Tag Archives: Example in Mathematical Economics

I have defined patterns of switch points in considering perturbations of examples of the choice of technique. For example, I have defined three-technique and four-technique patterns. An obvious extension is to consider how these patterns arise in models of joint production. A simplification is to only consider models of fixed capital without superimposed joint production. This post lays out an example in which, maybe, some parameter values can lead to a three-technique pattern. I am...

Figure 1: A Partition of a Parameter Space for the Schefold Example1.0 Introduction I want to revisit a perturbation analysis of an example, from Bertram Schefold, of reswitching with fixed capital. Suppose workers use a machine to produce something or other, where the machine lasts several production periods. It is a possible choice to run the machine for less than its full physical life. One might think than choosing to adopt a technique with a longer economic life of the machine...

1.0 Introduction I have not posted about a non-fluke switch point in a while. This is an example from Bertram Schefold. I have examined perturbations and variations of this example before. Here I present an example with tables exhibiting arithmetic. Is this any more transparent than examples presented with graphs? I have been listening to some lectures on YouTube, especially Richard Wolff. I now have another hypothesis why mainstream economists have been promoting lies, ignorance, and...

Figure 1: A Switch Point On The Wage Frontier with Wage Curves Tangent This post extends the example in my article in Structural Change and Economic Dynamics, suitably emended. Figure 2 shows an enlargement of part of the parameter space. The parameters of the point where the boundaries of Regions 1, 2, and 3 intersect are shown. In Region 1, the Beta technique is uniquely cost-minimizing for all feasible wages; there are no switch points. Region 2 is a reswitching example, with Beta...

Figure 1: Switch Points On The Axis For The Rate Of Profits And At r = -100 Percent This is an example of a fluke case in the analysis of the choice of technique. The interest in flukes, for me, is that they show how the characteristics of markets can change. They provide insight into structural economic dynamics, as Luigi Pasinetti calls it. I have previously shown a fluke case, with a switch point on the axis for the rate of profits with a real Wicksell effect of zero. A perturbation...

Figure 1: Specification of a Market Algorithm1.0 Introduction This article is heavily based on Bidard (2004). An approach to the analysis of the choice of technique, in keeping with construction of the outer envelope of wage curves, is to consider replacing processes, more or less, one at a time. This post presents this approach as following an algorithm. Assume that a set of techniques exist where all techniques are at least viable, indecomposable, and produce the same set of...

Figure 1: Real Factor Price Frontier1.0 Introduction I am planning on posting at an even slower rate for a while. This post continues my exploration of a way of visualizing the choice of technique proposed by Carlo Milana. In this post, I show how to correctly apply his visualization to an example from my 2017 ROPE paper. 2.0 Technology Two techniques are available for producing corn, the consumption good. Each technique consists of a flow-input, point-output technology, with a finite...

Maybe this post should be titled "Erratum" or "corrigendum". I have an example in my paper last year in which wage frontiers are supposed to vary with two parameters. One is the markup in the "iron" industry. And the other is σ t. The example should be as in Table 1. All the theory and the visualizations in the paper work out with this example. Table 1: Technology for Producing Steel and Corn InputIndustryIronCornAlphaBetaLabora0,1 = 1aα,0,2(t) = (5191/5770) e(1/10) - σ taβ,0,2 =...

Figure 1: Two Dimensional Pattern Diagram1.0 Introduction This post extends an example from Bertram Schefold. It presents markup pricing in an example with a machine that can be operated for two years or junked after one year. This is a case of joint production in which, unlike in some cases, the choice of technique can still be analyzed by the construction of the wage frontier. Also, I do not think the question of requirements for use enter in here, and all matrices are square. As usual,...

I have a new working paper. Abstract: Does the Cambridge equation, in which the rate of profits in a steady state is equal to the quotient of the rate of growth and the savings rate out of profits, hold in an economy with widespread non-competitive markets? This article presents a multiple-good model of markup pricing in an attempt to answer this question. A balance equation is derived. Given competitive conditions, this model can be used to derive the Cambridge equation. The Cambridge...