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.