poor attempt at economic modeling

our economy has a single kind of coin.  give every person on the planet ten of these coins.

pretend every person has a job, and produces some service or good.  pretend every person wants/needs ten services/goods per day.  for each of these things, they pay one coin.

imagine after one day, a person has spent ten coins, and earned one coin.  now the person only has 1 coin for the next day, so they are broke.  everyone is broke.  this economy fails.  obviously, a person needs to earn as much as they spend every day for the economy to succeed.

so pretend again a person spends 10 coins on 10 things per day, but this time the person earns 10 coins the same day.  now this economy will succeed.  if every good/service sells for 1 coin, then each person must sell to ten people a day.

so our successful economy is each person buys 10 things/day, and sells 10 things/day.

now, let's pretend, instead of goods and services, the things are simply widgets.  assume a person survives and is happy simply by consuming 10 widgets/day.  then this system works perfectly.  everyone is buying & selling 10 widgets/day.  no one gains more than the other, no one has less than the other.

in this system, we can initialize the economy at the outset by issuing 10 widgets per person, and then it will sustain itself.

-- good/service life cycle --

what if the widgets don't last forever, though?  what if they slowly get used up, and need to be replaced?  (you know, like any physical object in the real world.)  let's assume a widget is all used up after 10 days.  so, on average, 1 out of 10 widgets must be replaced every day.

a simple solution is before any widget is sold, it is inspected.  if it's no longer good, then at no cost the holder throws it away and creates a new widget.  then that widget is sold.  this keeps the system running just as it was before, same number of buys & sells per day per person.

but, we assume a widget can be discarded and created at no cost.  we know by analogy that no physical object is neither thrown away nor created at zero cost.  these both cost money.

let's explore a possible solution.  we can allow the price of a widget to decline as it ages.  say the price of the new widget is 1 coin.  the next sale it's 0.9 coin.  then 0.8 coin. etc.  until it's bought for 0.1 coin by the last person.

in this system, that last person got a great deal.  they have a working widget, and only paid 0.1 coin!  however, once they are done using it for the day, it's too old to be sold the next day.  so, now they must expend 0.9 coin to throw out the old widget and produce a new one.  then they sell the new widget for 1 coin, and recoup their initial 0.1 coin expenditure.

now, what about all the other sales during the life of the widget except the aforementioned case?  each time, the widget is sold for 0.1 coin less than it was purchased.  statistically, each person will experience this 0.1 coin loss 9/10 days, and then will make a new coin 1/10 days.  if the profit of the 1/10 days covered the cumulative loss of the other 9/10 days, then it would equalize the losses and gains.

this means when a widget is purchased for 0.1 coin, thrown away, recreated, and sold for 1 coin, the profit must be 0.9 coin -- thus again, logic says the coin must be discarded and created for free!  this possible solution will not work.

perhaps we can redefine how coins are exchanged for widgets to clarify things.

every day, per person:

• 9 used widgets are sold
• 1 new widget is sold
• 1 new widget is created
• 1 old widget is thrown away
• 10 widgets are purchased

simple enough, once we define the system in terms of time.

so the price of all these transactions must sum to zero for balance to be maintained.

• 9 old sold, (+wallet)
• 1 new sold, (+wallet)
• 1 new created (-wallet)
• 1 old trashed (-wallet)
• 10 bought (-wallet)

in other words:

• 10 sold = 1 created + 1 trashed + 10 bought

and we can see the average purchase price must be less than the average sale price.  this is a problem.  for any given transaction, the purchase price is the same as the sale price.  that is, both buyer and seller agree to the same number.  if every person is selling to every person buying, then the average sale price must equal the average buy price.

once again, logic tells us the creation & destruction of widgets must occur for free.  but this isn't practical.

a solution to this dilemma would be to balance the equation:

• 10 sold + ??? = 1 created + 1 trashed + 10 bought

which can be reduced to

• ??? = 1 created + 1 trashed

sales of widgets, as shown above in the per person budget, adds money to a person's wallet.  so the ??? in our above equation must add money to a person's wallet.

how about each person performs the service of creating and trashing a widget for another person.  so now:

every day, per person:

• 9 old sold, (+wallet)
• 1 new sold, (+wallet)
• 1 new creation performed (+wallet)
• 1 new trash performed (+wallet)
• 1 new creation purchased (-wallet)
• 1 old trash purchased (-wallet)
• 10 bought (-wallet)

now this fixes the math, but it's silly.  why pay another person to do a service you'll also do for someone else in the same day?  just do it yourself.  hence, creation & trashing is done by yourself, and must be done for free!! argh.

conclusion

free exchange of widgets is simple to model economically.  but as soon as you start throwing out & creating new widgets, i run into problems.  it seems, since all monetary exchanges involve equal prices on the part of the buyer and seller, that there is no "extra cash" in the system to create new widgets or throw away old ones.

i think my model is flawed.  especially considering, in the real world economy, very few physical products are exchanged much.  most products are created, sold, used, and trashed.