Tag Archives: Example in Mathematical Economics

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....

Figure 1: Variation in the Cost-Minimizing Technique with Selected Coefficient of Production This post reports on some work with Steedman's corn-tractor model. I have yet to find an instance of triple-switching. I have found a case of reswitching, though. Figure 1 above and Table 1 below show how switch points vary with perturbations of the labor needed to produce a bushel of corn in the corn industry with Type I tractors. Only one switch point exists in region 1. Around this switch point...

1.0 Introduction I would like to illustrate triple switching, in the corn-tractor model, with one of my one-dimensional diagrams. I have a triple-switching example, from Bertram Schefold, but the wage-rate of profit frontier is not visually striking in it. Such an example would not be worthy of a research paper. But perhaps I could modify a section of my recent working paper to submit somewhere. Besides, posing a new problem might motivate me to update my computing technology. 2.0...

1.0 Introduction I have explained this before. Suppose one insists socialism requires central planning. In his 1920 paper, 'Economic calculation in the socialist commonwealth', Ludwig Von Mises claims that a central planner requires prices for capital goods and unproduced resources to successfully plan an economy. The claim that central planning is impossible without market prices is supposed to be a matter of scientific principle. Von Mises was mistaken. His error can be demonstrated to...