Showing posts with label just for fun. Show all posts
Showing posts with label just for fun. Show all posts

Monday, 1 November 2021

Coase and profit maximisation

One assumption not discussed much in the mainstream theory of the firm is that of profit maximisation. Most theories of the firm take it as a given, a non-controversial notion to base their theory on. Ronald Coase's view isn't so clear cut.

In one case he seemed to have been that in practice profit maximisation was unlikely to be achieved by any firm:
"[i]t would be Utopian to imagine that a businessman, except by luck, could manage to attain this position [MR=MC and the avoidable costs of the total output less than the total receipts] of maximum profit"(Coase 1981: 102)
and
"[t]his being so, it seems to me that any claim that modern cost accounting (at any rate in the form in which it is to be found in the textbooks) enables unprofitable lines to be discovered and eliminated is misleading. It is only possible to discover whether or not a particular activity is profitable by comparing the avoidable costs with the receipts. And this, as I understand it, is a task which modern cost-accounting methods do not enable one to perform" (Coase 1981: 113).
But he also seemed to have seen it as a useful tool for economic investigation:
"[w]ell, all this suggests that economists are satisfied. Now the fact is that they are satisfied. They are very pleased. To go to a meeting of the American Economic Association is to see thousands of self-satisfied economists. Now there is a reason why this is so. They have found economics useful and are quite happy therefore to go on using it. Now it’s true: it is useful. The concepts which have been developed for handling various problems are useful for handling a wide range of problems. Opportunity costs, supply and demand schedules, marginal costs, marginal revenues, maximization of profits – they’re all very useful concepts that you can use, and not simply for economic problems but for others as well" (Coase 2002: 4).
and
"[n]ow take a person in a firm situation. A man who buys something for 10 dollars and sells it for 8 dollars doesn't last very long. These's an immediate punishment that comes in within the economic system if you don't try to maximise profits and so on. So, I'm very happy with the assumption that people make, that firms make profits. And you can study what firms do and of course, it fits very nicely. They drop the lines that make losses. They expand the lines that make profits and so on. So, I make this difference between people acting in the productive system and people acting as consumers" (Becker 1995).
When discussing the nature of opportunity costs, Coase writes,
"[t]his particular concept of costs would seem to be the only one which is of use in the solution of business problems, since it concentrates attention on the alternative courses of action which are open to the businessman. Costs will only be covered if he chooses, out of the various courses of action which seem open to him, that one which maximizes his profits. To cover costs and to maximize profits are essentially two ways of expressing the same phenomenon. In practice it is probably better to regard the cost of doing anything as the highest alternative receipts that might have been obtained rather than vaguely as all the alternatives that are open" (Coase 1981: 108).
In a comment on Heflebower (1955) - which critically examined one attack on the standard neoclassical model including profit maximisation, that of full-cost pricing - Coase wrote that he wasn't yet ready to give up on the standard marginal analysis:
"I am not willing on the basis of the arguments brought forward so far to abandon ordinary marginal analysis (taking account of demand) as a first approximation. It is clearly not the whole story and there is need for much more research on business behavior. But we should not be disappointed if a good deal of economic theory turns out to be usable after our investigations are completed'' (Coase 1955: 394).
So it appears that while Coase thought that businessmen could not enact profit maximisation in practice, it was still a useful simplification for theoretical purposes.

For a short overview of the attacks on the neoclassical model, including those concentrating on profit maximisation, during the 1940-1970 period see Walker (2021: chapter 6).

Refs.:
  • Becker, Gary S. (1995). 'Gary Becker Discussions: Consumer Behavior'. Video of discussion between Gary Becker and Ronald Coase on the question of, Is the economic theory of utility a useful way of understanding consumer behavior?
  • Coase, Ronald Harry (1955). 'Comment' (on Heflebower (1955)). In Universities-National Bureau Committee for Economic Research, Business Concentration and Price Policy (pp. 392-4), Princeton: Princeton University Press.
  • Coase, Ronald Harry (1981). 'Business organization and the accountant'. In J.M. Buchanan and G.F. Thirlby (eds.), L.S.E. Essays on Cost (pp. 95-132), New York: New York University Press.
  • Coase, Ronald Harry (2002). 'Why Economics Will Change: Remarks at the University of Missouri, Columbia, Missouri, April 4, 2002', International Society for New Institutional Economics Newsletter, 4(1) Summer: 1, 4-7.
  • Heflebower, Richard B. (1955). 'Full Costs, Cost Changes, and Prices'. In Universities-National Bureau, Business Concentration and Price Policy (pp. 359-92), Princeton: Princeton University Press
  • Walker, Paul (2021). Foundations of Organisational Economics: Histories and Theories of the Firm and Production, London: Routledge.

Friday, 15 January 2021

The Theory of the Firm: An Overview of the Economic Mainstream, Revised Edition

This is a revised edition of Walker (2017). New sections or subsections have been added on the X-inefficiency model, the division of labour and the firm - both pre and post-1970, ownership of the firm and the human capital based firm. Additions have been made to sections on entrepreneurship, the incomplete contracts approach to the firm, the discussion of Coase’s paper on the ‘The Nature of the Firm’, the discussion of industry-level analysis versus intra-firm analysis, reasons for ignoring firm, a small addition has been made to the Sreni material in section 2.1 and material on Commenda, Waqf and the Clan Corporation has also been added to section 2.1. Appendix 4 has been deleted.
Walker, Paul (2017). The Theory of the Firm: An overview of the economic mainstream, London: Routledge.

The Theory of the Firm: An ... by Paul Walker

Friday, 22 May 2020

Foundations of Organisational Economics: Histories and Theories of the Firm and Production

This essay provides introductions to five of the major topics to do with the history of the theory of production and the theory of the firm. The first chapter is an introduction. The second considers the change from a normative approach to the theory of production to a largely positive approach. Before, roughly, the 17th century the main approaches to the theory of production were normative. The third looks at the relationship (or the lack of a relationship) between the division of labour and the theory of the firm. Even today the mainstream of economics does not emphasise the division of labour in the theory of the firm. In the fourth chapter, the development of the proto-neoclassical approach to production is examined. The development of theories of monopoly, oligopoly and perfect competition as well as the theory of input utilisation are discussed. The fifth chapter looks at Marshall’s idea of the representative firm. This was the main early neoclassical approach to the theory of industry-level production. Marshal wished to be able to construct an industry supply curve without having to assume all firms were identical. The sixth examines the challenges to the neoclassical model in the period 1940-1970. The last chapter is a short conclusion.

Foundations of Organisation... by Paul Walker on Scribd

Sunday, 12 April 2020

Saturday, 22 February 2020

X-inefficiency

A basic assumption of the neoclassical model of production is that production is carried out in a technically efficient manner.(1) Leibenstein (1966) challenges this assumption. First, he argues that the empirical evidence suggests that producers typically do not achieve technical efficiency and he called this technical inefficiency, `X-inefficiency'.(2) Secondly, he argues, in terms of a theoretical explanation for this inefficiency, that there are four major reasons for X-inefficiency:
  1. Labour contracts are incomplete. Such contracts do not and can not completely specify what is to be done by employees. The hiring of labour involves the hiring of time on the job but the intensity of effort is variable, that is, there are, in addition to incompleteness, moral hazard problems to contend with.(3)
  2. Not all of the factors of production needed to achieve technical efficiency are markable and thus some of these factors may not be available to a producer. In particular, significant problems can arise when there are market imperfections in the market for management, meaning the quality of managers is hard to assess ex ante, that is, there are adverse section problems in the market for managers.
  3. The production function is not completely specified nor completely known by the producer. Prior experience and ability to experiment are factors affecting the producer's knowledge of the production process. But if the producer does not fully understand the production function, it will struggle to achieve fully efficient production.
  4. If there are strategic interactions between producers and uncertainty about competitors' reaction to a move by any given producer, then tacit collusion and imitation between producers can result and this could prevent producers from achieving fully efficient production. Put simply, competition matters for efficiency.
In later work, Leibenstein (1975, 1976), the theory of X-inefficiency has been expanded. It is noted that organisations are collections of individuals, each of whom has their own self-interest and whose efforts on behalf of the organisation are variable. Leibenstein emphasises the variability of effort by the individual rather than the mutuality of individuals' interests within the organisation. Individuals will pursue their own interests, which may (or may not) contribute to the interests of the organisation in its entirety. But there are constraints placed on the individual's actions by the organisation.
"The 'tightness' of these constraints depends upon the nature of the job being done, the system of payments (e.g. payment by results, payment by time, etc.), and the type of organization. Two important factors in determining the tightness of the constraint are likely to be the strength of the competition in the markets where the firm operates, and its degree of success" (Sawyer 1975: 131).
It is worth noting that the idea of X-inefficiency is related to the concept of `slack' noted in the sections above. It arises in this context due to the pursuit of self-interest by individuals, variations in their effort and incomplete monitoring of individuals. In the behavioural theory, it arises because of the bargaining processes within the organisation while in the managerial models it is due to the pursuit of self-interest by managers. But the presence of slack, for whatever reason, suggests the non-minimisation of costs and thus the non-maximisation of profits.

