I was looking for something, and ended up in a set of pages at
amazon.ca where most pages of stuff, were things that were "on
target". So, I waded through 20 pages of ads on items for sale.
There were a few (2?3?) main sellers or what I was looking at, and some
If one just looked at one seller, they had ads for 1 item, 2 items, 3
items, 5 items, 6 items, and so on. And the price per unit varied.
Fine. What random distribution that is readily available, occurs for
positive real numbers and has finite variance? Probably lots of them,
but lognormal is common.
my $cost = 0.15;
my $markup = 0.3;
my $z = random_normal( 1, 1, 1 );
my $n = random_poisson( 1, 2 ) + 1;
my $unit = exp( log( $cost * (1 + $markup) ) + $markup * $z );
$unit = int( ($unit + 0.005) * 100 ) / 100;
my $bundle = $n * $unit;
print "Selling $n for $bundle\n";
which as written, loops forever. In 100 trials, I had 2 bundles sell
for (slightly) less than cost, and the incoming revenue from all the
sales was almost twice the cost.
Some item pages had statements about inventory, which could be real or
not. This process can generate bundles of number and price that have
been seen before.
What it does, is make it possible to be seen by the shopping public
many more times, than if you just bundled up everything into 5's and
sold them at one price.
Not every shopper is going to look at all pages to see the totality of
ads you have. They may look enough to see that you have the same
number of the same item multiple times. Does this stop them from
shopping at your "store"? I would imagine that some of your items,
with the higher per unit costs don't see as fast as the lower priced
items, but do they all sell eventually? Or do you have to "pull
inventory" and selling them at a lower cost?
I don't know that sellers are doing this, but it sure looks close to
what my Monte Carlo model came up with.
The lognormal distribution is assymetric, and hence possibilities of
prices much larger than average are larger than prices much smaller
than average. One kind of expects this kind of random pricing to
return better than a constant price, if you can sell the stock I guess.
But, how I was calculating the standard deviation part of the lognormal
was dumb. I was saying the variance in price was a constant. I don't
know, maybe it is. But in this circumstance, the constant used had no
research behind it, and it need not even be close to what happens in
the real world.
One probability distribution which provides an estimate of standard
deviation as a function of size is the Poisson. Normally used for
situations where counting is involved. Sometimes used in other
situations, where some kind of "natural unit" is present, such that the
standard deviation of an estimate of N, is sqrt( N ).
Okay, I plugged something like that in to my formula, and as the penny
is no longer in circulation, I used a nickel as the natural unit. I
also did a run with the penny as the natural unit.
The Poisson distributions for nickels and pennies are quite different,
the penny distribution is much closer to symmetric. On a fractional
basis (all data divided by the mean, which will be the same for the 2
runs), the penny distribution should also be sharper. The end result
is that the amount of profit seen is quite close to the specified
markup of 30% (a tiny bit higher, could easily not be significant). I
guess the thing to do is to figure out just what unit of currency
people think in terms of, for the expected average price you are
starting from. Here, the price was in the neighbourhood of $1. Do
more people think a dollar is 4 quarters, or 100 pennies?