Tag Archives: Example in Mathematical Economics

I am not sure about the economic logic in this post. Maybe somebody like D'Agata or Zambelli could do something with this. These ideas were suggested to me by email with a sometime commentator. I start out with notation for Sraffa's price system, modified in an unusual way to allow for persistent variations in the rate of profits among industries: a0 is a row vector of labor coefficients in each of n industries. A is a Leontief input-output matrix, where ai, j is the quantity of the ith...

Figure 1: Wage Curves and The Price of Corn for the Fluke CaseIntroduction This post extends a previous post. I am basically introducing structural dynamics into an example, by Bidard and Klimovsky of fake switch points. At a rate of profits of zero in the example, the price of corn is zero for Alpha, one of the two techniques that is cost-minimizing there and for somewhat higher rates of profits. At a time before the fluke case, only the Gamma technique is cost-minimizing at a rate of...

Figure 1: Wage Curves with Corn as Numeraire1.0 Introduction This post presents an example of a fluke switch point in which the choice of technique cannot be analyzed by the construction of the wage frontier. Under joint production, the technique that is cost-minimizing, for a given rate of profits, does not necessarily maximize the wage. Nevertheless, one can still see what I call a pattern over the wage axis in this case. The example is a generalization of the numerical example in...

This post, as suggested, extends this one-good example. I assume a constant returns-to-scale technology, as specified in Tables 1 and 2. Labor is advanced to the capitalists, and wages are paid out of the surplus at the end of the year (period of production). The capitalists (incorrectly) expect the technology in existence at the start of the year to continue to exist. I assume prices of (re)production prevail. Table 1: Inputs for The Technology InputProcess(I)(II)(III)Labor30 eσ0,1(1 -...

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...