Tag Archives: Example in Mathematical Economics

I have written up a series of post as a research paper: first post, second, third, fourth, fifth, sixth, seventh. Here I present the abstract and most of the introduction. Abstract: Empirical research indicates that the reswitching of techniques, as well as multiple switching with more switch points, is rare. This article explores parameter spaces in the analysis of the choice of technique to suggest why reswitching and triple-switching might be hard to find in empirical data. An example...

Figure 1: Actual and Stylized Partitions of Parameter Space with Triple-Switching This post is a continuation of this series of posts. The partitioning of the parameter space by fluke switch points in these posts can be combined into one picture. The left pane in Figure 1 illustrates. The dashed line is a ray from the origin, discussed below. I find this complete picture for this example hard to perceive by eye. The right pane provides a highly stylized presentation of the partitions,...

Figure 1: Extra Profits at Gamma Prices for the Sixth Double-Fluke Switch Point This post is a continuation of this series of posts. In the last double-fluke case, the three switch points between Alpha and Gamma coincide as a ingle switch point. Figure 1 illustrates, while Figure 2 depicts how the parameter space is partitioned around this double-fluke case. Region 7, in which one switch point occurs, is connected. At the point corresponding to the double-fluke case, the two boundaries...

Figure 1: Extra Profits at Gamma Prices for the Third Double-Fluke Switch Point This post is a continuation of this series of posts. The next double-fluke case to be considered arises for parameters on intersection of the upper and lower boundaries of regions 3 and 5. Figure 1 illustrates this case, while Figure 2 depicts local perturbations of this double-fluke case. Perturbations that lead to either of the switch points at the extremes of the rate of profits no longer being at a feasible...

Figure 1: Extra Profits at Gamma Prices for the Second Double-Fluke Switch Point This post is a continuation of this series of posts. A switch point in which wage curves are tangent on the axis for the rate of profits is a double-fluke case symmetrical to the double-fluke case in the previous post. As shown in Figure 1, this case arises in this example as well. The roles of the Alpha and Gamma techniques are reversed. Alpha is always cost-minimizing, while Gamma is cost-minimizing only at...

Figure 1: The Wage Frontier for a Double-Fluke Switch Point This post is an expansion of a previous one. That post defines the technology and the price system for the three techniques conprising the technology. In Alpha, labor and corn inputs are used to produce corn. Beta and Gamma are more roundabout. In each, Labor and corn are first used to make a machine that lasts two years and can be used to produce corn each year. In Beta, the machine is discarded after being operated one year. The...

Figure 1: Triple Switching with Strucutral Economic Dynamics1.0 Introduction I have been using fluke switch points to partition two-dimensional slices of parameter spaces. I know, I think, how reswitching can appear and disappear. But I am confused how more switch points can appear. So this post is a start on exploring a triple-switching example. I have stumbled upon two examples of triple-switching, so to speak. I have not yet replicated Steedman's claim that triple-switching can arise...

Figure 1: A Parameter Space1.0 Introduction I have been reconstructing some of my examples. The first example in this post is from here. I am thinking of writing a draft article, as mentioned here. While I am at it, I thought I would also work through the examples in Garegnani (1966) and Bruno, Burmeister & Sheshinski (1966), both from the symposium in the Quarterly Journal of Economics of that year. 2.0 The Emergence of the Reverse Substitution of Labor This section presents an...

Figure 1: Wage Curves for the Two Techniques1.0 Introduction Economists following the Austrian school often represent the structure of production with Hayekian triangles (Hayek 1931, Rothbard 1962, Skousen 1990, Garrison 2001, Machaj 2017). Typically, goods of the highest order are produced with unaided labor or other unproduced original resources. (Fillieule (2007), in which a Hayekian triangle is constructed with an infinite stream of unproduced inputs, is an exception.) Rarely, is a...

1.0 Introduction This post illustrates a derivation of prices of production, based on certain properties of duality theory as applied to linear programming. I strive to be more concise and elementary than previous expositions. This exposition is based on John Roemer's Reproducible Solution (Analytical Foundations of Marxian Economic Theory, Cambridge University Press, 1981). You will find no utility maximization or supply and demand functions below. I have no need for such hypotheses....