Technical Change and Triple-Switching in the Corn-Tractor Model

I have another working paper, Technical change and triple-switching in the corn-tractor model, at the Centro Sraffa. The abstract follows.

Abstract: With triple-switching, each of two techniques are cost-minimizing in two disjoint intervals of the wage or rate of profits. Technology that supports multiple switch points between two techniques can only be a temporary phenomenon, as one technique supplants another with technical progress. A perturbation analysis of a triple-switching example in the corn-tractor model illustrates this claim. A parameter space, defined by two selected coefficients of production, is partitioned by loci corresponding to fluke switch points. The analysis of the choice of technique does not qualitatively vary within each of the resulting regions. Technical progress corresponds to specific trajectories through this parameter space.

Keywords: Cambridge Capital Controversy; Fixed Capital; Reswitching of techniques

JEL Codes: B51: Sraffian; C67: Input-Output Models; D24: Production, Cost, Capital

Visualizing Variations In The Analysis Of The Choice Of Technique

I have another working paper, Visualizing variations in the analysis of the choice of technique, at the Centro Sraffa. The abstract follows.

Abstract: This article describes a diagram that depicts how the analysis of the choice technique varies with perturbations of selected parameters in models of the production of commodities. Fluke switch points partition the graph. Three examples are provided, of circulating capital with markup pricing, of fixed capital with structural economic dynamics, and of intensive rent with markup pricing.

Reswitching in a Model of Extensive Rent

My article with the post title is now available at the Bulletin of Political Economy (Volume 16, issue 2, pp. 133-146). The abstract follows:

Abstract: This article presents an example of the reswitching of the order of fertility and of the order of rentability. Whether or not these orders differ from one another varies with distribution for certain parameter ranges in the example. This analysis emphasizes that more rent per acre is not necessarily associated with more fertile land and that the ranking of lands by fertility cannot, in general, be determined from only data on physical inputs and outputs for the available processes.

Characteristics of Labor Markets Varying with Pertubations of Relative Markups

My article with the post title is now available at the Review of Political Economy. The abstract follows:

Abstract: This article examines a model of long-period positions with markup pricing. The variation in certain characteristics of the wage frontier with perturbations of relative markups is illustrated. This analysis provides a demonstration of the emergence of the reswitching of techniques and of capital reversing, for example, in non-competitive markets.

Fluke Switch Points in Pure Fixed Capital Systems

I have a working paper at the Centro Sraffa.

Abstract: This article considers structural economic dynamics, in models with fixed capital and a choice of technique, of the production of commodities. Fluke switch points are described and cataloged. For fluke switch points, parameter perturbations create a qualitative change in how the choice of technique varies with distribution. Techniques are presented for visualizing partitions of parameter spaces such that the analysis of the choice of technique does not vary within each region. Implications are drawn about the choice of the truncation of the operation of (or the economic life of) machines and about the adoption of roundabout techniques.

Structural Economic Dynamics, Markups, Real Wicksell Effects, And The Reverse Substitution Of Labor

I am being published in Structural Change and Economic Dynamics. Currently, this link is without my corrections to proofs, I guess.

Research highlights:

• Technical progress and variations in industry markups can change characteristics of the labor markets.
• A numeric example illustrates the theory of the choice of technique.
• In the example, switch points are created and destroyed with varying coefficients of production and varying markups.
• Around some switch points, higher wages are associated with greater employment, given the level of net or gross output
• Graphical displays are provided for visualizing these results.

Abstract: This article presents an example in which perturbations in relative markups and technical progress result in variations in characteristics of the labor market. Around a switch point with a positive real Wicksell effect, a higher wage is associated with firms wanting to employ more labor per unit output of net product. Around a switch point with a reverse substitution of labor, firms in a particular industry want to hire more labor per unit output of gross product. Technical progress and variations in markups can bring about and take away circumstances favorable for workers wanting to press claims for higher wages. This article presents specific fluke switch points in which variations in technology and markups change these circumstances, as well as novel diagrams for visualizing the effects of such variations.

Normal Forms for Switch Point Patterns

My article with the post title is now available at the Review of Behavioral Economics. The abstract follows:

Abstract: The choice of technique can be analyzed, in a circulating-capital model of prices of production, by constructing the wage frontier. Switch points arise when more than one technique is cost-minimizing for a specified rate of profits. This article defines four normal forms for variations in the number and sequence of switch points with a perturbation of, for example, a coefficient of production. The 'perversity' of switch points that appear on and disappear from the wage frontier is analyzed. The conjecture is made that no other normal forms for local patterns of co-dimension one exist.

The Choice Of Technique With Multiple And Complex Interest Rates

My article with the post title is now available on the website for the Review of Political Economy. It will be, I gather, in the October 2017 hardcopy issue. The abstract follows.

Abstract: This article clarifies the relations between internal rates of return (IRR), net present value (NPV), and the analysis of the choice of technique in models of production analyzed during the Cambridge capital controversy. Multiple and possibly complex roots of polynomial equations defining the IRR are considered. An algorithm, using these multiple roots to calculate the NPV, justifies the traditional analysis of reswitching.

