Re: Is there a generally accepted theory of value?

From: Zerge (zerge_at_hotmail.com)
Date: 03/07/05 

Date: 7 Mar 2005 12:10:09 -0800

smithaa02 wrote:
> robert j. kolker wrote:
>
> >
> >
> > Zerge wrote:
> >
> >> Inbeed Bob. But that's a tautology.
> >> WHY are they willing to settle for a specific price? You are not
saying
> >> it's a random process, are you?
> >
> >
> > No. It is because they felt like it. Just because two people act as

> > though they agree on something does not mean there is a thing out
there.
>
> They can never agree upon the price.
>
> The logical proof why:
>
> Two or more parties only trade to increase their wealth. This
> collective gain is the benifit from the division of 'labor'. The
> parties can not agree upon how this benifit is to be split, because
all
> parties seek the full share of the increment of association. They
must
> come to a 'random' comprimise else the parties of negotiation will
> withdraw from the bargainning table. eg:
>
> Bob produces 5 food and 5 housing by himself.
>
> Jo produces 5 food and 5 housing by himself.
>
> Together through trade and the division of labor they can
collectively
> produce 15 housing and 15 food units.
>
> There is no equilibrium price by which they will trade on (I dare you
to
> come up with a supply and demand graph for this example). Bob could
> consume merely 6 food and 5 housing to Jo's 9 housing and 10 food,
> because Bob would benifit from the increment of association, and
would
> fear Jo not trading (declaring a strike), thus leaving Bob with
merely 5
> food and 5 housing.
>
> This all means price is a poor communicator of information.

1.- Our most limited resource is time.
2.- Let us assume Bob and Jo have each only 10 hours per day to produce
either food or housing.
3.- When you produce food, you stop producing housing and viceversa.
This means that there is an "opportunity cost" to producing one
commodity. (This is what seems to escape you).
4.- You say that through trade they can produce 15 housing and 15 food.
If Bob specializes in food and Jo in housing, it means that Bob is
spending 0.67 hours in food (10 hours of work divided by 15 units of
food). I'm assuming that for each additional unit of food that Bob
manufactures, he stops manufacturing 0.5 units of housing. In this way,
Bob's production possibilities look like this:

Bob
Food Housing

0 7.5
1 7
2 6.5
3 6
4 5.5
5 5
6 4.5
7 4
8 3.5
9 3
10 2.5
11 2
12 1.5
13 1
14 0.5
15 0

(I did the 0.5 assumption to fit the 5 with the 5 and the 15 with the
zero, assuming a linear relationship).

Jo's production possibilities are similar, except that Jo specializes
in housing, which costs her 10/15=0.67 hours per housing unit:

Jo
Food Housing

7.5 0
7 1
6.5 2
6 3
5.5 4
5 5
4.5 6
4 7
3.5 8
3 9
2.5 10
2 11
1.5 12
1 13
0.5 14
0 15

5.- So in summary, Bob the food maker can make a unit of food in 0.67
hours and a unit of housing in 1.33 hours (10/7.5). Jo the house maker
can make a unit of housing in 0.67 hours, and a unit of food in 1.33
hours. In other words, Bob's OPPORTUNITY COST is 1.33 hours per food
units, and Jo's OPPORTUNITY COST is 1.33 hours per housing unit. That
means they have to sacrifice that amount of TIME (only truly limited
resource). So obviously it is much better if they specialize and then
trade.
Profit/loss is measured in hours gained/lost.

6.- Variables:

BHC= Bob's Housing Cost
BFC=Bob's Food Cost
JHC= Jo's Housing Cost
JFC= Jo's Food Cost

HU= Housing Units traded
FU=Food Units traded

Price=FU/HU

7.- Profit formulas:

Bob's profit=BHC*HU-BFC*FU

Jo's profit=JHC*HU-JFC*FU

8.- Price

The Nash equilibrium solution is a price if 1 Food unit in exchange for
1 housing unit. Any other combination is Nash unstable.
For example a price of 2 would give Bob 0 hours gained, whereas Jo
would gain 2. Bob might accept, but it wouldn't be an economical
choice.
Actually the price can reasonably vary between 1 and 2. Anything below
1 and Jo loses, anything above 2 and Bob loses. So the price will most
likely be 1, but it may vary along that bracket according to Bob's and
Jo's food and housing needs.
No supply and demand, "only" opportunity cost and Nash equilibrium.

QED.
Any questions?

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