Basic Economics: Car Wash Edition

I am approached by an 11 year old kid at church yesterday morning offering to sell me a car wash ticket for $3. I hand him $5. He looks at that five dollar bill like he expected operating instructions. (I considered yelling at him to give me back $2, but then his Mom would have yelled at me and I'm not sure she could have figured out this daunting puzzle either. But I digress.) So I pay $5 for a car wash. This is a fixed (or sunk) cost. It no longer figures into my analysis of whether or not to go to the car wash.

So what are the variable costs of going to the car wash?

1. The car wash is 25 miles away so the round trip will take me 2 gallons of gas at $3.10 per gallon for a total of $6.20.
2. It will take a half hour to drive one way to the car wash. I will probably spend half an hour waiting for my truck to be washed. So it will cost me one and a half hours. Assuming the opportunity cost of my labor is $6 per hour (what I could earn moving dirt), the total opportunity cost of my time is $9.00.
3. There is a high probability that the car wash will not be to my satisfaction. While they will wash off the top layer of grim, I doubt that will shine my wheels and tires, scrub the bugs off the grill, and wash my windows properly. Therefore, I will have to wash my truck again when I get home. Assume it takes an hour (at an opportunity cost of $6 per hour) and I use $1 worth of supplies to wash my truck for a total of $7.00.

So the total variable costs of going to this car wash is $6.20+$9.00+$7.00 for a total of $22.20. I would be willing to pay $10 to have my truck spotless.

Needless to say, I won't be going to this car wash.