Saturday, 23 April 2016

Coyle on Distribution.


Diane Coyle reviews Adam Ozanne's book "Power and Neoclassical Economics".

Coyle is very positive about the book, whose thesis -- it seems to me -- is "surely one of the longer-term outcomes of the crisis will be -- must be -- to turn economics back to political economy" (emphasises mine). They believe power relations should be reintroduced into economic theorising.

Fair enough.


There is something, however, wrong in Coyle's review:
"The book goes on to argue that the fact that mainstream economics has nothing to say about the distribution of income and wealth is an important part of the explanation for cynicism about the subject -- both among the general public and students like our university's active and enthusiastic Post-Crash Economic Society."
As I haven't read the book, I can't say whether that is faithful to its content.

Regardless, it's not true that "mainstream economics has nothing to say about the distribution of income and wealth". Quite to the contrary, it has plenty to say and it has been repeating it since the 1870s (which Coyle mentions in passing).

The problem is that what mainstream economics says about income and wealth distribution is both incoherent and evidently false: that income and wealth distribution follow the just deserts principle.

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The astute reader should be asking where, exactly, does mainstream economics say that?

In microeconomics textbooks, from undergraduate all the way to post-graduate/doctorate level (and please, don't come with the 101ism thing popular of late).

Let q = q(K, L) be a production function (there are some technical assumptions -- continuity, differentiability, et cetera -- but we'll leave that for another opportunity). q is output in physical units, K is capital, L is labour (K and L either measured in physical or monetary units, it makes no difference here).

What matters a lot is this assumption: q(K, L) must have the property that q(t*K, t*L) = t*q(K, L), for any real number t (i.e. linear homogeneity). Keep this in mind.

For a firm in a perfectly competitive market in the long run, revenue is p*q(K, L); costs are r*K + w*L (p is the output sale price; r, the capitalist's return; w, the workers' wage, all constants and measured in $/relevant unit).

By choosing levels of K and L (remember: long run), the firm maximises its profit


(1)               p*q(K, L) - r*K - w*L


They do that by choosing a combination of K and L such that the marginal product of labour (MPL), in the LHS, 

                      d(q(K, L)  w
(2)                   -------- = -
                         dL      p

And the marginal product of capital (MPK) [*]

                      d(q(K, L)  r
(3)                   -------- = -
                         dK      p

(2) is purported to mean that the addition to revenue by the last unit of labour (p*MPL) equals the wage workers are paid (w). A similar interpretation follows for (3). [&]

So far, no use has been made of linear homogeneity. It comes in handy now. By the theorem of the sum, due to Euler, a linear homogeneous production function like q(K, L) can be decomposed like so:

                     d(q(K, L)      d(q(K, L)
(4)        q(K, L) = -------- * L + -------- * K
                        dL             dK

Substituting (2) and (3) in (4):

                          w       r
(5)             q(K, L) = - * L + - * K
                          p       p


In other words p*q(K, L) = r*K + w*L. Compare this to (1).

Together, and in English, this means that (i) workers' wages (w) and capitalists' return (r) reflect their contribution to output and revenue (aka just deserts), and (ii) they exhaust both output and revenue (aka non-exploitation). John Bates Clark understood that.

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Now, for all we know, Keynes (depending on the lunar cycle) believed that. Big shot mainstream Keynesians claim not to believe that (thus, the 101ism thing) but keep teaching it just the same and see no implication whatsoever for exploitation.

Post Keynesians apparently don't believe that, but it's hard to say what they do believe: they have little coherent to say and no alternative to offer (excepting the nonsense of "profits are produced by specific macroeconomic flows of funds"). The only thing one can say for sure about post Keynesians is that for them everybody else is wrong, wrong, wrong, for methodological reasons. That's when "apodictic", "synthetic", "non-ergodic", "metaphysics", "ideology", "ontology", "epistemology" start to pop up in the discourse and the only thing missing is the one they need the most: "proctology".

And the only alternative is unacceptable to all Very Serious People.

Thank goodness I'm just a grunt.


Notes:

[*] Technically, those are only the first order conditions for the maximization problem

            Max p*q(K, L) - r*K - w*L
          (K, L)

            s.t.
                K >= 0
                L >= 0


For reasons irrelevant here, we can forget the non-negativity constraints, Lagrange multipliers or any of that. You just find the first two partial derivatives of profit, make them zero and solve the system of two equations -- equations (2) and (3).

[&] Incidentally, that explains why Prof. Nick Rowe sees no difference between wages and returns to capital and feels free to speak of wages of robots: capital (means of production) and labour, expressed symbolically (K) and (L), are only letters, therefore that's how reality is.

2 comments:

  1. Good work. As a suggestion, apply that to the Cobb-Douglas production function

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  2. Funny how the good and mighty suddenly found distribution interesting:

    http://www.thefiscaltimes.com/Columns/2016/05/17/Economic-Models-Must-Account-Who-Has-Power

    https://www.theguardian.com/business/2016/may/13/-new-era-monopoly-joseph-stiglitz

    http://robertpaulwolff.blogspot.com/2016/05/in-desperate-effort-to-stay-sane.html

    Nigel O.

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