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.

Latest Blogwatch column

My Blogwatch column from the latest issue (Issue 61, April 2018) of the NZAE magazine Asymmetric Information.

Sam Hammond on co-determination, corporate governance, and the accountable capitalism act

From David Beckworth’s podcast series, Macro Musings comes this audio of an interview with Sam Hammond on Co-Determination, Corporate Governance, and the Accountable Capitalism Act.

Sam Hammond is a policy analyst and covers topics in poverty and welfare for the Niskanen Center. Sam is a previous guest on Macro Musings, and he joins the show today to talk about his new article in National Review which addresses Senator Elizabeth Warren’s new proposal, the Accountable Capitalism Act, and its potentially negative effects. David and Sam also discuss the problematic stereotypes surrounding ‘corporate bigness’, the positive and negative features of co-determination, and why we need universal safety nets.

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.

The development of agriculture

From the History of the World podcast comes these two podcasts on the development and spread of farming.

F. A. Hayek: Economics, Political Economy and Social Philosophy

From the Cato Institute comes this audio of an interview of Peter J. Boettke by Caleb O. Brown about Boettke's new book on F. A. Hayek.

The project of F. A. Hayek had its historical context, and it’s worth exploring. Peter J. Boettke is author of F.A. Hayek: Economics, Political Economy and Social Philosophy.

Series of Unsurprising Results in Economics (SURE)

If you, or your students, are looking for somewhere to publish your unsurprising results think about the new journal Series of Unsurprising Results in Economics (SURE).

SURE is an e-journal of high-quality research with “unsurprising”/confirmatory results and as such aims to mitigate the publication bias towards provocative and statistically significant findings.

Aim and Scope

The Series of Unsurprising Results in Economics (SURE) is an e-journal of high-quality research with “unsurprising” findings.

We publish scientifically important and carefully-executed studies with statistically insignificant or otherwise unsurprising results. Studies from all fields of Economics will be considered. SURE is an open-access journal and there are no submission charges.

SURE benefits readers by:

• Mitigating the publication bias and thus complementing other journals in an effort to provide a complete account of the state of affairs;
• Serving as a repository of potential (and tentative) “dead ends” in Economics research.

SURE benefits writers by:

• Providing an outlet for interesting, high-quality, but “risky” (in terms of uncertain results) research projects;
• Decreasing incentives to data-mine, change theories and hypotheses ex post or exclusively focus on provocative topics.

The editor is Dr Andrea K. Menclova, Department of Economics and Finance, University of Canterbury

To learn more, please visit: http://surejournal.org