Tag Archives: Example in Mathematical Economics

Figure 1: Convergence of Newton Method This post steps through an algorithm for finding a fluke switch point. I used a different example when I tried to explain this before. Today, I use an example building on my draft ROPE Article. Consider Figure 3 in this post, repeated below as Figure 2. Let s1 = s2 = 1. I want to find s3, the markup in the corn industry, such that the wage curves for Gamma, Delta, Eta, and Theta intersect at a single switch point. One wants to find a function one of...

We compare the conditions of two isolated market systems A and B. Both are equal in size and population figures, the state of technological knowledge, and in natural resources. They differ from one another only in the supply of capital goods, this supply being larger in A than in B. This enjoins that in A many processes of production are employed with which the output is greater per unit of input than with those employed in B. In B one cannot consider the adoption of these processes on...

1.0 Introduction I have decided that this previous post is inadequate. If intensive rent exists on some type of land, the system of equations for prices of production cannot include a process that only partially cultivates some other type of land producing the agricultural commodity. So to form an example with both intensive and extensive rent, I need the technology to specify the possibility of cultivating at least three types of land. I might as well include markup pricing so as to...

Figure 1: Wage Curves For A Fluke Case1.0 Introduction This post examines perturbations around a fluke case in a model of intensive rent. The model illustrates an analysis of prices and the choice of technique in which the quantity of commodites produced matters. Yet the level and composition of net output are taken as given, independent of any variation, for example, from their dependence on distribution and relative prices. The model also illustrates a case in which prices of production...

Figure 1: Structural Economic Dynamics of the Price of a New Machine I am not sure that there is any great insight here. But this post depicts the evolution of prices in an example which I have been explaining in two posts. For some parameters, I have found that a shorter economic life of a machine may be associated with a more capital-intensive technique around a switch point. This can occur at both a 'normal' and a 'perverse' switch point. This finding raises difficulties for tradional...

Figure 1: Variation of Switch Points with Technological Progress in Industry This post is an expansion on this post. Technological progress in industry, in which the machine is produced, can be illustrated in Figure 1 in the previous post by a movement roughly from off the graph to the upper right to below the lower left. More concretely, suppose each of the two non-zero coefficients of production in the machine industry decrease at a constant rate of σ0 and σ1 respectively. The two...

Figure 1: A Part of the Parameter Space1.0 Introduction This post presents a perturbation of an example from Salvatore Baldone. It follows the style of some posts that almost add up to a draft research paper. A widespread view among Austrian-school and mainstream economists is mistaken. Given competitive markets, if the supply of capital were increased, in some sense, the rate of profits would supposedly be driven down. At the level of abstraction here, no distinction exists between the...

Figure 1: Prices of Corn and Ale in an Iterative Process1.0 Introduction Anwar Shaikh proposed, sometime in the 1970s, I guess, an interpretation of Marx's transformation problem. Marx's solution in volume 3 of Capital is the first step of an iterative process. I thought I might work through this idea with an example from an old exposition of mine. I am not sure how faithful I am to Shaikh's approach. I notice that as I explain it, the equality of total values and of total prices is...

1.0 Introduction Stefano Perri has a working paper, "Sraffa's response to Eaton's review: a note on the standard commodity and Marx's general profit rate". In this post, I present the analysis rewritten in matrix notation. The claim is, more or less, that the rate of profits in the system of prices of production is the weighted average of the rates of profits, by industry, in the system of labor values. Each weight is the product of the labor value of capital advanced in that industry and...

Figure 1: A Part of a Parameter Space This post revisits my numerical examples in which I demonstrate the possibility of the reswitching of the order of fertility and of the reswitching of the order of rentability. Each of those posts presents a numeric example. In each, different ranges of the coefficients of production a0,2 and a1,2 are considered. This post combines those ranges, while still not considering the full parameter space, even for the slice for these coefficients. In the...