Notes.

(1) This section is based on Sawyer (1975: section 8.4)

(2) A more formal model of X-inefficiency is given in Crew (1975: 110-5).

(3) Hawkins (1973: 50) explains that human beings are different from other factors of production in important ways.
``Machines have a potential output which can be achieved by pressing the right switches. Human beings by contrast can adjust the quality and pace of their work in line with their own preferences. By supervision, by punishments and incentives, human effort can be varied. There is no reason why a shop-floor worker, or manager, should have a utility function which coincides with that of the firm as a whole or of its shareholders. Employees may maybe compelled to produce a minimum output - or lose their job. There may also be a maximum output of which they are capable given all the right sticks and carrots. But between these levels they can choose to vary the amount of time they spend on various activities, the pace at which they work and the quality of the work they do. There is no single-valued relationship between the number of man-hours purchased and the quality or quantity of effort that is expended in production. As a result, it is unlikely that every employee's choices will be exercised in such a way as to give maximum output per unit of input. So X-inefficiency almost always exists".
Refs.
  • Crew, Michael A. (1975). Theory of the Firm, London: Longman.
  • Hawkins, C. J. (1973). Theory of the Firm, London: The Macmillian Press.
  • Leibenstein, Harvey (1966). 'Allocative Efficiency vs. X-Efficiency', The American Economic Review, 56(3) June: 392-415.
  • Leibenstein, Harvey (1975). 'Aspects of the X-Efficiency Theory of the Firm', Bell Journal of Economics, 6(2) Autumn 1975: 580-606.
  • Leibenstein, Harvey (1976). Beyond Economic Man, Cambridge Mass.: Harvard University Press.
  • Sawyer, Malcom C. (1979). Theories of the Firm, London: Weidenfeld and Nicolson.

Tuesday, 8 October 2019

The representative firm

Marshall's idea of  'representative firm' was created to reconcile his dynamic view of individual firms with the static view of industries. But this idea was somewhat nebulous and did not last very long in the economics literature. Marshall first wrote about the representative firm in his Principles of Economics published in 1890 but the idea was driven out of the literature by 1928, when it was replaced by A. C. Pigou's idea of the `equilibrium firm'.

Friday, 4 January 2019

What is a firm?

This seems an obvious question which many people would assume would have an obvious answer. And yet it doesn't.

No one can agree on a definition. For neoclassical theory, a firm is little more than a production function or production possibilities set. For Demsetz a firm is an organisation in which production is carried out exclusively for sale to those formally outside the organisation. For Coase the firm is defined as an employment relationship. X is a firm because the owner of X employs A and B to work for him. For Williamson and Hart a firm is defined in terms of the ownership of alienable assets. The question for them is who owns what rather than who employs who. Spulber sees a firm as a transaction institution whose objectives differ from those of its owners. For Foss and Klein a firm is made up of an entrepreneur and the assets owned by them. All of these ideas have some merit. Its much like a group of blind men trying to describe an elephant, each man can tell you about the part he can feel while remaining unaware of the rest of the animal.

At first, it may seem odd that economists can not agree on what a firm is. But is it really that strange? When you think about it, coming up with a definition that covers every organisation from a sole proprietorship to a partnership to a limited liability company to a multinational is asking a lot, maybe too much. Foss, Klein and Linder (2015: 275)  suggest that a "[...] better question than "what is a firm" is "what are the important research questions that can be answered when the firm is defined in a particular way?" ".

That idea does seem to have merit.  At least then you can use a definition which is useful for the question under consideration rather than trying to come up with an all-embracing definition. A lot of otherwise wasted time and energy could be saved by not having to come up with the perfect one size fits all definition.

Ref.:
  • Foss, Nicolai J., Peter G. Klein and Stefan Linder (2015). 'Organizations and Markets'. In Peter J. Boettke and Christopher Coyne (eds.), The Oxford Handbook of Austrian Economics (pp. 272-95), Oxford: Oxford University Press.

Friday, 16 November 2018

Revised version: Being neoclassical before it was cool to be neoclassical: the case of the theory of the firm

This essay looks at the contribution made by pre-1870 writers to what would later become the neoclassical theory of the firm. In particular it briefly considers the work of Dionysius Lardner, Johann von Thunen, John Stuart Mill, Charles Ellet, Jr. and Antoine Augustin Cournot. The neoclassical theory of the firm should, in many ways, be more properly called the proto-neoclassical theory of the firm

Thursday, 1 November 2018

Being neoclassical before it was cool to be neoclassical: the case of the theory of the firm

This essay looks at the contribution made by pre-1870 writers to what would later become the neoclassical theory of the firm. In particular it briefly considers the work of Dionysius Lardner, Johann von Thunen, John Stuart Mill, Charles Ellet, Jr. and Antoine Augustin Cournot. The neoclassical theory of the firm should, in many ways, be more properly called the proto-neoclassical theory of the firm

Monday, 22 October 2018

JS Mill and the firm

Another, possible, proto-neoclassical, who wrote on the economics of the firm, if not strictly on the theory of the firm, was John Stuart Mill. While Mill is most often thought of as a classical economist, Ekelund and Hebert (2002: 198) argue he can be considered as a proto-neoclassical economist.

According to Schumpeter (1954: 556), Mill introduced the concept of the entrepreneur to the English speaking economics literature. The influence of J. B. Say helped Mill go beyond just analysing the role of the owner of the factors of production and begin focusing on the role of the entrepreneur and on the internal organization of the firm (Zouboulakis 2015: ???).

For Mill, the number of collective organisations, including firms - both investor controlled and co-operatives, would increase as wealth increases,
"[a]s wealth increases and business capacity improves, we may look forward to a great extension of establishments, both for industrial and other purposes, formed by the collective contributions of large numbers ; establishments like those called by the technical name of joint-stock companies, or the associations less formally constituted, which are so numerous in England, to raise funds for public or philanthropic objects, or, lastly, those associations of workpeople either for production, or to buy goods for their common consumption, which are now specially known by the name of co-operative societies" (Mill 1848: 699).
Mill gave the first discussion of joint production and of the importance of the scale of production. With regard to joint production, George Stigler writes,
"Mill clearly formulated the problem of joint production, i.e., production of two or more products in fixed proportions. He gave the complete and correct solution: the sum of the prices of the products must equal their joint cost, and the price of each product is determined by the equality in equilibrium of quantity supplied and quantity demanded" (Stigler 1955: 297).
As to the significance of the scale of production Stigler adds that,
"Mill's chapter (Bk. I, c. IX), " Of production on a large, and production on small, scale", is the first systematic discussion of the economies of scale of the firm to be found in a general economic treatise. It would take us afield to analyse this chapter in detail, but we may point out that Mill was the first economist to notice that one can deduce information on the costs of firms of different sizes from their varying fortunes through time" (Stigler 1955: 298).
Zouboulakis (2015: ???) writes that "[a]mong the advantages of production on a large scale, he [Mill] mentions the more advanced division of labour, the less than proportionate increase of "the expenses of a business”, the greater possibility of investment to "expensive machinery" and ``the saving in the labour of the capitalists themselves" (1848, 132-6)".

Mill also scrutinised the advantages and disadvantages of the joint stock company. "On the one hand, only such a company can afford the amount of capital necessary to build important projects such as a railway, and to guarantee the continuity of such costly and risky business operations such as banking and insurance. On the other hand, he recognizes that "joint stock or associated management" has some disadvantages over ``individual management"" (Zouboulakis 2015: ???). Mill, like Smith, saw the potential for, what today we would call, principal-agent problems in the relationship between the owners and the managers of joint stock companies. The interests of the managers may not be aligned with the interests of the owners. When discussing methods to the alleviate such problems Mill makes the observation that
"[i]n the case of the managers of joint stock companies, and of the superintending and controlling officers in many private establishments, it is a common enough practice to connect their pecuniary interest with the interest of their employers, by giving them part of their remuneration in the form of a percentage on the profits. The personal interest thus given to hired servants is not comparable in intensity to that of the owner of the capital ; but it is sufficient to be a very material stimulus to zeal and carefulness, and, when added to the advantage of superior intelligence, often raises the quality of the service much above that which the generality of masters are capable of rendering to themselves" (Mill 1848: 141).
Interestingly, such observations give Mill more of a proto-modern feel than a proto-neoclassical feel. But, again, like Smith, Mill did not develop his insights into a full-blown theory of the firm.

