Thursday, December 26, 2019

2019 Nobel Prize Celebrating The Triumph Of Institutionalism?

Elizabeth Warren Echoing A View Institutionalists Understand

This year, the "Nobel prize" in economics went to Abhijit Banerjee, Esther Duflo, and Michael Kremer. They champion empirical economics over theory. Previously, institutionalist economics was described as 'theory without measurement' (Koopmans 1947). Does institutionalist economics parallel the supposed mainstream empirical turn?

Although institutionalists, as far as I know, did not have the resources to create randomized control trials (RCTs), they did collect and analyze statistical data. I think especially of Wesley Clair Mitchell and the National Bureau of Economic Research (NBER).

Institutionalists was not atheoretical, I think. They developed qualitative analytical concepts. I think of C. E. Ayres extension, for example, of the Veblenian dichotomy. Sometime, I intend to read John R. Commons' 1924 book to see how he breaks up a transaction. John Kenneth Galbraith's concept of the technostructure and Alfred Eichner's idea of the megacorp are other examples here. Institutionalists contributed to the development of Industrial Organization. John Maurice Clark had, at least, a verbal description of the business cycle that combined the multiplier and the accelerator.

Institutionalist economics is not a strictly American school of thought. I include Geoffrey M. Hodgson and Gunnar Myrdal as institutionalists. I suppose I should read the Journal of Economic Issues or the Journal of Institutional Economics more frequently. The Association for Evolutionary Economics (AFEE) puts out the JEI.

References
  • John R. Commons. 1924. Legal Foundations of Capitalism Macmillan.
  • John S. Gambs. 1946. Beyond Supply and Demand: A Reappraisal of Institutional Economics. Columbia University Press.
  • Tjalling C. Koopmans. 1947. Measurement without theory. Review of Economics and Statistics 29(3): 161-172.

Saturday, December 14, 2019

A Fake Switch Point in an Example With Circulating Capital

Figure 1: A Switch Point and a Fake Switch Point on Wage Curves
1.0 Introduction

In the analysis of the choice of technique, I typically consider examples of technology with a finite number of techniques. For each technique, I find the wage as a function of the rate of profits. The outer envelope of these curves shows the cost-minimizing technique at each rate of profits (or each level of the wage). Points on more than one wage curve are switch points.

This approach is valid when, for example, all techniques produce the same set of commodities, and each commodity is basic, in the sense of Sraffa. That is, all commodities enter directly or indirectly into the production of all commodities.

But another requirement is that prices of all commodities in common between two techniques be identical at a switch point. Points of intersection on wage curves without this property of identical prices are known as fake switch points. I have previously considered fake switch points in (an extension of) an example from Christian Bidard. In this post, I present an example of a fake switch point in an example with single production (or circulating capital) only. It is critical to this example that a non-basic commodity is the numeraire and that the techniques vary in the process used to produce a non-basic commodity.

The necessity to consider prices in the analysis of the choice of technique is, as I understand it, a critical point from Milana. I think he extends this point, though, to examples in which it cannot be used to criticize Sraffians.

2.0 Technology

Table 1 shows the coefficients of production for this example. Coefficients of production specify inputs per unit output. Each process takes a year to complete. Inputs are totally used up in the production of the outputs.

Table 1: Coefficients of Production for The Technology
InputCorn IndustrySilk Industry
AlphaBeta
Labor112 Person-Yrs
Corn1/53(38/15) Bushels
Silk000 Square-Yds

The first produced commodity, corn, enters directly into the production of both commodities. It is a basic commodity, in the sense of Sraffa. Silk is a non-basic commodity. It does not enter, either directly or indirectly, into the production of corn.

3.0 Price Equations

I take a square yard of silk as the numeraire. The same rate of profits is assumed to be made in both industries when prices of production prevail. Labor is advanced, and wages are paid out of the net product at the end of the year.

