Absolute Rent, Extensive Rent, And Intensive Rent

Figure 1: Rent Curves With and Without Competitive Markets

This post is a continuation of the example in this and this post. It is the first example, in the tradition building on Sraffa, of a numerical example combines absolute, intensive, and extensive rent.

The analysis in those posts can be extended to apply to non-competitive markets. Assume that the rate of profits is s₁ r in the price equation for the process producing iron and s₂ r in any process for producing corn. I now call r the scale factor for the rate of profits. As a normalization, let the sum of s₁ and s₂ be unity. These coefficients are given parameters. They express the existence of persistent barriers to entry between industry and agriculture. For concreteness, I take s₁ ≈ 0.0208506. This parameter expresses a case of the reswitching of the order of rentability, with agriculture obtaining a higher rate of profits than industry.

Capitalists in agriculture have market power in this post. The changes in rent, including increases, is not the result of market power by landlords. The increased market power of farmers changes wage and rent curves. The specific parameters for markups considered here eliminate the reswitching of techniques and capital-reversing, at any level of net output. Otherwise, the capital-intensity of industries is not analyzed in this post. For Marx, absolute rent is created from more surplus value being generated in agriculture, given its low organic composition of capital. This additional surplus value is not shared in a common pool because of the market power of the class of landlords. This article neither investigates nor justifies Marx's specific mechanism. Nevertheless, I identify the differences in rent brought about relative market power among capitalists in different economic sectors with absolute rent.

The price systems for each technique are altered by the differences in relative markups between industry and agriculture. The variation of the feasibility of techniques with net output is independent of prices. Table 3, in this post, applies to this numerical example of a model of non-competitive markets. Omicron, Rho, Tau, and Omega remain feasible at the highest level of net output. Figure 2 presents the wage curves for this example of non-competitive markets, and Figure 3 is a detail.

Figure 2: Wage Curves With Non-Competitive Markets

Figure 3: Wage Curves With Non-Competitive Markets (Detail)

With these specific values for relative markups, Omicron and Rho are each cost-minimizing for a range of the scale factor for the rate of profits when net output is towards its maximum (Table 5). Type 1 land is not scarce and pays no rent when Omicron is cost-minimizing. Type 2 land is not scarce under Rho. At the highest level of net output, only extensive rent is obtained. No intensive rent is paid, whatever value the scale factor for the rate of profits takes on. The orders of efficiency and rentability match and do not vary with the scale factor for the rate of profits when Omicron is cost-minimizing. The order of efficiency varies, when Rho is cost-minimizing. Rho exhibits the reswitching of the order of rentability.

Table 1: Cost-Minimizing Technique

Range	Technique	Order of Efficiency	Order of Rentability
0≤r≤9.5%	Omicron	3,2,1	3,2,1
9.5≤r≤41.7%	Rho	3,1,2	3,1,2
41.7≤r≤87.8%		1,3,2
87.8≤r≤114.9%			1,3,2
114.9≤r≤122.0%			3,1,2

Figure 1, at the top of this post, graphs the rent curves for the example. Both the wage and rent per acre are functions of the (scale factor for the) rate of profits. The analysis of the choice of technique would be different if the wage were taken as given exogenously. In the case in this post, rent per acre is less under Omicron when the capitalists in agriculture have more market power. The variation in rent per acre with increased market power for farmers otherwise reflects the change in the cost-minimizing technique. Landlords who own Type 1 land obtain greater rent from the increased market power for agriculture in the example. The same is true for landlords who own Type 3 land, expect for low rates of profits. Landlords who own Type 2 land, on the other hand, are better off with competitive markets.

This level of increased market power for the capitalists in agriculture alters the analysis the choice of technique at every level of net output (Figure 4). Consider the range of the scale factor for the rate of profits at which Delta is cost-minimizing. As output expands, at the bottom of this range, capitalists choose to operate processes IV and V on Type 3 land to expand output. When output can no longer be expanded by extending cultivation with process IV, they bring Type 2 land under cultivation, and then, with the adoption of Omicron, Type 1 land enters into the mix. At a slightly higher scale factor, the capitalists cultivate Type 1 land after Type 3 land is completely farmed with process IV. Ultimately, under Rho, they also cultivate Type 2 land. Consider a still higher scale factor, but still within the range where Delta is initially cost-minimizing. The capitalists first expand output, when Type 3 land is fully cultivated, by starting to farm Type 1 land. They operate processes IV and V side-by-side on Type 3 land only after Type 1 land has become scarce.

Figure 4: Cost-Minimizing Techniques With Non-Competitive Markets

In all of these cases, and for even a higher scale factor, process IV is ultimately operated on Type 3 land alone, and only extensive rent is obtained. Yet, with intensive rent being obtained somewhere along the expansion of output, process V enters into the determination of the order of efficiency. The switch points between the wage curves for Alpha and Gamma and between Alpha and Phi are irrelevant to the determination of the order of efficiency when Rho is cost-minimizing. The order of efficiency varies, though, around the switch point between Alpha and Delta. As with competitive markets, the existence of intensive rent as output expands affects the order of efficiency under extensive rent at the highest level of output.