Refs.:
  • Mill, J.S. (1848). Principles of Political Economy with some of their Applications to Social Philosophy, 7 th edition 1873, re-edited by William J. Ashley 1909, New York: A. Kelley reprint, 1973.
  • Schumpeter, J.A. (1954). History of Economic Analysis, London: Allen & Unwin.
  • Zouboulakis, Michel S. (2015). 'Elements of a Theory of the Firm in Adam Smith and John Stuart Mill'. In George C. Bitros and Nicholas C. Kyriazis (eds.), Essays in Contemporary Economics: A Festschrift in Memory of A. D. Karayiannis (pp. 45-52), Heidelberg: Springer Cham.

Sunday, 21 October 2018

Johnann von Thunen and the (proto)neoclassical theory of the firm

Johnann Theunen has been described as a proto-neoclassical. One reason for this is the, before his time, contribution he made to the theory of the firm. While Dionysius Lardner analysed the firm's output market, Thunen looked at the firm's input markets. He argued that the firm should use inputs up to the point where the value of the marginal product of the input equals the price of that input. His treatment of the issue has become known as the marginal productivity theory of distribution. To illustrate Thunen's argument we will look at the simplest possible model.

We will assume a central marketplace which is surrounded by agricultural land, all of which is of equal fertility. There will be one good, which we call wheat. The landowners hire a single input to production, labour. L units of labour produces W(L) units of wheat. The price of wheat in the marketplace is p while the costs of transporting the wheat to the market is $t per mile per ton. Thus the earnings generated from wheat grown m miles away from the marketplace is p-t.m per ton. Total revenue from the wheat will be W(L).(p-t.m). Assume that the landowner pays workers a wage of w resulting in a total wage bill of w.L. This means that the landowner's profit from producing wheat m miles from the marketplace will be W(L).(p-t. m)-w.L.

Further, assume that the landowner selects L to maximise profits. This results in a problem we can represent mathematically as
max_L W(L).(p-t.m)-w.L
Maximising this objective function with respect to L gives the first order condition,
(dW(L*)/dL).(p-t.m)-w=0
this implies
(dW(L*)/dL).(p-t.m)=w
where dW(L*)/dL is the marginal product of labour and (dW(L*)/dL).(p-t.m) is the value of the marginal product of labour. Equation \ref{thunen} tells the firm it wants to select the level of labour such that the value of the marginal product of labour equals the marginal cost of labour, the wage rate.

Put more generally, a profit maximising firm will choose the level of an input so that the value of the marginal product of the input equals the price of that input. Therefore, from the point of view of a firm, the theory indicates how many units of a factor it should demand.

Blaug (1985: 17-8) sums up Thunen's analysis by saying,
[h]is analysis culminates in the perfectly modern statement that net revenue is maximized when each factor is employed to the point at which its marginal value product (Wert des Mehrertrags) is equalized to its marginal factor cost (Mehranfwand). Although the discussion proceeds in verbal terms, illustrated by numerical examples, Thunen correctly points out that the marginal product of a factor is a partial differential coefficient of a multivariable production function. Moreover, apart from clearly recognizing the distinction between fixed and variable factors, and between the average and the marginal returns of a factor, he took great care to define the inputs of capital, labor, and land in strictly homogeneous units, observing that this condition was rarely obtained in practice--this too was literally more than sixty years ahead of his time.
Refs.:
  • Blaug, Mark (1985). 'The Economics of Johann Von Thunen', Research in the History of Economic Thought and Methodology, 3: 1-25.
  • Thunen, Johann H. (1826; 1850; 1863). Der isolierte Staat in Beziehung auf Landwirtschaft und Nationalokonomie. Pt. I: Untersuchungen uber den Einfluss, den die Getreidepreise, der Reichtum des Bodens und die Abgaben auf den Ackerbau ausuben. Hamburg: Perthes; Pt. II: Der naturgemasse Arbeitslohn und dessen Verhaltniss zum Zinfuss und zur Landrente. Rostock: Leopold; Pt. III: Grundsatze zur Bestimmung der Bodenrente, der vorteilhaftesten Umtriebszeit und des Werts der Holzbestande von verschiedenem Alter fur Kieferwaldungen. Rostock: Leopold. English translation, The Isolated State, Volume 1. Carla Wartenberg, trans. Oxford: Pergamon Press, 1966; Volume 2 in The Frontier Wage. B. W. Dempsey, trans. Chicago: Loyola University Press, 1960.

Tuesday, 9 October 2018

Dionysius Lardner and the theory of the firm

The classical economists did not leave us much in terms of a theory of the firm. But one person who did make a contribution during the later classical era, albeit a contribution largely forgotten now, was Dionysius Lardner. Lardner is part of a group of pre-1870 writers that Ekelund and Hebert (2002) has referred to as "Proto-Neoclassicals". They summarise Lardner's contribution made in his 1850 book Railway Economy as he "[a]nalyzed railroad pricing structures; developed simple and discriminating monopoly analysis; analyzed monopoly firm in terms of total cost and total revenue, both mathematically and graphically (with an implicit demand curve)" (Ekelund and Hebert 2002: Table 1, p. 199).

One important contribution Lardner did make was to foreshadow aspects of the neoclassical theory of the firm. Lardner modelled a profit maximising firm and analysed its choice of price (and thus implicitly quantity) using revenue and cost curves, and implicitly a demand curve. He effectively showed that a profit maximum would occur when "marginal revenue" equals "marginal cost".

To understand Lardner's reasoning consider Figure 1


Figure 1

Source: Lardner (1850: 288).

In this Figure, the solid bell-shaped curve is what we would refer to today as a total revenue curve, but where the curve is graphed in revenue/output-price space rather than the standard revenue/quantity space, that is, the horizontal axis measures the price of output. At low prices revenue is also low, but as demand is inelastic revenue increases as price increases. It reaches a maximum, point P in Figure 1, and then as demand becomes more elastic, revenue falls as price continues to increase. While Lardner did not argue explicitly in terms of decreases elasticity, he did come close,
"[n]ow, if a less value still be assigned to the tariff, such as Om", the receipts will be augmented, because the influence of the increased number of objects booked, and the increased distances to which they are carried, owing to the diminution of the tariff, will have a greater effect in increasing the gross receipts than the reduction of the tariff has in diminishing them. By thus gradually diminishing the tariff, the traffic will increase both in quantity and distance, and the gross receipts will be placed under the operation of two contrary causes, one tending to increase, and the other to diminish them. So long as the influence of the former predominates, the gross receipts will increase ; but when the effect of the reduction of the tariff counterpoises exactly the effect of the increase of traffic in quantity and distance, then the increase of the gross receipts will cease. After that, the influence of the reduction of the tariff in diminishing the receipts will predominate over the influence of the increased traffic in augmenting them, and the consequence will be their diminution" (Lardner: 287-8).

The negatively sloped dashed line, Yy, is the total cost curve, again where the curve is graphed in cost/output-price space rather than cost/quantity space. This explains why the curve is negatively sloped. As the price of output increases the quantity demanded falls, i.e., implicitly Lardner is using a demand curve here, and as quantity falls the variable costs of production fall. Fixed costs, the vertical distance Xy, still needed to be paid. Lardner's cost curve shows total costs, fixed plus variable, declining due to the reduction in variable costs.

Lardner notes that the profit maximising point is to be found somewhere between P and s' in Figure 1, at a point where the vertical height of the revenue and cost curves decrease at the same rate. Fortunately, he then clarifies this by stating,
"[t]his may be geometrically expressed by stating it to be the point at which the two curves become parallel to each other" (Lardner 1850: 292).
This observation would be expressed today by saying that "marginal revenue" equals "marginal cost". Note however that for Lardner both "marginal revenue" and "marginal cost" would be defined in terms of the derivative with respect to output-price rather than quantity.

Lardner's explanation also shows that the profit maximising price is greater than the revenue maximising price, point P, that is, the profit maximising quantity is less than the revenue maximising quantity.

Lardner also hints at the advantages of price discrimination, insofar as he sees an advantage to having a lower tariff [price per mile per ton] on longer distances [think, larger quantities of "railway services"]. For example he writes,
"[i]t is clear, therefore, that every reduction which can be made on the tariff affecting the larger class of distances, will have the effect of increasing the area over which the producer can carry on a profitable business, and will proportionally increase the available traffic of the railway. For lesser distances, the reduction of the tariff will only have the effect of augmenting the quantity of the articles transmitted, and this can only be effected in the proportion in which the reduction of the tariff can effect a diminution of price in the market.

