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The following is an attempt to explain the prices of clamps, using data gathered at Brimfield, 2002 Spring, on the Friday. Please note the special nature of the sample, and do not over-generalize the findings.

Intro to a Model of Prices

Intro

The raw data gives the details. I have noted the maker, the model, and the condition for each clamp I saw.

The weather all week was poor, and on Friday morning, the prediction was that Friday afternoon would be dry, but Saturday all day would be wet. (In fact, it snowed.) So I went down for a very quick check, which lasted only two hours, and which involved only five clamps as two dealers.

Data

Assumptions

My basic assumption is that the price of a clamp can be estimated from the product of two functions.

Price = Size_Function * Condition_Function

I constrain the Condition_Function so that "good" is worth 1, and the function is monotonic, that is, better condition must not imply lower prices. The conditions are defined to be poor, fair, good, and very good.

In order to establish a model, we must define what it means for an estimate to "be close" to the asking price. Errors can be defined in either of two ways: absolute, or relative. Absolute error implies we think an estimate that is a dollar off a $5 asking price is as good as an estimate that is a dollar off a $25 asking price. Relative error implies we think that being off by 10% is equally good, no matter the asking price.

The usual technique is to compute the square root of the average of the squares of the errors. (This is called the rms error, for root mean square error.) This implies that we believe a too low estimate is as bad as a too high estimate, and that all estimates are of equal importance.

The rms error is a measure of how close the estimates are. Approximately two thirds of the estimates will be within the rms error of the true value. Clearly, smaller rms errors are better.

It's an easy matter to set up a spread sheet of asking prices, initialize the model parameters, and to use the Excel Solver function to vary the model parameters in order to the minimize the rms error.

Summary of Results

Clamps in Fair to Good condition, of moderate size, went for about $10.

last revised and validated