The Law Of Diminishing Returns, or Cash for Clunkers for Dummies

Years ago, when I drove a Honda Civic that got 40 miles to the gallon, I dreamed of a car that did better. In fact, I once had a car that got 23 mpg and I never forgave it. This was because my very first car was a diesel VW Rabbit which got 55 mpg no matter how badly I drove. (Ok, I used to like to park the jerks who thought they were going to use a left-turn-only lane to pass me at stoplights. Did I mention I went through my first clutch pretty quickly? That was definitely not cost-effective.)

So one day I whined to an engineer friend that I missed my Rabbit because my Civic wasn't as good on gas. He tried to explain to me the law of diminishing returns, and I couldn't buy it.

So when the Honda Insight came out, I built myself some spreadsheets to see how long it would take me to save the price of the car. I was horrified to discover that I never would. Not unless I could get 80mpg or the price of gas went up to $4/gal. and stayed there for the life of the car.

I bought the car anyhow and I've never been sorry. In fact, I now own one Insight (lifetime mpg 61.3 and fast approaching 200,000 miles) and one Hybrid Civic (no lifetime average - usually does better than 50 mpg on a tank and just past 50,000 miles).

If the law of diminishing returns doesn't mean anything to you, consider the following spreadsheet.

	Cost to drive 10,000 miles
		dollars per gallon
		1	2	3	4	5
miles per gallon	10	$1,000	$2,000	$3,000	$4,000	$5,000
	15	$667	$1,333	$2,000	$2,667	$3,333
	20	$500	$1,000	$1,500	$2,000	$2,500
	25	$400	$800	$1,200	$1,600	$2,000
	30	$333	$667	$1,000	$1,333	$1,667
	35	$286	$571	$857	$1,143	$1,429
	40	$250	$500	$750	$1,000	$1,250
	45	$222	$444	$667	$889	$1,111
	50	$200	$400	$600	$800	$1,000
	55	$182	$364	$545	$727	$909
	60	$167	$333	$500	$667	$833
	65	$154	$308	$462	$615	$769

So, at $1/gal, my old Civic cost me $250 to drive 10,000 miles. My Insight would cost me $167 to drive the same distance. I would say over the life of the car, gas has averaged a little over $2/gal. So, old car math - $2/gal price of 10,000 miles = $500 * 20 = $10,000 spent in gas over 200,000 miles. Insight math - $2/gal price of 10,000 miles = $333 * 20 = $6,660 spent in gas over 200,000 miles. So over the past 200,000 miles I've saved $3,340.

Now, let's just say you decided to participate in the cash for clunkers program. Let's say you turn in a car that gets you 15 mpg for a car that gets you 20 mpg. Let's say you drive this car for no more than 50,000 miles. Old car math - $2/gal price of 10,000 miles = $1,333 * 5 = $6,665. New car math - $2/gal price of 10,000 miles = $1000 * 5 = $5,000. So in 50,000 miles you've saved $1,665. In 50,000 miles you've saved more than half what I saved in 200,000 miles. And the government will pay you another $3,500. $3,500 + $1665 = $5,165. Not bad, but compelling?

Let's say you get greedy and want the $4,000 rebate from the government. (Actually, I think it's more than that. I can't be bothered to look it up.) And you want a pretty sporty car, so you only get a car that gets 25mpg. Old car math stays the same over 50,000 miles. $2/gal price of 10,000 miles = $1,333 * 5 = $6,665. New car math - $2/gal price of 10,000 miles = $800 * 5 = $4,000. So in 50,000 miles you've saved $2,665. $2,665 + $4,000 = $6,665. That's starting to look really nice.

Then there's my friend Jim. He's looking at a hybrid. That will get him 45 mpg. I think his old car gets 15mpg, so we'll go with that. Old car math - $2/gal price of 10,000 miles = $1,333 * 5 = $6,665. New car math - $2/gal price of 10,000 miles = $444 * 5 = $2,220. Over 50,000 miles he can save $4,445.

But that's not where the real savings comes in. The real savings comes in when you look at the price of gas over time. Gas isn't $2/gal. Gas really cost over $4/gal not all that long ago. Consider the following and think of your monthly budget.

How far can you drive on a tank of gas?
		size of tank in gallons
		10	20	30	40	50
miles per gallon	10	100	200	300	400	500
	15	150	300	450	600	750
	20	200	400	600	800	1000
	25	250	500	750	1000	1250
	30	300	600	900	1200	1500
	35	350	700	1050	1400	1750
	40	400	800	1200	1600	2000
	45	450	900	1350	1800	2250
	50	500	1000	1500	2000	2500
	55	550	1100	1650	2200	2750
	60	600	1200	1800	2400	3000
	65	650	1300	1950	2600	3250

		How much does a tank cost you?
		dollars per gallon
		1	2	3	4	5
size of tank in gallons	10	$10	$20	$30	$40	$50
	15	$15	$30	$45	$60	$75
	20	$20	$40	$60	$80	$100
	25	$25	$50	$75	$100	$125
	30	$30	$60	$90	$120	$150
	35	$35	$70	$105	$140	$175
	40	$40	$80	$120	$160	$200
	45	$45	$90	$135	$180	$225
	50	$50	$100	$150	$200	$250
	55	$55	$110	$165	$220	$275
	60	$60	$120	$180	$240	$300
	65	$65	$130	$195	$260	$325

The savings isn't huge, but the higher the price of gas, the less the increase hurts. And that, my friends, is why I'm so glad I bought my hybrid, even if it hasn't saved me all that much.