A due consideration of these circumstances will easily demonstrate the advantage which must result to the railways from such a graduated tariff as would favour transport to greater distances, [ \dots ]" (Lardner 1850: 299)
and he also said,
"[i]t follows, therefore, that for traffic generally, but more especially for every description of merchandise and of live stock, a tariff graduated upon the principle of diminishing as the distance transported increases, must be the source of largely augmented profits, [ \dots ]" (Lardner 1850: 301)
All this explains why Mark Blaug can write that Railway Economy is "a book containing the first exposition in English of what approximates to the modern [neoclassical] theory of the firm" (Blaug 1997: 293).

Refs.
  • Blaug, Mark (1997). Economic theory in retrospect, 5th ed., Cambridge: Cambridge University Press.
  • Ekelund, Robert B. Jr. and Robert F. Hebert (2002). 'Retrospectives: The Origins of Neoclassical Microeconomics', Journal of Economic Perspectives, 16(3) Summer: 197-215.
  • Lardner, Dionysius (1850). Railway Economy; A Treatise on the New Art of Transport, its Management, Prospects, and Relations, Commerical, Financial, and Social, with an Exposition of the Practical Results of the Railways in Operation in the United Kingdom, on the Continent, and in America, London: Taylor, Walton, and Maberly.

Friday, 24 August 2018

The ownership of firms

Who owns a firm and why? Investor-owned firms are the most common form of ownership for large-scale enterprises in most of the world, but in a market economy there are a number of other forms of ownership which are commonly utilised. We see, in many sectors of the economy, producer cooperative, customer cooperatives, nonprofit firms and mutual enterprises. Why? What determines who owns a firm?

This is a question addressed by Hansmann (1988, 1996, 2013). To understand Hansmann's theory of firm ownership we first need two definitions. Hansmann defines a firm's owners to be those persons who have two formal rights: the right to control the firm and the right to appropriate the firm's profits. That is, owners have control and income rights over the firm(1). Compare this to the property rights approach to the firm which see a firm's owners as those who have just control rights over the firm. Note also that this definition means some firms do not have owners. In nonprofit firms the control rights are separated from the income rights, no one can receive the residual earnings, meaning such firms are ownerless. A second useful definition is that of a firm's "patrons". Patrons are those persons who transact with the firm either as purchases of the firm's outputs or as suppliers of factors of production to the firm.

Significantly nearly all large firms are owned by persons who are also patrons.
"In principle, a firm could be owned by someone who is not a patron. Such a firm's capital needs would be met entirely by borrowing; its other factors of production would likewise be purchased on the market, and its products would be sold on the market. The owner(s) would simply have the right to control the firm and to appropriate its (positive or negative) residual earnings. Such firms are rare, however" (Hansmann 1988: 272).
But
"[i]f a firm were entirely owned by persons who were not among the firm's patrons, then all the firm's transactions involving inputs and outputs would take the form of market contracting. Although feasible in principle, in practice this is likely to be quite inefficient. Market contracting can be costly, especially in the presence of one or more of those conditions loosely termed ``market failure"-for example, where there is an absence of effective competition, or where one of the parties is at a substantial informational disadvantage. [\dots] For the present we need simply note that, where these costs are high, they can often be reduced by having the purchaser own the seller or vice versa. When both the purchaser and the seller are under common ownership, the incentive for one party to exploit the other by taking advantage of market imperfections is reduced or eliminated. Assigning ownership of a firm to one or another class of the firm's patrons can thus often reduce the costs of transacting with those patrons-costs that would otherwise be borne by the firm or its patrons. To assign ownership to someone who is not among the firm's patrons would waste the opportunity to use ownership to reduce these costs" (Hansmann 1996: 20).
There are two basic types of relationship between firms and patrons, a "market contract" or "ownership". Under a market contract the patron interacts with the firm only through a contract and is not an owner. Under ownership the patron is also an owner of the firm.


This raises an obvious question of what are the costs of contracting and of ownership? We will briefly survey the most significant types of costs that arise with market contracting and ownership.

The costs of contracting include market power, "lock-in", asymmetric information and the risks of long-term contracting.

In some situations a firm can have market power with respect to some of its patrons. The affected group of patrons have an incentive to own the firm to avoid price exploitation. For example, if the firm has monopoly power with respect to its customers, the customers could takeover and reorganise the firm as a consumer cooperative. Or if the firm has monopsony power with regard to its suppliers, the suppliers could create a producer cooperative as a way to avoid receiving the monopsony price (Hansmann 1996: 24-5).

Monopolistic exploitation can occur after a person has been dealing with the firm for sometime, even if at the beginning of the relationship there was competition for which firm the patron would contract with. Such ``lock-in" can occur if the patron has to make transaction-specific investments, which have little or no value outside of the relationship, and the contract between the firm and the patron is incomplete so that not all important aspects of future transactions can be specified in an ex-ante contract. This leaves the patron open to ex-post exploitation by the firm. Assigning ownership to the effected patrons mitigates the effects of such lock-in. This can be, for example, one reason for worker ownership of firms where firm-specific investment is required by the workers (Hansmann 1996: 25-6).

Asymmetric information can increase contracting costs via both moral hazard and adverse selection. If, for example, a firm knows more about the quality of its products than consumers know, then the firm may offer lower quality products than it says it will. This is the "lemons" problem (adverse selection) made famous by Akerlof (1970). In such situations consumer ownership has the advantage that it reduces the incentive for the firm to exploit its informational advantage. Consumers will not exploit themselves. Another example would be where workers know more about their effort levels than the firm knows. This gives rise to moral hazard issues. Worker ownership could act to reduce the incentive for workers to act opportunistically, since as owners the workers suffer more if effort levels are low. They also are likely to be better at monitoring each others level of effort. Asymmetric information can also give rise to strategic bargaining. A firm's management has private information about the firm and the firm's patrons have private information about their preferences and opportunities. If the patrons do not own the firm then each group has little incentive to reveal their information. Each group can use their private information strategically when bargaining with the other and thus increase the costs of negotiation. Patrons ownership reduces strategic behaviour since it decreases the incentive to hide information or to take advantage of information the other party lacks (Hansmann 1996: 27-9).

When patrons can not credibly communicate their preferences the costs associated with contracting increase. Not knowing patrons true preferences the firm's management may not be able to determine the least-cost combination of contractual terms that satisfies the firm's patrons. In addition patrons have an incentive to misrepresent their preferences to their strategic advantage. Ownership by patrons reduces the conflict of interest between patrons and owners and thus makes communication easier (Hansmann 1996: 30).

It is often the case that firms have to treat all patrons in a given class the same even when individual patrons in that class have different preferences. In such a case market contracting may result in an inefficient compromise being made among the patrons' differing preferences. This is because market contracting satisfies the preferences of the marginal patron whereas efficiency generally requires the choosing of conditions that satisfy the preferences of the average patron(2), and the marginal and average preferences can be very different. When patrons own the firms and a voting rule - in particular the majority rule - is used to make decisions then the results tends to favour the median patron rather than the marginal. The median will not in general be the average, but it will likely be closer than the marginal. Thus patron ownership has an advantage in decision making when patrons preferences differ (Hansmann 1996: 30-1).

Long-term contracting comes with its own problems. One such issue is that transaction-specific investment can leave one of the parties exposed to opportunistic behaviour by the other. Another is how can the parties allocate specific risks between them. Yet another issue is how can the parties mitigate the problems of adverse selection that occur in insurance and related markets (Hansmann 1996: 27).

Next Hansmann considers the costs of ownership, which involve risk bearing, principal agent problems and collective decision making.

One group of patrons may be able to better bear the risks associated with owning the firm than others. They may, for example, be better able to diversify their investments. Assigning ownership to this group can bring important economies. This is a common argument for having investors as the owners of a firm. However, Hansmann argues that investors are not the only low-cost risk bearers and that the evidence suggests that the importance of risk bearing as a reason for investor-ownership is overstated (Hansmann 1996: 44-5).