Some Financial Analysis in Software Engineering

Warning: Lots of navel-gazing in this post.

Example of Financial Analysis of Two Methods for Detecting Software Bugs (from Vienneau 1995)

Consider a specific industry, namely the production of software. (This industry would correspond to a column in an input-output matrix.) Many methods have been proposed for improving the productivity, the quality, and management control in software development, operations, and management. And, as software became a more important component in, for example, embedded systems, various measures, and various methods for choosing among possible measures, have been proposed for software processes and products. Some time ago, some researchers argued that analyses of such metrics should be oriented towards economic analysis of, for example, efforts to introduce new methods into the software lifecycle. I think of the following two articles as early exponents of this thesis:

• Sandra A. Slaughter, Donald E. Harter, and Mayuram S. Krishnan. Evaluating the Cost of Software Quality, Communications of the ACM. V. 41, No. 8 (Aug. 1998): pp. 67-73.
• Robert L. Vienneau. The Present Value of Software Maintenance, Journal of Parametrics (April 1995).

Slaughter et al. is more high level and is published in a more prestigious journal. My article is more a tutorial.

One can apply economics to analyze specific decisions during the software lifecycle. For instance, the following article looks at when testing should stop and software should be released:

• Robert L. Vienneau. The Cost of Testing Software, Proceedings of the Annual Reliability and Maintainability Symposium, Orlando, FL (29-31 Jan. 1991).

The optimal release date can be justified by a simple marginal rule: the final phase of testing should stop, and software should be released, when the cost of an increment of testing reaches or exceeds the marginal benefit to gained from that increment of testing. The marginal benefit can be conceptualized as the product of the expected number of bugs to be observed during that increment of time and the savings in finding those bugs during test, instead of operations. (Various software reliability models exist for estimating the parameters needed to implement this rule.)

I have not been aggressive in promoting my work in software engineering economics. Once in a while, I search the web to see who, if anybody, is referencing this stuff. This post concludes with a number of papers, theses, and selected technical reports citing one or the other of the above papers, or related work from me. I do not know why so many of these references are so recent; perhaps software processes must attain a certain level of maturity before these financial analyses become useful.

• Majed Alyahya, Rodina Ahmad, and Sai Peck Lee. Impact of CMMI-Based Process Maturity Levels on Effort, Productivity and Diseconomy of Scale, International Arab Journal of Information Technology. V. 9, No. 4 (Jul. 2012): pp. 352-360
• Hanna Farnstrand. Introducing Structured Testing, Lund University (16 Jun. 2008).
• Matt Ganis. Agile Methods: Fact or Fiction, Trenton Computer Festival. (Apr. 2010).
• Warren Harrison, David Raffo, John Settle, Nancy Eickelmann. Technology Review: Adapting Financial Measures: Making a Business Case for Software Process Improvement, Software Quality Journal. V. 8, No. 3 (1999): pp. 211-231.
• Chin-Yu Huang, Jung-Hua Lo, Sy-Yen Kuo, and Michael R. Lyu. Optimal Allocation of Testing-Resource Considering Cost, Reliability, and Testing Effort, Proceedings of the 10th IEEE Pacific Rim International Symposium on Dependable Computing (PRDC'04) (2004): pp. 103-112.
• Chin-Yu Huang and Jung-Hua Lo. Optimal Resource Allocation for Cost and Reliability of Modular Software Systems in the Testing Phase, Journal of Systems and Software. V. 79, Iss. 5 (May 2006): pp. 653-664.
• Zhengrui Jiang, Sumit Sarkar, and Varghese S. Jacob. Postrelease Testing and Software Release Policy for Enterprise-Level Systems, Information Systems Research. V. 23, No. 4 (Dec. 2012).
• J. Dennis Lawrence. Software Reliability and Safety in Nuclear Reactor Protection Systems, Lawrence Livermore National Laboratory, UCRL-ID-114839 (11 Jun. 1993).
• Tuomas Paasonen. Methods for Improving the Maintainability of Application Software. Master Thesis, Aalto University (13 April 2012).
• David Raffo and Tim Menzies. Evaluating the Impact of a New Technology Using Simulation: The Case for Mining Software Repositories. [I am unsure of the status of this paper].
• Tobias Scherner and Lothar Fritsch. Early Evaluation of Security Functionality in Software Projects - some Experience on using the Common Criteria in a Quality Management Process, Johann Wolfgang Goethe - Universitat, Franfurt am Main (2007).
• Leon van Delft. Automated GUI Testing in Industry. Master Thesis, Delft University of Technology (28 Dec. 2011).

Update (28 February 2013): Added Huang and Lo (2006) to remind me to check if my search with Google Scholar yielded an accurate reference.

Update (13 March 2013): Added Huang et al. (2004).

"On Labour Demand and Equilibria of the Firm"

The above is from my 2005 Manchester School article. H/T to Crooked Timber.