Gerry writes: ____________________________________________________________________ You describe the following [FROP cycle (PEN-L 5752-3)-AF] as a "toy model", hence, it is difficult to be overly critical of an acknowledged work-in-progress. ____________________________________________________________________ Thanks for your interest. There are strong grounds to be critical and myself, I would be; I said it was a toy to stop it being taken too seriously. It's been going nowhere on my desktop for a year and I thought it would be better off going nowhere on other people's desktops. You have five questions. I apologise for taking them in the wrong order. ____________________________________________________________________ 5) what intellectual traditions in political economy (e.g. specific works) does your model relate to and how? ____________________________________________________________________ My general aim was to lower the tone of the discussion. I'm a fan of spreadsheet dynamic models because you can do them with no math and hardly any reading. You put in formulas, poke around, and out come graphs. People should do it more. I'd like for us to do for computers what Bertill Ollman did for board games. The serious point is; you can't do this with simultaneous equations. Equilibrium = No Fun. I cooked it up teaching neoclassical dynamics (Cobwebs, Accelerator- multiplier, Harrod-Domar growth theory) and I thought, this is ridiculous, Marx is the archmage of chaos and there are no Marx chaos models, not even toy ones. I wanted something to give students and say, this is cool, and it's based on Marx. So here you are, it's based on Marx, it goes up and down and crashes. Hey, no-one else can do that. And the graphs are sexier. ____________________________________________________________________ 1) what are the specific steps in your analysis that you feel need to be developed further? ____________________________________________________________________ Fancy buttons and animations; little workers fighting little capitalists, hammers smashing things, factory wheels turning, people jumping out of windows, that kind of thing. Perhaps some sound FX. Then I would like for us to put it on the internet and get mentions in cafe fanzines, such as 'Today's cool site: Virtual Capital from the marxists'. I hope others get encouraged to play around with spreadsheet models. This includes newcomers who, I realise, can get deterred by math and erudition. This is an atonement for past heaviness. ____________________________________________________________________ 2) could you be more specific about the assumptions of the model? ____________________________________________________________________ I wanted the minimum set of assumptions which could produce cycles from profit rate movements. I was always very impressed with Goodwin's nonlinear accelerator model but I don't like the variables. It's too Keynesian for me. The whole emphasis of adjustment goes into output and wage movements, and I think these are effects not causes. The cause is the self-movement of capital and I wanted to isolate this without imposing simple reproduction. Goodwin understands the mechanical requirements to get oscillations and make them perpetuate. He has patiently explained this for fifty years and far too few listen. Then, in my opinion, he is quite pragmatic. He takes a procedure known to produce oscillations, namely the combination of the accelerator with the multiplier, and introduces a nonlinearity (this is dead easy to illustrate with a spreadsheet and requires no technical math at all) to make sure the cycles don't go away. Actually, if you have any dynamic process you can make it do cycles by an analogous method. So I rigged the falling rate of profit to do cycles, in the simplest way I could. I brazenly confess the assumptions are deduced from the need to make the model do tricks. I'd rather get that off my chest now. Having said that, I can still read backward from model to assumptions (a quality assurance technique which I think should be applied to any and every model), which are: 1) the rate of profit falls as described by Marx. Each year the value of capital stock grows by the value of net investment. Punkt. It shrinks only if you disinvest. This is the only position I would defend; as I said in re Okishio, I think Andrew Kliman and myself have shown that the 'refutations' of this discovery come from a simple error, forgetting lags and, as Mike Perelman and Jim Devine said, capital gain effects; put this right and Marx is exactly and precisely true, as simple as that. 2) the surplus value produced each period is constant. This is patently unrealistic. It serves a purpose; I wanted to abstract from everything except the mechanism of investment and profit. Models using fluctuations in the wage, employment, consumption, or even output all obscure Marx's idea, that the mechanism of the business cycle is *endogenous* to accumulation. I froze out labour effects to show they weren't needed; that this mechanism *could* be purely endogenous. It's neither underconsumption nor overproduction, disproportion nor really overaccumulation; it's as near as I can get to a pure FROP cycle. This probably makes it completely unrealistic - though no more so than simple reproduction- but it shows that if you abstract from all other sources of instability, the falling rate of profit remains as the granddaddy of all sources of instability. I'm turning it over to PEN-L because I hope others will help flesh out what the complete mechanism concretely is. I think this is a more useful line of enquiry than a lot of other things studied by people writing in Marx's tradition and also what Marx himself was most concerned about. 3) the capitalists invest each period a proportion of surplus value and either consume, or hoard in liquid form, the remainder. The two control variables are thus the stock of capital and the mass of invested profits. An orbit plot of one against the other is a nice elliptical spiral. Outwards. I think this is quite close to reality. Slump is an accumulation slowdown - capitalists appropriate profits but don't invest them, in fact at the trough they disinvest (consume or liquify fixed capital), restoring the profit rate. Account for this withdrawal of profit from productive investment, and we are 90% of the way to explain cycles. 4) to make it oscillate I needed a second-order coupling between profit rates and investment behaviour. I took a short cut: investment is driven by whether profits are higher or lower than a threshold. The change in investment is proportional to the divergence of profits from the threshold. This is essentially an accelerator triggered on profit. I make no excuses at all for this assumption except that in general, capital seeks high profit rates, which is standard Marx. It's there to make the model work. But at least I admit it. ____________________________________________________________________ 4) how can moral (social) depreciation be factored into the equations? ____________________________________________________________________ Haven't a clue. Any ideas? ____________________________________________________________________ 3) how is the issue of the depreciation of constant fixed capital handled? ____________________________________________________________________ See (4); However, I would stick with assumption (1)above: "the rate of profit falls as described by Marx. Each year the value of capital stock grows by the value of net investment. Punkt. It shrinks only if you disinvest." Then one has to think through what this means for relations between value and use-value, productivity etc; but that's another story. What matters is that in each period you have some money profits: invest them and your capital stock goes up; supplement them by withdrawing capital from production and capital stock goes down. This is not to dismiss the very interesting discussion you've been having with Chris, John and others about moral depreciation. I do have some ideas on depreciation, which I'll post to you, but I don't think they add anything new to what you've said already. For me the law that the money value of capital stock rises at a rate equal to the money value rate of investment applies regardless of depreciation. That's my understanding of a law: something which remains true regardless of particular circumstances. I think it causes problems to conceptualise it too much in physical quantities. It's a money thing; quantities and unit values adjust round it. If money capital needs an outlet and the hi-tech equipment is out of stock, you just put it into lo-tech, so unit values of means of production are greater than the optimum. What else could happen? The money needs an outlet. I have $2000 and I want a Pentium 150 notebook but I can't wait forever. On the other hand if I am stupid enough to borrow $10000 to buy one now, by 1996 I will have $3000 in assets and $10000 in liabilities, which I call losing $7000 but society calls a 'cost'. This $7000 won't vanish; it'll be with Intel financing P6 production. So overall, the balance sheet of the whole thing is that $10,000 has been added to society's capital stock however the depreciation cake is cut. In my virtual capitalism, I don't know who has made out: the tiny Intel simulacra, the tiny Alan Freeman homunculus or the tiny banker gnome. The model doesn't say. But what I do know, is they have $10000 to invest between them and it has to go *somewhere*. Overall, society's stock of capital *must* go up by $10,000 unless the capital isn't invested. I think, finally, that this is how Marx sees it; he starts from the money - the conversion of surplus value into capital. So there is a serious side to it after all, I admit it. But it's also fun. Again thanks for your interest. I'll mail you separately with some references and comments on depreciation. Alan