Hansmann (1996: 35-8) divides agency costs onto two board groups, costs of monitoring the firm's managers and the cost of opportunism by the managers given they can not be perfectly monitored. For effective monitoring of the managers, patrons must: 1. inform themselves about the operations of the firm and 2. communicate among themselves to exchange information and made decisions and enforce those decisions upon the managers. Each of these activities is costly but the costs will vary among the different groups of patrons. Patrons who transact with the firm frequency, for important transactions, over a long period of time will, most likely, be better informed about the firm. The ease of organising patrons for collective action will also affect the costs of monitoring. Thus patrons who are physically closer to one another and the firm will have lower costs. The size of the group of patrons will also affect monitoring costs. Given the public good nature of monitoring the larger is the group, the smaller is any individual's share of potential gains from monitoring, and thus the smaller is the incentive to monitor. Therefore when the group of patrons is large it can be prohibitively expensive for the owners to undertake effective monitoring.
"In itself, this [costly monitoring] argues for smallest group of owners possible--preferably a single owner. The fact that, despite this, a large firm often has a very large class of owners therefore suggests that either or both of two things must be true. First, the costs of market contracting would be much higher under any alternative assignment of ownership. Second, the costs of managerial opportunism are modest even though the firm's owners cannot actively supervise the managers" (Hansmann 1996: 36-7).
Managerial opportunism can be thought of as being divided into two groups: self-dealing ("putting their hand in the till") and deliberate managerial inefficiency. There are a number of sanction on self-dealing that do not require collective action by the firm's owners. There are moral, contractual, tort and criminal actions that can be taken against a transgressing manager which, for the most part, limit self-dealing activities. While self-dealing may be limited, this does not mean that managers always work hard and make the best commercial decisions. Managers may not always be acting in the best interests of the owners. But Hansmann argues that for the types of people who win the winner-takes-all management type contest and make it to the top of the management hierarchy pride and moral suasion provides important motivation. Also the need for the firm to prosper so that a manager's career can be enhanced provides additional incentive for effort. But Hansmann, more controversially, argues that the potential gains from better monitoring are often exaggerated. There is one area in which Hansmann does think managers may be able to act against the interests of owners, excessive retention of earnings. Retentions provide managers with a buffer against adverse times, enhance the survival of the firm and increase the size of the firm the manager controls. But retentions are costly to owners if the rate of return on retentions is lower than that on outside investments or if retentions can not be recovered by the current owners. This is seen in some mutuals and cooperatives.

Hansmann explains that in most firms collective decision making is enacted via some form of voting scheme. But when the interests of owners are diverse such schemes involve costs. Such costs fall into two general groups: costs from inefficient decisions and costs of the decision making process, see Hansmann (1996: 39-44).

As has already been noted majority voting leads to the outcome which is preferred by the median voter while efficiency requires the outcome preferred by the average voter. Where these two preferences differ it can lead to inefficient decisions. Also the decision making process can become dominated by the majority even when the costs of the agreed outcome are greater than the benefits. Hansmann gives the example of a broken lift in a hypothetical four-story cooperative apartment building. If residents on the first two floor don't use the lift and outnumber those on the top two floors then a vote would result in the cheapest method of repair being chosen rather than the quickest, despite the fact that any money saved could be less than the pecuniary and nonpecuniary costs borne by the top floor residents. Alternatively the decision process could be dominated by a motivated, better informed, if unrepresentative minority resulting, again, in an inefficient outcome. All that is needed for a costly outcome is for the dominant decision makers' self interest to be given greater weight than the interests of others.

The process of collective choice can be costly in and of itself. Time and resources must be invested to obtain information about the firm and other patron's preferences as well as in attending meetings and carrying out other activities required to reach and enforce decisions. The possibility of voting cycles increase as differences in preferences among patrons increase. This can be costly if it results in continued alterations to a firm's policies. Such cycles also give power to whomever gets to set the voting agenda. Setting the agenda strategically can help the setter get the outcome they want. Strategic behaviour by owners will also increase costs via the costs of hiding or finding information or making and breaking coalitions.

But the costs of collective decision making need not be large even when the owners of the firm have heterogeneous interests as long as there is a simple criteria for harmonising those interests. If there is not then reaching agreement can be long and costly. Think of a worker owned firm where the workers differ in the work they do. Reaching agreement on the division of earnings may be straightforward as long as it is easy to account for the net benefits to the firm of each owner's efforts. If, on the other hand, it is difficult to measure every owner's net benefits then agreement may be difficult to reach.

The process of collective decision making may bring benefits to participants as well as costs. Hansmann identifies three such benefits. First, individuals may enjoy the experience of participating in decision making as a social activity in and of itself. Second, it can be argued with regard to worker ownership that workers gain psychological satisfaction from being in control, that is, from participating directly in decision making. Third, again with regard to worker ownership, participation in the firm's decision making process is useful training for participation in the democratic processes of society in general. Hansmann does note however that while such benefits are real the evidence suggests that they do not outweigh the costs of collective decision making.

The takeaway message from Hansmann is that
"[t]he preceding survey points to several reasons for the dominance of investor-owned firms in market economies. One is that contracting costs for capital are often relatively high as compared with contracting costs for other inputs--including labor--and for most products. A second reason is that, however poorly situated investors may be to exercise effective control, there is seldom any other group of patrons who are in a better position to assert control. Where either of these conditions fails, other forms of ownership arise. Thus, when there are serious imperfections in the firm's product or factor markets, the firm is often organized as a consumer or producer cooperative or as a nonprofit. Similarly, when some group of patrons other than suppliers of capital is in a good position to exercise collective control, consumer or producer cooperatives often arise even when the patrons in question are faced with only modest problems of market failure. This suggests either that the effectiveness of the oversight exercised by shareholders--even with the assistance of the market for corporate control--is distinctly limited or that other factors may be more important in constraining managerial opportunism.

In determining whether the costs of ownership are manageable for a given class of patrons, homogeneity of interest appears to be an especially important consideration. In particular, it is evidently a significant factor in the widespread success of the modern investor-owned business corporation, and it may be among the best explanations for the relative paucity of worker­ owned firms, which otherwise have some significant efficiency advantages" (Hansmann 1988: 301-2).
Footnotes:
  1. While having both sets of right controlled by the same people is not necessary it is the most common form of allocation. For efficiency reason you would expect that both sets of rights would be held together. Put simply control rights give you the ability to do things while income rights give you the incentive to do things. Having them controlled by the same people lowers the cost of achieving an efficient outcome.
  2. In a footnote Hansmann makes reference to Spence (1975) as an explanation for this result. See Krouse (1990: section 6.1) for a simple exposition of Spence's result. There is a result from public choice theory that says for a public good the Pareto efficient quantity of the good is the same as the medians' voters demand only if the median voter is also the average voter. So when the median and average differ the result is inefficient.

References:
  • Akerlof, George A. (1970). 'The Market for 'Lemons': Quality Uncertainty and the Market Mechanism', Quarterly Journal of Economics 84(3) August: 488-500.
  • Hansmann, Henry (1988). 'Ownership of the Firm', Journal of Law, Economics, & Organization, 4(2) Autumn: 267-304.
  • Hansmann, Henry (1996). The Ownership of Enterprise, Cambridge, Mass: Harvard University Press.
  • Hansmann, Henry (2013) 'Ownership and Organizational Form'. In Robert Gibbons and John Roberts (eds.), The Handbook of Organizational Economics (pp. 891-917), Princeton: Princeton University Press.

Saturday, 21 October 2017

The division of labour and the firm: Rauh (forthcoming)

An interesting new paper which develops a theory, incorporating the division of labour and specialisation and a stochastic ('O-ring') production function, to explain the incentive structure and size of the firm is The O-ring theory of the firm by Micheal T. Rauh, which is set to appear in the Journal of Economics & Management Strategy.

A note on the name 'O-ring'. The O-ring production function was introduced by Kremer (1993). The name comes from the fact that it was an O-ring failure that caused the space shuttle Challenger disaster. The basic idea is that the failure of a small component can have large adverse consequences. Here one part of the production process failing causes the whole process to fail.

Rauh assumes a production process that can be divided into a number of distinct tasks. This makes it possible for the tasks to be allocated across workers (the division of labour) and for workers to make investments in task-specific human capital (specialisation). This is the kind of situation just discussed in the Becker and Murphy paper. We saw that an increase in employment gave rise to a greater division of labour, that is, fewer tasks assigned to each worker, and greater specialisation and thus higher productivity. Importantly Rauh postulates an additional feature of the production process: a breakdown at any point in production, which could be due to shirking, poor decision-making or a negative shock, will have serious adverse consequences for the successful manufacturing of the product--this is the 'O-ring' type production function.

This second condition has important implications for the moral hazard problems that arise within a firm. In the first best case, the principal can directly monitor individual worker effort and thus will be able to identify and respond to any shirking by workers with probability one. In the second best case, individual output can be monitored and again shirking can be punished with probability one. Note that in this case a worker who experiences a negative shock will also be punished. In the third best case all workers will be punished, with probability one, if any single worker shirks. In each of the three cases there will be no free rider issues since shirkers cannot hide behind the efforts of their co-workers.