3.1 The Alpha Technique

The following two equations specify prices of production for the Alpha technique:

(1/5) p1, α (1 + r) + wα = p1, α
3 p1, α (1 + r) + wα = 1

The variables are:

  • r: The rate of profits.
  • wα: The wage, for the Alpha technique.
  • p1, α: The price of corn, for the Alpha technique.
The solution, in terms of the rate of profits, is:

wα(r) = (4 - r)/(19 + 14 r)
p1, α(r) = 5/(19 + 14 r)

3.2 The Beta Technique

The price equations for the Beta technique are:

(1/5) p1, β (1 + r) + wβ = p1, β
(38/15) p1, β (1 + r) + 2 wβ = 1

The solution is:

wβ(r) = 3(4 - r)/[2( 31 + 16 r)]
p1, β(r) = 15/[2( 31 + 16 r)]

4.0 Switch Points

Suppose, at the given rate of profits, the Alpha technique is in use and prices of production for the Alpha technique prevail. Figure 2 shows the cost of producing silk, for each process, at these prices. The advances, at the beginning of the year, for produced inputs are costed up at the going rate of profits. The cost of producing silk with the process in the Alpha technique, under these assumptions, is unity for any feasible rate of profits. Extra costs are not incurred in the Alpha technique. Neither are supernormal profits available.

Figure 2: Cost of Producing Silk at Alpha Prices

But supernormal profits are available for the silk-producing process in the Beta technique if the rate of profits is feasible and exceeds the rate of profits at the switch point. The Beta technique is cost-minimizing here, while the Alpha technique is only cost-minimizing at lower rates of profits. The same conclusion about when each technique is cost-minimizing would be drawn if one started with prices of production for the Beta technique.

The switch point occurs at a rate of profits of 50 percent. The wage is (7/52) square yards per person-years, and the price of corn is (5/26) square yards per bushel at the switch point. Prices of production are the same, at the switch point, whichever technique is used.

5.0 A Fake Switch Point

Figure 1, at the top of this post, graphs the wage curves for the two techniques. Consider rates of profits that equate wages:

wα(r*) = wβ(r*)

The wage curves have two intersections. One is at the switch points, at a rate of profits of 50%. At the maximum rate of profits of 400 percent, the wage is zero. In the Alpha system, the price of corn is (1/15) square yards per bushel, while it is (3/38) square yards per bushel in the Beta system. Since, prices of production vary among techniques at the maximum rate of profits, it is not a switch point. Rather, it is a fake switch point.

6.0 Conclusions

I would like to find another example of a fake switch point in a circulating capital example with a choice of processes for producing a non-basic commodity. I want a fake switch point not at an extreme, with a wage of zero. The example in Stamatis (2001) seems not to work; maybe there is a misprint in the coefficients of production. Both techniques, however, have the structure of Sraffa's "beans".

References
  • Carlo Milana. 27 Nov. 2019. Solving the Reswitching Paradox in the Sraffian Theory of Capital
  • Georg Stamatis. 2001. Why the comparison and ordering of techniques is impossible. Political Economy 9: 5-44.

Tuesday, December 10, 2019

The Interest Rate: Prime, Overnight, Or The Rate On T-Bills

As far as I am concerned, cost-push inflation is a manifestation of class conflict between workers and owners. In the late 1970s, Paul Volker and Ronald Reagan took the side of the owners. I am willing to accept that Volker genuinely believed in Milton Friedman's incorrect quantity theory of money. And, since then, workers have been getting a smaller share in increased productivity. Some obituaries of Paul Volker exhibit an understanding of what he did.

But I want to talk about my recollection of how interest rates have been covered in the press from that time. Of course, at any given time, there are a whole range and time structures of interest rates. When Volker drove the interest rate above 20 percent, the focus in news coverage was, as I recall it, on the prime rate, that is, the best interest rate commercial borrowers, such as large corporations, can obtain. My perception is that now, when movements in interest rates are reported on in the press, the emphasis is more likely to be on one of two rates. One is the overnight rate, that banks charge each other overnight. One can hear about the repo market, I guess, in this context. The other much-discussed rate is the rate on short term treasury bills (T bills).

Is my perception accurate? When did this change occur, if so? Is it actually an example of society learning? After all, the Federal Reserve has much more direct control over the latter interest rates and only indirect and tenuous control over the prime rate. Has Volker's demonstration that the quantity theory is wrong been generally taken on board?

Friday, December 06, 2019

The Cambridge Equation, Expanded Reproduction, and Markup Pricing: An Example

1.0 Introduction

I have sometimes set out Marx's model of expanded reproduction, only with prices of production instead of labor values. I assume two goods, a capital good and a consumption good, are produced with constant technology. If one assumes workers spend all their wages and capitalists save a constant proportion of profits, one can derive the Cambridge equation in this model.

