Hi everyone. I've pushed massive changes to the program I linked weeks ago. I also have some results to share accompanying this that I have written on in a paper that I will be seeking a publisher for. Paper available to read in the post underneath this.🧵

Link to paper: The tl;dr is this: Extensive computer simulation testing within multiple variations of cross-dual dynamical models demonstrate that the rumors of Marx's theory of the falling rate or profit have been greatly exaggerated. Let me show you.

To VERY briefly summarize the model, prices change according to supply and demand, wages inclusive, outputs change according to profits, interest rate fluctuates according to a fixed money supply. Capitalists and workers consume with distinct tastes using their savings.

For details on the model, see my paper, or @ianpaulwright's PhD thesis, which is linked in the GitHub wiki, or see my previous thread on an earlier version of the program here: Now on to the results

Firstly, let us witness Okishio's theorem. With the real wage fixed, the rate of profit rises in response to any cost-reducing technological changes. This is true in the case of discrete shock and in the case of continuous technical changes, as is seen here.

When we remove that assumption of a fixed real wage and allow all quantities to float according to Wright's model, things are very different. Capital using, labor saving innovations appear to have the UNIQUE effect of causing the rate of profit to fall.

This is confirmed by extensive testing in both the case of discrete shocks (fits and starts) as well as in the case of continuous technical change. The result even appears to hold with different proposed variations of price and output equations are used. No exceptions are found.

's model assumes an interest rate which floats according to capitalist savings, which is consistent with Marx's assumptions but not with the real world, where it is more appropriate to assume it to be constant. While fixing interest rates does prevent the fall...

in the case of discrete technical change, the rate of profit still falls decisively in the case of continuous change.

I'll let you read the paper to see the rest. If you are a publisher my DMs are open. I'll be making a video soon touring the application as well as a few blog posts about aspects of the model aside from just the behavior of the rate of profit.

So throughout the whole model, the money supply is fixed?

Yes but the app allows you to do money injections over fixed intervals. Also even though it's fixed it's a state variable, meaning you can easily make it change in complex ways by editing the get_delta_M function in the file

If the model shows falling rate of profits even in endogenous money framework it would be much more impressive

What do you mean by endogenous money framework

Since here the money supply is fixed, and it is only increased through injections of money (by a hypothetical central bank, I presume), similar to the monetarists' understanding of the economy. However, in the real world, money is endogenous; it is created within the system, not injected exogenously (see Randall Wray, Basil Moore, and Louis Philippe Rochon)

very very interesting. do you assume here that workers and capitalists are rational, i.e they maximize profit/utility in some sense? (i'm not saying this as a critique, i think it's fine. i just want to be clear about some modeling choices)

My model doesn't, but the most current iteration of Wright's model actually does have exactly that going on (hope that's not a secret). He hasn't published on that version of the model yet though so I can't use it.

and can the model be tested empirically through econometric methods or is that still 'pure theory'? (i'm sorry for the questions lol i come from mainstream econ so these matter to me)

I'm not sure if I'm the best person to speculate on how the observations here might be tested in the real world. I would like to say yes but I have not really thought much at all about this.

Really interesting paper thanks for sharing! I think the dynamic simulation work is valuable (altho I’m not a mathematician) and I agree with the broader point that Okishio-style comparative statics don’t govern actual accumulation dynamics once wages, money, etc., are endogenous

I assume this is all with constant returns to scale?

Uh no I don't think so. You can find a full description of the model in my paper.

@beverlymantle1 i believe the answer is yes. you don't have convex production functions.

@beverlymantle1 maybe I don't know what is being referred to by returns to scale, are we talking about profit returns? or real output?

@NiaFrome Yes, Ian's model uses constant returns to scale in output, ie for some production function f, t*f(x1, x2) = f(t*x1, t*x2). This is not a bad thing, I was just wondering. Pretty much all Marxian/Sraffian econ & a lot of neoclassical models assume CRS, incl general equilibrium.

@NiaFrome I think there's a bit of connecting which needs to be done between that sentence and your formulation of convex production functions. I haven't read those chapters of Roemer yet very closely, I'll do so asap.

@NiaFrome Right, in your paper the consumption & price bundles are dynamic functions of *time*. In Leontief systems the cost/production functions are homogeneous of degree one (this is what's traditionally meant by CRS - production functions are functions of inputs). So no contradiction.