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Linear Model of Prices, Fall 1997

The Data

The following is an attempt to explain the prices of clamps, using data gathered at Brimfield, Fall 1997, on the Saturday. Please note the special nature of the sample, and do not over-generalize the findings.

Brimfield gives me a chance to see lots of clamps, all at one time, and under fairly comparable conditions. However, I have to recognize that some are general dealers mostly selling users, some are selling lookers, some are tool dealers trying to sell to collectors, so there are several "markets" going on all at once.

The Model

Two things seem to determine the price: size, and looks. Scarcity is not a factor (probably because scarcity is unknown to most dealers). Married clamps sell the same as un-married (probably because the condition is not noticed).

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 further assume that the Size_Function is linear, a constant plus so much per inch of jaw.

Also, 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.

Results

Cut to the chase - what's a good price for a 20 inch user?

If you plot the data, a pattern may be apparent to you. What I see is that

  1. the prices tend to cluster around the line $ = 1.5 X inches; and
  2. the higher prices often seem to be multiples of 5$ and 10$; and
  3. there can be a 2 to 1 spread between highest and lowest prices.

(The coefficient in the equation is chosen for ease of use, rather than for very close fit.)

So, a 20 incher would be expected to be about 30$, give or take depending on condition.

The spread depends mostly on condition or looks. But the effect of condition cannot be summarized by a neat formula.

All these clamps were in fair working order or better, but some were dinged, grimy, or damaged to great or less degree, while others were cleaned up and polished. I didn't see any really broken ones.


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