Rauh considers a production process where the set of tasks is the unit interval. The principal chooses the number of workers, and the set of tasks to be performed is divided equally across all workers. Each of the workers is able to choose their production effort and their level of investment in task-specific human capital for each task they are assigned. To produce one unit of output requires one unit of output of each task. This means that you get zero output if any of the workers shirks or suffers an adverse shock in any of their assigned tasks. In line with Becker and Murphy (1992) greater levels of employment implies fewer tasks being assigned to each worker, which in turn means the workers can increase their investments in human capital for each of their reduced set of assigned tasks. This results in greater productivity and thus increasing returns to employment.

The stochastic (O-ring) nature of the production function is thought about in the following way.
"In addition to production effort and investments in human capital, each agent monitors his assigned tasks and makes decisions about whether or not a problem has arisen, whether or not to halt production to fix it, whether he can fix it himself, and which potential solution is appropriate. When there is only one agent, there is a high probability that at least some of these decisions will be faulty because he has limited cognitive resources and performs all the tasks himself. When there are two agents, the probability that either one will make a mistake should be lower because each performs only half the set of tasks and can therefore devote more care and attention to each of them. On the other hand, we now have two probabilities instead of one, so the effect of an increase in employment is ambiguous" (Rauh forthcoming: 2).
More formally, the probability that a worker suffers a negative shock to at least one of the tasks they have been allocated is an increasing function of the proportion of tasks being performed by that worker. Under an assumption of independence, the probability of a product defect is the product of the individual probabilities. If the number of workers is increased this results in two effects. First, it will decrease the probability that each worker will suffer a negative shock. Secondly, it will increase the number of points in the production process at which a negative shock can occur. Rauh then defines a production process as satisfying the O-ring property if the probability of a defect occurring is increasing in the number of workers and converges to one as the number of workers goes to infinity.

Given this background, the main question for the paper is then considered: What limits the size of a firm? For Rauh the answer has to do with the effects (or lack of effects) of moral hazard. Since there is a one-to-one relationship between the division of labour and the level of employment in the paper, the question can be rephrased as, What limits the division of labour? As has been noted above Becker and Murphy (1992) see this limit as be determined not by the extent of the market, as Adam Smith argued, but rather by coordination costs, including agency costs.

When determining the relationship between moral hazard and the size of the firm, "[ ... ] the optimal employment level balances the following considerations: (i) the increasing returns to employment due to specialization and division of labor, (ii) the O-ring property of the production technology, where the probability of team failure increases with the size of the team, and (iii) the marginal cost of employment (the cost of hiring another agent)" (Rauh forthcoming: 2).

In the first best case of no moral hazard Rauh shows that the standard zero incentive, full insurance contract is employed. Effectively the firm is behaving as if it were a perfectly competitive wage-taker despite it being a monopolist. Since, in this case, each worker's payment is fixed, the firm's labour costs (the number of workers times the expected payment to each worker) are linear in workers and the marginal cost of a worker is constant. Importantly, however, given increasing returns to employment, which arises from specialisation and the division of labour, but only linearly increasing costs to employment, these costs cannot limit the extent of employment. Thus, in this case, the extent of the market for labour or the O-ring property must be limiting employment and thus the size of the firm. If it wasn't for these constraints the first best firm would be of infinite size since there are increasing returns to employment.

Next Rauh considers the second best contract. Here effort cannot be observed but individual output can. Rauh shows that the optimal (second best) contract involves awarding a bonus to a worker when their individual output is high, i.e., when the worker's effort is first best and there is a positive shock, and replacing the worker otherwise. Rauh shows that the worker’s bonus is decreasing in employment. This follows from the fact that as employment increases the proportion of tasks carried out by each worker falls which increases the likelihood of a positive shock. This increases the expected value of the worker’s payment if the worker selects the first best effect level. This means the principal can reduce the bonus paid to the worker. It is also shown that this reduction in the bonus reduces the expected payment to the worker and this implies that the payment is decreasing in employment as well. If this type of effect is large enough then the marginal cost of an extra worker can decline with employment and could even be negative. In this situation the second best cost of employment could be less than the first best (constant) marginal cost of employment. This would mean the second best firm could be larger than the first best firm. Thus, the second best firm would have weak incentives (low bonus), low expected pay (small worker payment) and an excessive division of labour (and an excessive amount of specialisation). Motivation is provided by the fact that shirking workers will be identified and fired, rather than through the use of incentive schemes. As before, as the level of employment increases fewer tasks are carried out by each worker and the probability of a positive shock converges to one. This means that the second best expected payment to a worker converges to the first best payment. In turn, this means that the second best cost function tends towards the (linear) first best cost function. Thus as with the first best case the increasing returns resulting to employment resulting from the division of labour and specialisation cannot be contained by an asymptotically linear cost of employment. Rauh concludes from this that when the principal can monitor individual output, even if not effort, the size of the firm under moral hazard is again limited by either the total number of workers available or the O-ring property .

Lastly, Rauh looks at the third best situation where the where the principal can observe only team output. Here the results are the opposite of the second best case. This is because the third best incentive relies on the probability that all workers experience a positive shock rather than depending on the probabilities that individual workers experience a positive shock. Given the O-ring property, an increase in workers increases the probability that an individual worker experiences a positive shock but reduces the probability that all workers experience a positive shock. In this case increasing the number of workers decreases the team probability of success and this decreases the expected payments made to workers when they put in the first best level of effort. This means that the principal will increase the third best bonus, which increases the third best expected payment to workers and the marginal cost of employment. From this it is clear that all of the third best bonus, expected payments and the marginal cost of a worker are increasing in the number of workers. This is the opposite of the second best case above.

As the number of workers employed continues to increase, the third best bonus, expected payments and the marginal cost of employment all explode. This is contrary to the second best case where all these variables tended to their first best levels. The third best marginal cost of employment is shown to always exceeds the first and second best marginal costs of employment. This means the third best firm is usually smaller than either the first or second best firms.

Thus for Rauh's model moral hazard concerns only limit the division of labour, and the size of the firm, when the principal can monitor just the output of the whole team. When either worker's effort or individual output can be observed either the extent of the labour market or the O-ring property limit the extent of the division of labour or the size of the firm.

Rauh's paper is interesting in part because it combines, in some ways, the older division of labour approach to the firm with the more modern principal agent approach to the firm. The more modern mainstream approaches to the firm don't emphasise the division of labour with their emphasis being more on incomplete contracts and agency problems. The division of labour approach has largely fallen out of favour.

Well worth a read if you are into the theory of the firm.

Refs.:
  • Becker, Gary S. and Kevin M. Murphy (1992). 'The Division of Labor, Coordination Costs, and Knowledge', Quarterly Journal of Economics, 107 (4) November: 1137-60.
  • Kremer, M. (1993). 'The O-ring theory of economic development', Quarterly Journal of Economics, 108(3) August: 551-75.
  • Rauh, Michael T. (forthcoming). 'The O-ring theory of the firm', Journal of Economics & Management Strategy.

Saturday, 3 December 2016

The division of labour and the firm: Robinson (1931)

This material relates to Robinson (1931).

One of the earliest attempts to relate the division of labour to the size of firms was Robinson (1931). In The Structure of Competitive Industry Robinson offered an analysis of the factors that determined the optimum size for a firm. For Robinson the interaction of five factors determined the size of the firm: technique, management, finance, marketing and risk of fluctuations. These various theoretical optima have then to be reconciled in the size or constitution of a real firm after allowing for difficulties and anomalies of growth. The division of labour has a role to play with regard to technique and management. Because of this we will concentrate on these two factors here.

For Robinson the optimum firm is that firm which in existing conditions of technique and organising ability produces at the minimum of long-run average costs. Under the conditions of perfect competition we would expect to see the optimum firm emerge but under conditions of imperfect competition, Robinson notes, it may not materialise. Consider, for example, the case of monopolistic competition in which a firm will be in equilibrium at less than the minimum of average cost.

The first application of the division of labour to the size of the firm that Robinson considers is the relationship between the division of labour and the optimum technical unit. Robinson follows Adam Smith in seeing three different reasons for the division of labour giving rise to more efficient production. First is the increase in dexterity of workmen; secondly, the saving of time which is commonly lost in passing from one type of work to another; and thirdly, the invention of a great number of machines which facilitate and abridge labour, and thus enable one person to do the work of many.

With regard to the issue of dexterity, Robinson notes Smith's observation that a person who works at a given task for some time is likely to develop a skill or knack for doing that task. In addition the division of labour can allow those people with a natural skill for carrying out a given task to specialise in that task.

Adam Smith (and Robinson) also saw an advantage in the division of labour in that specialisation at a task saved the time that would otherwise be spent on passing from one task to another. Time could be saved because workers do not have to move between machines or processes. Also time would be lost if machines had to be reset to perform a different function. The division of labour saves time by concentrating both workers and machine upon a given function, and a larger factory enjoys an advantage over a smaller one in so far as it makes this concentration possible.

