Motivated by recent empirical studies of business firm growth, we develop a dynamic percolation model which captures some of the features of the economical system--i.e., merging and splitting of business firms--represented as aggregates on a d-dimensional lattice. We find the steady-state distribution of the aggregate size and explore how this distribution depends on the model parameters. We find that at the critical threshold, the standard deviation of the aggregate growth rates, sigma, increases with aggregate size S as sigma approximately S(beta), where beta can be explained in terms of the connectedness length exponent nu and the fractal dimension d(f), with beta=1(2nud(f)) approximately 0.20 for d=2 and 0.125 for d-->infinity. The distributions of aggregate growth rates have a sharp peak at the center and pronounced wings extending over many standard deviations, giving the distribution a tent-shape form--the Laplace distribution. The distributions for different aggregate sizes scaled by their standard deviations collapse onto the same curve.
The growth of business firms is an example of a system of complex interacting units that resembles complex interacting systems in nature such as earthquakes. Remarkably, work in econophysics has provided evidence that the statistical properties of the growth of business firms follow the same sorts of power laws that characterize physical systems near their critical points. Given how economies change over time, whether these statistical properties are persistent, robust, and universal like those of physical systems remains an open question. Here, we show that the scaling properties of firm growth previously demonstrated for publicly-traded U.S. manufacturing firms from 1974 to 1993 apply to the same sorts of firms from 1993 to 2015, to firms in other broad sectors (such as materials), and to firms in new sectors (such as Internet services). We measure virtually the same scaling exponent for manufacturing for the 1993 to 2015 period as for the 1974 to 1993 period and virtually the same scaling exponent for other sectors as for manufacturing. Furthermore, we show that fluctuations of the growth rate for new industries self-organize into a power law over relatively short time scales.
We model a vertical merger of an upstream monopolist with one of two downstream producers engaged in Bertrand competition. The theoretical model suggests a statistic – the "Net Downstream Pricing Pressure" ("NDPP") statistic – that can serve as a screen for which vertical mergers are most likely to result in consumer harm. We simulate the effect of a vertical merger for four different functional forms of demand. In the simulations, relatively few vertical mergers lead to price increases that harm consumers. Of those that do, many would be unprofitable absent efficiencies, and many would be with the smaller of the two downstream firms. Moreover, predicted merger effects are not robust to the assumption about the functional form for demand. In contrast, the NDPP statistic is highly correlated with the change in real output for all functional forms and we believe is a practical tool for identifying potentially anticompetitive mergers.
We present a stochastic, dynamic model of firm growth that captures the essential features of Coase׳s theory of the firm and reproduces important statistical regularities in firm size and growth. For the model to generate these statistical regularities, the parameters must be tuned so that firms involved in “unrelated” activities evolve. Thus, at the same time that the model predicts the statistical properties of firm growth, it suggests that attempts to validate Coase׳s theory at the level of the individual firm might be futile. The model draws on models of critical phenomena from statistical physics, the motivation being that the observed statistical properties of firm growth are similar to the statistical properties of physical systems near their critical point.
Patents declared to standard development organizations (SDOs) as potentially essential for compliance with standards under development within the SDO are typically bound by so-called FRAND commitments – promises from the patent holder to license the patents on fair, reasonable, and nondiscriminatory terms and conditions. It is widely agreed that FRAND commitments impose certain constraints on the terms and conditions that patent holders may seek from licensees in comparison to licensing patents without a FRAND commitment. But exactly what those constraints might entail has been the subject of heated debate for at least a decade. The particular constraint discussed in this paper is whether FRAND prohibits patent portfolio licensing, where both FRAND committed and non-essential, non-FRAND-committed patents are bundled together into a single license. We explain that the answer to that question is “No, FRAND does not create a blanket prohibition against portfolio licensing.” Whether such a patent portfolio license honors a FRAND commitment depends on the specific licensing terms and conditions comporting with FRAND.
I analyze cliff discounts when an incumbent monopolist faces competition from a competitor that can compete for a portion (but not all) of the market, and compare them with both simple pricing and pricing formulas in which the incumbent can cut prices just in the competitive portion of the market. The optimal cliff discount does not require exclusivity by the buyer. By leaving a portion of the market to the competitor, the incumbent gives it the choice between accepting its allocated share at a high price and offering deep discounts for any increase in market share. The optimal contract allows the competitor to earn higher profits by charging a high price for its allocated share, which in turn allows the incumbent to charge a high price. Average prices are higher with the cliff discount than with pricing that targets price cuts to the competitive segment. The model can apply to bundled discounts for multiple products as well as all-units discounts on a single product.
Abstract The growth of business firms is an example of a system of complex interacting units that resembles complex interacting systems in nature such as earthquakes. Remarkably, work in econophysics has provided evidence that the statistical properties of the growth of business firms follow the same sorts of power laws that characterize physical systems near their critical points. Given how economies change over time, whether these statistical properties are persistent, robust, and universal like those of physical systems remains an open question. Here, we show that the scaling properties of firm growth previously demonstrated for publicly-traded U.S. manufacturing firms from 1974 to 1993 apply to the same sorts of firms from 1993 to 2015, to firms in other broad sectors (such as materials), and to firms in new sectors (such as Internet services). We measure virtually the same scaling exponent for manufacturing for the 1993 to 2015 period as for the 1974 to 1993 period and virtually the same scaling exponent for other sectors as for manufacturing. Furthermore, we show that fluctuations of the growth rate for new industries self-organize into a power law over relatively short time scales.
Tying the sale of products that could be sold separately is common in competitive markets - from left and right shoes, to the sports and living sections of daily newspapers, to cars and radios. This paper presents a cost-based theory for why tying occurs in competitive markets and uses this theory to examine bundling and tying in pain relievers and cold medicines, foreign electrical plug adapters, and mid-sized automobile sedans. It shows that product-specific scale economies are needed to understand tying but that these scale economies might be hard to detect even when they are present. We draw two principle conclusions for tying doctrine. First, per se condemnation in its various manifestations is wrong as a matter of economics. Neither the Jefferson-Parish test in the United States nor the Hilti/Tetra-Pak approach in the EU is capable of screening anti-competitive from pro-competitive tying. Second, if it is hard to establish efficiencies when practices could not arise for anticompetitive reasons, it might also be hard to establish the efficiencies required by the rule of reason or per se approaches. Both approaches are therefore likely to result in the frequent condemnation of efficient tying - that is a high rate of false convictions.
