0% | 16.7% |
continued...
| 40 | 50 | 75 | 100 | 1000 |
| 0.025 | 0.02 | 0.01333 | 0.01 | 0.001 |
| 0.1 | 0.08 | 0.05333 | 0.04 | 0.004 |
| 25.0% | 20.0% | 33.3% | 50.0% | 90.0% |
| $0.30 | $0.32 | $0.35 | $0.36 | $0.40 |
| 75.0% | 80.0% | 86.7% | 90.0% | 99.0% |
| $0.06 | $0.08 | $0.11 | $0.12 | $0.16 |
| 37.5% | 50.0% | 66.7% | 75.0% | 97.5% |
Assuming gas costs 4$/g, we see going from the Excursion (i.e. 10 mpg) to my '93 Bonneville (i.e. ~ 25 mpg) gives rise to a 50% reduction in per-mileage cost. However, going from my Bonnie to say a good hybrid (~50 mpg) would also be a 50% price reduction... so something is fishy.
Ah! He must be talking about absolute cost! For the first 50% reduction (Excursion to Bonnie), we see the net reduction is 20 cents. For the Bonnie to Hybrid, we see the reduction is just 8 cents!
It makes sense, though, for what we pay per mile is an inverse function of our car's efficiency. Thus, we expect a hyperbolic cost function with the associated diminished returns.
It looks like my biggest impact move away from Bonnie will be to ride my bike!
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