Tag Archives: Example in Mathematical Economics

Figure 1: A Pattern Diagram I have put up a working paper with the post title. Abstract: This article considers Harrod-neutral technical progress in the context of an analysis of the choice of technique. In a model of the production of commodities by means of commodities, neutral technical change is compatible with the reswitching of techniques, capital reversing, process recurrence, and the reverse substitution of labor. A taxonomy of fluke switch points is applied to an example,...

Figure 1: APP Around Switch Points1.0 Introduction I take it that the Austrian theory of the business cycle builds on Austrian capital theory. The following two claims are central to Austrian capital theory: Given technology, profit maximizing firms adopt a more capital-intensive, more roundabout technique at a lower interest rate. The adoption of a more roundabout technique increases output per worker. Originally, Eugen von Böhm-Bawerk proposed a physical measure of the average period...

Figure 1: A Pattern Diagram Consider an example of the production of commodities, in which many commodities are produced within capitalist firms. Suppose two techniques are available to produce a given net output. These techniques use the same set of capital goods, albeit in different proportions. They differ in process in use for only one industry. Given the qualification about the same capital goods, generic (non-fluke) switch points are the intersection of the intersection of the wage...

Figure 1: Wage-Rate of Profits Curves Consider a comparison of comparison of stationary states. Net output is taken as given, and a unit of net output is the numeraire. Technology consists of a finite set of techniques. In each technique, net output is produced from inputs of labor and produced circulating capital goods. No fixed capital is used, and land of the best quality is in such abundance that it is free. Also assume constant returns to scale. One can find a wage-rate of profits...

Figure 1: Intercepts of Production Possibilities Frontiers for England1.0 Introduction In this example, gains and losses from trade vary with international prices. Given rates of profits are compatible with an interval of relative international prices for linen and corn, when trade exists only in consumer goods. I explore whether, when trade exists in capital and consumer goods, more than one pattern of specialization among countries is possible, depending on relative international...

Figure 1: Production Possibility Frontiers1.0 Introduction Suppose foreign trade is possible in consumption goods, but not in capital goods. In this example, whether or not England achieves gains from trade depends on relative international prices. If foreign trade were possible in both consumption and capital goods, both England and Portugal would obtain gains from trade. The numeric example in this post is a modification of one in a previous post. As I understand it, most students of...

Figure 1: Production Possibility Frontiers1.0 Introduction This post presents a numeric example of foreign trade in a model of the production of commodities by means of commodities. This is a modification of the model here, which considers a flow-input, point output technology. As usual, I show neoclassical economics is mistaken. Frictions, increasing returns, information asymmetries, principal agent problems, and so on do not need to be introduced to explain why the outcomes of free...

I have made a working paper with the above title available on SSRN. Abstract: This article illustrates the application of pattern analysis to structural economic dynamics with a choice of technique. A numerical example is presented in which technical progress is introduced. Examples of temporal paths through the parameter space illustrate variations of the wage frontier. A single technique is initially uniquely cost-minimizing for all feasible rates of profits. Eventually, the technique...

Figure 1: A Two-Dimensional Pattern Diagram1.0 Introduction This post continues this example of the application of pattern analysis to the study of fixed capital. I generalize the technology in the previous post. Technical progress can now proceed at different rates in the production and use of machines. I partition the resulting two-dimensional parameter space based on how the distribution of income, in the system of prices of production, alters the economically efficient length to run...

Figure 1: A Pattern Diagram1.0 Introduction In this example, I perturb parameters in an example of Bertram Schefold's. I was disappointed in that, as far as I can see, one can analyze the choice of technique in this example by the construction of the wage-rate of profits frontier. As far as I understand, this is not true for joint production in general. I guess I also need to find an example in which the physical life of a machine is at least three years so as to find a three-technique...