The Cambridge equation shows that, along a steady state growth path, the economy-wide rate of profits is determined by the ratio of the rate of growth and the saving rate out of profits. Maybe one should not use causal language here. The Cambridge equation is a necessary, consistency condition for smooth reproduction in a capitalist economy.

This post derives the Cambridge equation with markup pricing, in a highly aggregated model of expanded reproduction. I am curious how far this result generalizes. I am thinking of a model in which, say, n capital goods are produced in Department I and m consumer goods are produced in Department II. At this point, I am not thinking of generalizations in which workers save and therefore own some of the capital stock. Nor am I worrying about fixed capital, depreciation, and technical change.

Table 1: Definition of Variables
VariableDefinition
a01The person-years of labor hired per unit output (e.g., ton steel) in the first sector.
a02The person-years of labor hired per unit output (e.g., bushel corn) in the second sector.
a11The capital goods (measured in tons) used up per unit output in the first (steel-producing) sector.
a12The capital goods (measured in tons) used up per unit output in the second (corn-producing) sector.
p1The price of a unit output in the first sector.
p2The price of a unit output in the second sector.
s1Relative markup in producing steel.
s2Relative markup in producing corn.
The scale factor for the rate of profits.
rThe rate of profits.
σThe savings rate out of profits.
wThe wage, that is, the price of hiring a person-year.
cConsumption per worker, in units of bushels per person-year.
X1The number of units (ton steel) produced in the first sector.
X2The number of units produced (bushels corn) in the second sector.
gThe rate of growth.
2.0 The Model

Certain quantity equations follow from the assumptions. No produced capital goods remain each year after subtracting those used to reproduce the capital goods used up in throughout the economy and those needed to support the given rate of growth:

0 = X1 - (1 + g)(a11 X1 + a12 X2)

Consumption per person year is the output of the second department:

c = X2

The model economy is scaled such that one person-year is employed:

a01 X1 + a02 X2 = 1

I have the usual price equations, with labor advanced:

p1 a11 (1 + r̂ s1) + a01 w = p1

p1 a12 (1 + r̂ s2) + a02 w = p2

The consumption good is the numeraire:

p2 = 1

As with Marx in volume 2 of Capital, industries are here grouped into two great departments (Table 1). Means of production (also known as capital goods) are produced in Department I, and means of consumption (or consumer goods) are produced in Department II.

Table 2: Value of Outputs by Department and Distribution
DepartmentCapitalWagesProfits
I. Capital Goodsa11 X1 p1a01 X1 wa11 X1 p1 s2
II. Consumption Commoditiesa12 X2 p1a02 X2 wa12 X2 p1 s2

The overall, economy-wide rate of profits is defined in terms of profits and capital advances, aggregated over both departments:

r = (a11 X1 p1 s2 r̂ + a12 X2 p1 s2 r̂)/(a11 X1 p1 + a12 X2 p1)

The economy experiences expanded reproduction when it consistently expands each year. In this case, the demand for capital goods from the second department includes the savings of the capitalists receiving profits from that department. Likewise, the demand for consumption goods from the first department excludes the savings of the capitalists in that department. Observing these qualifications, it is easy to mathematically express the condition that the demand for capital goods from the second department match the demand for consumption goods from the first department:

a01 X1 w + (1 - σ) a11 X1 p1 s2 r̂ = a12 X2 p1 + σ a12 X2 p1 s2

3.0 Some Aspects of The Model Solution

Quantity variables (c, X1, and X2) can be found as a function of the rate of growth. Price variables (w, p1, and p2) can be found as a function of the scale factor for the rate of profits. These solutions allow one to use the balance equation to find a relation between the scale factor for the rate of profits:

r̂ = (g/σ){1/[s2 - (1 - g)(s2 - s1)a11]}

One can use the above relationship and the solution quantities and prices to find the economy-wide rate of profits:

r = g/σ

Along a path in which the economy steadily expands, the rate of profits must be equal to the quotient of rate of growth and the savings rate out of profits. The rate of profits is dependent on investment and savings decisions, out of the control of the workers. (In a two-class economy in which the workers save at a smaller rate than the capitalists, the Cambridge equation remains valid, with the savings rate in the denominator being that of the capitalists.) It is independent of the technical conditions of the chosen technique, and marginal productivity has nothing to do with it.

4.0 Conclusions

I know that this model can be generalized to hold when any number of consumer goods are produced. I have not yet been able to show the Cambridge equation holds when any number of capital goods are produced.