Thursday, May 8, 2008

The Desire Coefficient

This post will consider the role of desire on the inventory variable in the cash value equation, and its effect on the value of the dollar.

So far, it has been a given that all items of the inventory are equally desired. Now, take an economy whose available inventory consists of 3 houses, 100 barrels of oil, 395 bushels of wheat, and 2 gardeners who are paid by the month, with $10,000 to go around. So there are 500 items in the inventory. If everything is equally wanted, everything costs $20, or the value of the dollar is 1/20 of an item.

To address this error, the “desire coefficient” (D) is the proportion of the money supply (M)a fraction between 0 and 1that is spent in each economic sub-category. To start with, say the money supply is equally divided between houses (h), oil (o), wheat (w), and gardeners (g)—then desire coefficients for each is .25, since they all have to add up to 1. Dh, Do, Dw, and Dg are all .25. So, the money in this economy that goes to housing is Dh*M = .25*$10,000 = $2,500—and for now it is the same for all other subcategories. Since price ($) = money supply/inventory, $(houses)=Dh*M/Ih—and since there are 3 houses, the price for each is $2,500/3, or a little over $800. By the same math, oil is $25 a barrel, wheat is around $6 a bushel, and the gardeners work for $1250 a month.

This doesn’t sound quite right—houses should be worth a little more than the monthly salary of a gardener. Let’s push the desire coefficient for houses to .3, and for the gardener to .2. Wheat and oil stay the same. There is now $3000 for the housing budget, and $2000 that go to gardeners. Since there are 3 houses, and 2 gardeners, the cost of a house and the monthly salary of a gardener is the same: $1,000 all around. Let’s push it further: the desire coefficient of housing is .4 and gardener is .1. Now there is $4000 going to housing, so each of the 3 is worth $1333; and with $1000 going to gardeners, each one gets $500/month.

Here I’ve calculated the unit price as: $x=Dx*M/Ix. This equation can be shifted around to Dx=$x*Ix/M. This is the true, natural form of the equation. Desire is a psychological phenomenon that cannot be measured; however prices, inventory, and money supply can all be observed and tallied. In this example I was altering desire to set prices—in reality, desire can only be known from prices set by the market. Whatever prices happen to be, that reflects desire for the good. The desire per unit (Dx/Ix) is the desire coefficient divided by number of particular units, which equals $x/M once the Ix’s are cancelled—or individual desire is correlated with prices if money supply is constant. Now if increased desire causes prices to rise, it diminishes cash value for that item, simply because a given dollar would buy less of it.

So this is a way to give weight to preferred units within the inventory. Within each subcategory, additional desire coefficients can be used, to reflect subgroup preferences within each category. The desire coefficient for any individual unit is simply its market price divided by the money supply.

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