In the comments my previous post concerning my theory of asset prices – comments that have, I should add, been extremely productive so far – Nick Edmonds raised some questions as to whether I was dealing with stocks and flows. After a bit of back and forth I realised that what we were dealing with touched on some of the fundamental problems that I noticed with my theory just prior to publication. Therefore, in this post I am going to lay out in very clear terms exactly what we are dealing with and then briefly consider what implications this slightly altered approach has for one of my key conclusions – namely, what I have termed ‘the paradox of speculative profits’.
First and foremost there was some confusion about what I meant by ‘financial saving’ in the paper. I’ve decided that the best way to approach this is to work with my original intuition: financial saving will be any income accrued through the sale of financial assets. As the original paper already stated (note that government includes the central bank here),
What that means is that if I, say, take out a loan of $100 and buy $100 worth of assets from you my investment causes an equivalent rise in your savings. The same is the case for government purchases of financial assets and any taxes levied on these assets. All this is basically identical to the typical Keynesian macro-aggregate identity. Are we talking about stocks or flows? Well, we can talk about either so far as I can see.
So, how might we calculate this build-up in financial savings? Well, let’s take it from a stock point-of-view. Let’s also pretend that all assets are bought using borrowed money to avoid the problems that arise from buying assets using already existing savings. We can put down a simple formula to calculate this (note that for the rest of this post I will ignore the government side to avoid complications)**.
What that means is that financial savings/investment is equal to the sum of all realised bid prices. In order to conceptualise this it is probably best to give an example. Imagine that in a given period we have three distinct bids for an asset. These run as follows,
What this means is that there was three distinct sales of a financial asset in our imagined economy – it doesn’t matter whether this was three sales of the same asset or three sales of different assets of the same type. The sum of all these realised bids will be the amount of financial savings/investment in our economy; in this case, $330.
Now, there is also a different variable that we must consider to fully understand the dynamics here: namely, the final value of the asset in the final period. As Ramanan pointed out in the last post’s comments, this is something like the capital gains from a rise in the price of an asset. At the end of our period it is clear that the asset has risen from $100 to $120. The end value of all assets – i.e. the rise in capital gains – will be the number of assets outstanding times the final realised bid price. Or,
Let us imagine now that in our hypothetical economy there were only three of the asset in question. That means that the total end period value will be $120 times 3 or $360. This, again, is a final stock measure.
Now, how does this relate to my theory? Well, it should be clear that the final realised bid price in a given period is equal to the price level generally. So, we can now convert what we have laid out into the language of my article (note that I am dropping the small delta elasticity variable and no longer equating price with financial savings/investment – this relates to the flaws I pointed out in my original post),
We already know, of course, what the formula for this price on the demand side is. So, we can now put this in here (note that I am introducing time periods to make the exposition clearer),
While this is certainly a fairly substantial revision of the theory – one, in part, that I had been considering when I published the paper – most of the results obtained in the original still hold, albeit in a modified form. The paradox of speculative profits, for example, will now be dependent on the price expectations that each investor had at each successful bid. Thus, in contrast to how I originally formulated the theory, there will no longer be an aggregate of “average expectations” and so forth. Rather, each successful bid will have its own specified version of equation 1.5. I will discuss this in more detail in a forthcoming post.
While I think the above framework is much clearer and consistent than what I originally laid out and also avoids the problems that I noted when I published the paper it is by no means complete. The other variables – taking account of supply-side effects and ‘real’ demand-side effects for ‘impure assets’ – must be added in and I am still working out how to do this properly. The above, however, provides a firmer base from which to do it.
Comments welcome, as always. They were rather helpful in forcing me to write out the above in detail. I appreciate that as, until now, I have been working on this completely on my own and while I think I have most of the intuitive problems solved formalising these is very difficult to do without the criticism that spurs clarification and the illumination of errors.
**Apologies in advance for any poor use of algebra. Input welcome on this front.