The third economy Smith saw is due to the development of specialised equipment to carry out the tasks that the manufacture of an item is divided into. Separation of a process into its constituent parts makes development of machines to carry out those parts easier.

It is important to keep in mind when considering the size of a firm that the principle of the division of labour requires a firm of sufficient size to obtain the maximum profitable division of labour. This size will differ across industries depending on the nature of the production process for that industry and how detailed a division of labour can be implemented for that particular process. Larger firms will, often, have the capacity to implement a greater division of labour than a smaller firm, giving the larger firm an advantage in terms of efficiency.

The next issue discussed by Robinson is what he calls `the integration of process'. Robinson explains that often a large firm has fewer rather than more processes of manufacture. They can utilise a large machine which has been designed to takeover what would otherwise be a series of manual, or at least less completely mechanical, operations. A complicated machine can perform two or three or more consecutive processes and it can thereby eliminate the labour and time which would be required to up the work on each of the successive earlier machines. Only large firms can keep such a machine running at its full capacity and this fact gives the large firm an advantage over the smaller, and less mechanised, firm. But this difficulty can be overcome by the small firm as long as the size of the market for the process is large enough. If a given process requires a scale of production too great for a smaller firm the small firm can outsource the process to specialist firm. But such outsourcing if only possible if the extent of the market for a particular process is large enough to allow the division of labour to develop to the point where a specialist firm is viable. Robinson refers to this outsoucing as 'vertical disintegration'.

The second of the areas for which Robinson sees the division of labour having a role to play is with regard to management. A manager in a small firm will have multiple tasks to preform, some of which he will be good at, others that he will not be so good at. In a larger firm a division of labour can develop which allows managers to specialise on those function for which they are best suited. The larger firm gains in two ways from its division of managerial labour: 1) special abilities to be used to their fullest extent. Talents are not wasted by having managers carry out functions which could be better assigned to another manager with a particular ability at that function. 2) a manger who specialises in a given task will increase their knowledge of that task.

A potential downside of the managerial division of labour is the problem of coordination. As the division of labour becomes greater the problems associated with the coordination of the different parts of the production process also increases. As new tasks are created by dividing up the production process, new administrative functions are also created to coordinate the ever more disjoint production process. The advantage that a larger firm has over the smaller depends, in a large part, on how well it solves this coordination problem.

An additional theoretical problem with Robinson's discussion follows from the implicate assumption in the competitive model that complete contracts can be written. In such a world it is not clear why a firm is needed to carry out production at all. As Coase (1937) first highlighted in a world of complete contracts any organisation form can mimic any other meaning that production could be carried out via the market just as efficiently as within a firm.

Refs.:
  • Coase, R. H. (1937). `The Nature of the Firm', Economica, New Series 4 No. 16 November: 386-405.
  • Robinson, E A G. (1931). The Structure of Competitive Industry, Cambridge: Cambridge University Press.

Wednesday, 23 November 2016

The "Adaptation Cost" theory of the firm

This material is covers chapters 3 and 4 of Wernerfelt (2016). These chapters are, in turn, based on Wernerfelt (1997) and Wernerfelt (2015), respectively.

Wernerfelt considers two questions to do with the firm that he thinks important but go largely unanswered in the standard theory of the firm literature: What determines the choice between the use of the market, a firm or a contract? Why are all of these mechanisms so commonly used?

His answer to these questions is contained in the "Adaptation Cost" theory of the firm.

Start with a situation where a worker is providing a particular service to an entrepreneur. The entrepreneur's needs change so that the worker's service would have to also change if he is to stay with that entrepreneur. But the worker's productivity will suffer if he, either, changes the service he provides or changes to another entrepreneur and in either of these cases costs would have to be incurred due to the process of bargaining over the terms of a new agreement.

But the costs of worker adaptation are not just those of bargaining, there are also costs, in terms of lower productivity, if the worker has to change, either, to a new service or a new business. A worker is most efficient when he is "double specialised". That is, when he is continually providing the same service to the same business. If this "double specialisation" is not possible it is often second-best to specialise in one of the two dimensions and deal with occasional adaption in the other dimension. Some such adaptations, whether it be between two businesses or two services, are more costly than others.

The basic theory of the Adaptation Cost theory was developed in two papers by Wernerfelt, Wernerfelt (1997, 2015). To begin with the 1997 paper (chapter 3 of Wernerfelt 2016). The focus is on workers who supply businesses with services. The problem is that the needs of the businesses change. Three mechanism to deal with the changing needs are considered: employment, sequential contracting and price lists. In chapter 3 adaptation costs are mainly price determination costs only, since production costs are held constant.

Under the employment mechanism, workers and entrepreneurs negotiate on a once-and-for-all basis over the wage and a large set of services to be supplied on demand. This is similar to the situation in Simon (1951). Here a firm is made up of an entrepreneur and a number of workers who provide the entrepreneur with services via the employment mechanism while the scope of the firm is determined by set of workers thus employed by the entrepreneur. The downside of this is that since there are a large number of things to be bargained over the initial bargaining costs are large, but once agreement is reached there are no further costs incurred so the gains from trade are realised in each period.

Under the sequential contracting mechanism a new price gets negotiated whenever the business's requirements change and thus bargaining costs are incurred on each such occasion. However as the bargains are simpler than those required for the employment contract - the parties are bargaining over a single, known service - the per-occasion bargaining costs are lower.

With the price list, a set of price are agreed upon ex ante and then the list is referred to as needed. As with the case of sequential contracting the per-service bargaining costs are low but if the initial bargaining is over a very long list of prices those costs are high. Here the diversity of needs - how long the price list needs to be - is important to the relative attractiveness of the mechanism.

When the need for a change in service adaptation arise with sufficient frequency, the folk theorem allows us to assume that all trades are efficient under the employment and sequential contracting mechanisms, while under the price list mechanism all trades actually covered by the list are efficient. An implication of this is that there are no trading inefficiencies and thus the only bargaining costs involved are those associated with the mechanism process itself. Given this, the performance of each of the three mechanisms depends only on the costs of adapting to changes in the requirements of the businesses.

In the employment mechanism, costs are a one-time thing related to the negotiation of the wage agreement; for the sequential contracting mechanism the costs are the per-occasion costs of agreeing a price for that particular event; while for the price list mechanism the costs are those one-time costs involved in negotiating the price list plus the loss in the gains from trade for any situations not covered by the list.

Given that the employment mechanism has the lowest costs of adaption - just a verbal instruction - there exists a region in the parameter space, situations in which needs change frequently, in which the employment mechanism (weakly) dominates the other two mechanisms, see Figure 1.


From Figure 1 it is clear that price lists are good when they can be kept short, i.e. there a small number of services needed, sequential bargaining is good when changes are infrequent and employment is good when needs change frequently and many diverse adaptations are required.

Next consider the Wernerfelt (2015) paper (chapter 4 of Wernerfelt 2016). Importantly in this case adaptation costs are expanded to include the costs due to less efficient production. Specifically Wernerfelt assumes that there are gains from specialisation - where specialisation implies little in the way of adaptation - along two dimensions, first businesses and second, services. The former is modelled as an increase in adaptation costs for the worker each time he wants to service a different business. The latter is captured by assuming different workers are good at different things. In this situation three mechanisms are compared: employment, sequential contracting, as before, and markets. Again it is assumed that trade is ex post efficient in all three mechanisms. Wernerfelt concentrates on minimising adaptation costs.

Under the employment mechanism performance is delineated by the gains from trade in each period minus the one-off costs of negotiating the employment contract. The performance of sequential contracting is the gains from trade minus the bargaining costs incurred each period. The important thing about the market mechanism is that it allows workers to specialise in the services at which they are most efficient. "For example, instead of being superintendents they can be plumbers, carpenters, or electricians" (Wernerfelt 2016: 19). The advantage of this is that the gains from trade are increased but the disadvantage is that workers incur business adaptation costs (lose gains from specialisation) every time they switch businesses.

Wernerfelt shows that there are three regions in the parameter space in which each of the three mechanisms (weakly) dominates both of the two other mechanisms.



The relative performance of each of the three mechanisms depends on the frequency with which the needs of the businesses change, the gains from specialisation in an particular service, the business adaptation costs and bargaining costs. See Figure 2 and Figure 3.

Consider Figure 2. Markets are good when workers' between-business adaptation costs are low, that is, the gains from business specialisation are low and thus workers can cheaply switch between businesses; sequential contracting is good when changes in needs are infrequent; and employment is good when the cost advantage of service specialists are small and needs are changing quickly.

Another parameter is shown in Figure 3. Here "service specialisation" - the gains from specialisation in a particular service - is considered. Markets are good when service specialists are a lot more efficient than an employee carrying out many different tasks.

