My pet interest in macroeconomics is the value of money. Now it seems that economists everywhere are queuing up to give lectures about how various phenomena will change the value of money. But if one dares ask the question "yes, but what is the money worth in the first place?" then you will be greeted by a stunned silence... or perhaps a feeble recourse to "well its all supply and demand innit". Well I'm not satisfied by this answer - it doesn't tell me very much, and I don't believe we need be so vague. I will suggest an improvement...

Supply and demand is an expression used to determine what price someone will pay for some product. Now when someone makes this choice, lets consider what they are gaining and losing. They are gaining the product which presumably they desire (otherwise they wouldn't even be thinking about buying it!) and they are losing some money. Now lets consider this win and loss a bit more mathematically... say we have a function W_gt(G,t) which expresses our feelings of wellbeing due to being the owner of a collection of goods G at time t. We can also have a similar function W_mt(M,t) which expresses our feelings of wellbeing due to being the owner of an amount of money M at time t. Then when we are faced with a purchasing decision to buy X at cost C at time t, when we already own goods G and we start with money M, the equation we use is:

Buy if: W_gt(G+X,t)+W_mt(M-C,t) > W_gt(G,t)+W_mt(M,t)

Now this is getting more interesting... these functions can be modeled using artificial intelligence and built in to a simulated "population". The simulation would then finally give us an answer to my original question and actually tell use what assorted goods will cost in terms of whatever money there is in the model economy.

A potential glitch... you may realize that actually W_mt() is in itself a function of the value of money. You see that if you have 10,000 shekels then your level of wellbeing will be dependent on what 10,000 shekels will buy. Now you may think that - all I've done is produced a circular argument which can never be resolved, but this is not the case. Its simply a dynamical systems problem that will need multiple iterations (i.e. a long simulated time to pass) in order for prices to reach an equilibrium. The simulation will have to start out with some random prices and then watch how they later converge towards a stable value.

Now it just so happens that my "day job" is that of an artificial intelligence programmer and I'm on the case!

P.S. please note that the change in well being due to the ownership of a new item X at time t is [W_gt(G+X,t) - W_gt(G,t)] and not simply something like W(X). The additional terms G and t in the function are to allow for effects like the fact that probably the greatest determinant of how much happier you will be made by gaining product X is whether or not you own one already!... If you already have a fridge why buy another, even if its a bargain? Then the "t" may come in to play for many different reasons, for example the desirability of some products may vary with the seasons.

P.P.S. Once you have a better grasp of the starting value of money, you would of course have a much better grasp of exactly how various phenomena would change the value of money. So perhaps you could make more accurate predictions than the "queue of economists" who attempt to make such predictions without even knowing what money is worth in the first place.

Update 12 Sept 2009: After a couple of false starts I have finally got down to some programming and have a small model economy up and running on my PC. There are an awful lot of factors that need to be got right before the system behaves in an orderly manner and I am not happy with the results yet. But watch this space.

Update 23 Oct 2009: Simulations going better. For the first time I have managed to get a model economy in which the value of money stabilizes.

## Sunday, 8 March 2009

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Does this model assume that W is greater for lower values of t? Dont some things become more valuable over time and other things reduce in value? Eg wedding rings, musical instruments...Wouldnt this model be more useful to illustrate a business cycle of a specific industry where W can be more easily quantified?

ReplyDelete"yes, but what is the money worth in the first place?" then you will be greeted by a stunned silence.

ReplyDeleteOh get a grip.

Try reading the Austrian school writings on money and credit and formulating your objections in those terms instead of demolishing this absolutely absurd and irrelevant straw man.

> get a grip

ReplyDeleteI have read Rothbard's mystery of banking and much other stuff besides. I have never seen any formulation of what money is worth (only *changes* in the value of money). If you think I've missed something then please give a *precise* reference.

>Does this model assume that W is greater

ReplyDelete>for lower values of t?

No, merely that W is often a function of t. W can go up or down with t and that's already fully incorporated in the model.

"what money is worth"

ReplyDeleteI don't understand the question I'm afraid so can't really answer. If you've read Rothbard then you'll know that all there is is barter and money just another commodity on the market which makes barter most convenient (usually). So does it make sense to ask what is it "worth" outside this framework?

Let me ask you a question? You say:

"..But if one dares ask the question "yes, but what is the money worth in the first place?" then you will be greeted by a stunned silence.....Well I'm not satisfied by this answer - it doesn't tell me very much".

I think this is one of those philisophy questions like "what is happiness?" which you can talk about until the cows come how but whose resolution or not has absolutely no bearing on anything in the real world.

Canh you convince readers that this question has a non-philosophical component?

That's a very good point. Maybe I should edit my post to make this clear. When I say "what's money worth", I mean in terms of some measure of the amount of goods or services. The answer could be expressed in a variety of ways, for example one could say "if the money supply was X units and there were Y people (and some other assumptions) then on average, a man could sell one days output for Z units".

ReplyDeleteIn that case you're going down the road of Marx and many others, trying to ascribe an absolute value to things. He and others tried a "labour theory of value".

ReplyDeleteThe problem is, things simply don't have an absolute value - marginal utility theory explains this. If you have two watches say, the second one is worth less than it would be if you only owned one - the amount of labour or goods or whatever you choose to measure about its creation is the same though.

If you want to capture this difference in value as some function, then clearly stating why the current supply is not sufficient to capture this should be the starting point.

I don't understand the last paragraph, could you re-phrase it?

ReplyDeleteThe problem your work addresses does not appear to be new. Under a barter economy, goods exchange for goods at ratios reflecting their supply and demand conditions, although it is difficult to see and measure these exchanges because they are not denominated in money. When one commodity is used as money, its value is determined by its own supply and demand compared with those of all other goods. If commodity money is entirely replaced by bank issued money (bank notes and bank account money), 'nominal magnitudes are yet anchored by the redeemability of bank monies for fixed quantities of gold and the relative price of gold as set by its non-monetary demand and supply.' (White, 1995, p. 12)

ReplyDelete> nominal magnitudes are yet anchored

ReplyDelete> by the redeemability of bank monies for

> fixed quantities of gold and the relative

> price of gold as set by its non-monetary

> demand and supply.

I am assuming a pure fiat currency, not backed by any commodity - like the dollar.