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Jul/29/2006
The Balance Between the Present and the Future

There are several reasons for why prices change. Interpretation of news or change in the level of optimism is often used as reasons for moves in the markets. Both are important, but to see the bigger picture I suggest using a graph I will define in this article.

Money In = Money Out
The most fundamental characteristic of the market is that for every buyer there must be a seller. If you buy $10,000 worth of stocks then somebody else must be selling the exact same amount. For the entire market, the same amount of money as is pouring into it is taken out of it. (Because of private placements this is not entirely correct, which I will come back to later.)

The Internal Struggle
Every single participant has to decide whether he wants to spend his money today or save it for later. This basically means that you would buy stocks for some of your income today, and sell them later if you lose your job - even if you expect the stock to be even more attractive in sense of estimated return and risk at the time of selling. This struggle applies to private persons, companies, governments, or any other market participant.

The Price
When trading a stock every participant has to figure out whether they find the price attractive or not, and so it follows that the more attractive the price is the more prone is one to invest. The price is what every participant has to deal with, and for the individual each price represents a combination of risk, expected return and whichever other preferences one might have.

The Graph for One Participant
The internal struggle indicates that the participant will have to divide his income between present consumption and savings for the future. It means the marginal utility, or the emotions, one derives for the last dollar consumed equals the amount one derives from the last dollar saved. By drawing the marginal utility of consumption from left to right, and doing the same for money saved from right to left, starting at the total income, the graph will look like this:

Or, if one would prefer to consume more than his income we will see an intersection on the right hand side of the total income. The line for marginal utility from saving will then be extended to the right for as long as the total value of all the stocks owned.

The Graph for the Entire Market
When looking at the entire market a slightly different kind of price is used. Since all stocks are substitutes, and traders actively try to benefit from - and thus remove - differences in the attractiveness of the valuation of different stocks, one can say that the price per some kind of investment molecule will tend to be the same. Every investment opportunity is also a substitute, so stocks, real estate, gold, baseball cards, or whatever storage of wealth you can think of should have the same price per molecule (Pm). Since all markets in the World are connected the Pm should be the same worldwide.

It is important to notice that only the money put into the market and the money taken out of it influence the Pm. If you sell one stock and buy another the Pm will not be influenced, nor will it if you sell your baseball cards and buy stocks.

To be entirely correct, one can invest without having a seller. Companies raise money by issuing shares, new gold is discovered, and real estates are being built. This means that more money is being put into the market than is taken out of. We will have a graph for the market where the accumulated utility of every participant for consumption and savings always intersect at the total income, adjusted for the change in the amount of investment molecules:

Conclusion
The market price depends on two variables; the income and the marginal utility derived from the price. The marginal utility at a given price depends on factors such as the expected return and the risk, which may be rational or irrational. The expected return will also vary based on expectations of future levels of income, so this will work as a buffer which reduces volatility. I will come back to this in a later article.

Some Symbols
Just to make things a little clearer when I write about this in the future I will use these symbols

MU = Marginal utility

MUc = the MU of a dollar consumed

MUs = the MU gained in the present of a dollar saved for the future

MUs(P) = the MUs of a dollar while investing at a given price

c = the dollar amount consumed for one participant

s = the dollar amount saved for one participant (positive if buying, negative if selling)

y = the income for one participant

C = ∑c = the total dollar amount consumed for all participants

S = ∑s = the total dollar amount saved for all participants

Y = ∑y = the total income for all participants

m = investment molecule, a universal unit in which defines investments

M = ∑m = the total number of investment molecules

= the investment molecule's depreciation rate

t = time

Some Equations
These short equations show the relationships between the symbols

The utility balance of one participant
MUs = MUc [s ≠ 0]

If s = 0 one is by definition not a participant

The utility balance of the entire market
MUs = ∑MUc

The disposal of money for one participant
y = c + s

Net savings for the entire market (explanation to come soon)
S = (dM/dt + M) * Pm

The disposal of money for the entire market
Y = C + S = C + (dM/dt + M) * Pm

Net consumption
C = Y - S = Y - (dM/dt + M) * Pm

(List likely to change)

More to come
I have ideas about several theoretical implications like multiple equilibria, financial gravity and up drift, price elasticity, and more which I will come back to as soon as possible.



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