Wernerfelt (2016: 59) illustrates the effects of specialisation, switching costs and adjustment frequency with the example of the maintenance of a medium-sized apartment building,
The owner [of the building] will typically have an employee, the superintendent, perform minor repairs (``the toilet leaks"). The building generates a steady flow of small problems, they tend to be urgent, and the superintendent can solve each of them pretty well. On the other hand, certain minor renovations, such as those having to do with electricity (``install LED light bulbs in public spaces"), are normally done through the market. The jobs are often larger, service specialists can do them better, and the building does not need a full-time electrician. Major renovations, for which advance planning reduces the need for in-process changes, are typically governed by a bilateral contract subject to occasional, though typically costly, renegotiations.

The same example can illustrate the effects of size. A landlord who owns just one or two units will typically go to the market even for minor repairs because these units do not generate enough work to support a superintendent. On the other hand, very large landlords, such as universities, typically use specialist employees (their ``own" electricians) for both repairs and minor renovations.

The major prediction of this theory is that the more frequent are changes in needs the more attractive the employment contract becomes.

Refs.:
  • Simon, Herbert A. (1951). "A Formal Theory of the Employment Relationship", Econometrica, 9(3) July: 293–305.
  • Wernerfelt, Birger (1997). "On the Nature and Scope of the Firm", Journal of Business, 70(4): 489-514.
  • Wernerfelt, Birger (2015). "The Comparative Advantages of Firms, Markets, and Contracts", Economica, 82 no. 236: 350-67.
  • Wernerfelt, Birger (2016). Adaptation, Specialization, and Theory of the Firm: Foundations of the Resource-Based View, Cambridge: Cambridge University Press.

Tuesday, 15 November 2016

The division of labour and the firm: Stigler (1951)

"The division of labor is not a quaint practice of eighteenth-century pin factories; it is a fundamental principle of economic organization."
Stigler (1951: 193)

The following discussion covers material from Stigler (1951) which is one paper that offers a theory of the boundaries of a firm based on the division of labour. Interestingly Adam Smith, despite his famous discussion of the division of labour in the pin factory, did not develop a theory of the firm based on it.

Stigler begins his argument by saying that the division of labour, and its limit due to the extent of the market, lies at the core of a theory of the functions, and thus the boundaries, of a firm. Stigler outlines this theory in the second section of his paper.

In this theory a firm is seen as engaging in a series of distinct operations leading to the production of a final product. That is, the firm is partitioned not among its input markets but among the functions or process that determine the scope of its activities. And thus determine the firm's boundaries.

To allow the graphical representation of the firm's costs of production we will assume that the average costs of each activity depends only on the rate of output of the firm. In addition, if we assume that there is a constant proportion between the rate of output of each activity and the rate of output of the final product then all the cost functions can be drawn on the same diagram and the vertical sum of these costs will be the conventional average cost curve for the firm. With reference to the diagram below to produce q units of final output requires a given number of units of activity 1, costing C_1(q), a number of unit of activity 2, costing C_2(q), and a number of units of activity 3, costing C_3(q). These costs can be summed to give the average cost of production for q units of output, C_1(q)+C_2(q)+C_3(q).


With respect to the shape of the average cost curves for the various activities, some are increasing continuously (C_1), some are falling continuously (C_3) and some are conventionally U-shaped, (C_2).

Now consider the Adam Smith's idea that the division of labour is limited by the extent of the market. First take the activities for which there are increasing returns, Why doesn't the firm exploit the returns more fully and in the process become a monopoly in the output market? Because as the firm expands outputs other activities also have to be increased and some of these are subject to diminishing returns and these cost increases are such that they overwhelm the cost advantages of the increasing returns and increase the average cost of the final product. So why then does the firm not abandon these C_3-like activities and let some other firm (and thus industry) specialise in them to exploit the increasing returns fully? At a given time the market for these activities may be too small to support specialised firms. Given this firms must perform these activities for themselves.

But with an expansion of the market for the increasing returns activity firms specialised in that activity would develop. The firms currently carrying out this activity for its own consumption would forgo this activity and let it be taken over by a new (monopoly) firm. This monopoly could not fully exploit its market power however since it has charge a price which is less than the average cost of production for the firm abandoning the activity. As the market for this activity grows even larger the number of firms specialising in it grows. That is the industry becomes increasingly competitive.

The abandonment of this activity by the original firms will change the cost function for each firm. The cost curve, C_1, will be replaced by a horizontal line (the black dashed line in the diagram above) in the effective region. This also changes the average cost curve for the final product with the new curve (black dashed curve in the diagram above) being lower than the current curve.

What about the increasing cost case? Why not abandon or reduce use of those activities with increasing cost? Much of the previous discussion carries over to this case with the exception that as the market and the industry grows the original firms does not have to stop utilising that activity completely. Part of the needed use of that activity can still be produced in-house without high average (and marginal) cost, with the rest being purchased via the market.

Ref.:
  • Stigler, George J. (1951). "The Division of Labor is Limited by the Extent of the Market", Journal of Political Economy, Vol. 59, No. 3 June, pp. 185-193.

Saturday, 23 November 2013

Just for fun: Marx on the firm

That Marx didn't much like markets is obvious enough, but what of firms? On the positive side Marx preferred the deliberate order of the firm to the anarchy of the market. After all he wanted to run the entire economy like a firm. This view that the firm can be seen as an organisational alternative to the market anticipated Coase in this regard. But on the other hand he saw the firm as the key locus where labour exploitation ad alienation was perpetrated and he has "issues" with the detailed division of labour that capitalism introduced. His model of communism, to be realised after single-firm socialism, was meant to overcome the depressing human condition existing in the capitalist firm.
Besides being a political proposal, single-firm socialism was, according to Marx, a historical necessity imposed by the development of productive forces. The firm’s greater efficiency (relatively to markets) had already been evinced by the growth in firms’ size during capitalism, and productive forces exerted strong pressure for their further growth. By eliminating private property, socialism did nothing other than complete an inevitable process of concentration, whose onset was 'scientifically guaranteed' by historical materialism (Pagano 2012: 42).
For Marx single-firm socialism’ would supersede the dualism of capitalism, under which firms and markets coexisted, and enable the greater development of the productive forces. The limitations of the market sprang from what Marx saw as its nature as a decentralised coordination mechanism dealing with the, often inconsistent, decisions made by buyers and sellers. This negative view of the market lead Marx to argue for the extension of firm-type organisation to society as a whole.
The extension of the planned organization of production of the capitalist factory would complete a process already ongoing in the historical dynamics of capitalism whereby productive forces tended constantly to increase the size of firms. Socialism was the final outcome of this tendency of the productive forces to shift production relations within the firm. The scientific certainty of the advent of socialism was, for Marx, inherent in the tendency of the productive forces to influence production relations. The extension of the authoritarian world of the capitalist firm to the whole of society was necessary to reap the benefits of a planned coordination made more and more necessary by the increasing interdependence among the production sectors (Pagano 2012: 43).
Even if firms are better than markets, firms are not all good. For Marx capitalism produced a very detailed and hierarchical division of labour. This was one of his major criticisms of capitalism. The capitalist-owned firm is a structure that involved a massive deskilling of workers and made labour alienated and painfully homogeneous. But, in the short term at least, socialism could do little about this:
[ ... ] in the early stage of socialism, planning could be made on an objective basis because, according to Marx, capitalism had eliminated the possibility of subjective preferences among repetitive and simple tasks. These conditions suggested, for the first phase of a socialist society, a form of authoritarian planning based on the theory of labour value that ignored the subjective preferences for different kinds of work (Pagano 2012: 43).
Over the longer term, of course, all this would change and
[ ... ] work would entirely match the preferences and development of individuals [ ... ] (Pagano 2012: 43).
Such an idea was constantly present in Marx’s critique of capitalism but its implications were postponed to a distant future.

Interestingly Marx, unlike Coase, saw costs in using the market but assumed that the firm could be used at basically zero cost.
In some respects, Marx made a mistake mirroring orthodox economics when he assumed that, while the costs of market coordination were very high, the costs of firm-type coordination were negligible, with the consequence that all the economic transactions could be coordinated at zero costs by centralized planning (Pagano 2012: 44).
The standard neoclassical model assumes that transactions costs are zero and thus there is no need for firms while Marx assumed that management coasts are zero and thus there is no need for markets. Coase's argument is that both firms and markets come with costs and it is the comparison of these costs that determined the boundaries of the firm.

Ref.:
  • Pagano. Ugo (2012). `Marx'. In Michael Dietrich and Jackie Krafft (eds.) Handbook on the Economics and Theory of the Firm (pp. 42-8), Cheltenham: Edward Elgar.