Tag Archives: Example in Mathematical Economics

Figure 1: Real Factor Price Frontier1.0 Introduction Carlo Milana has proposed a new way of visualizing the choice of technique, including in the case of reswitching. This way of describing what he has done is not neccessarily how he thinks of it. In this post, I describe his approach with a reswitching example, in a model of the production of commodities by means of commodities. 2.0 Technology Table 1 shows the coefficients of production for this example. Coefficients of production...

Figure 1: A Switch Point and a Fake Switch Point on Wage Curves1.0 Introduction In the analysis of the choice of technique, I typically consider examples of technology with a finite number of techniques. For each technique, I find the wage as a function of the rate of profits. The outer envelope of these curves shows the cost-minimizing technique at each rate of profits (or each level of the wage). Points on more than one wage curve are switch points. This approach is valid when, for...

1.0 Introduction I have sometimes set out Marx's model of expanded reproduction, only with prices of production instead of labor values. I assume two goods, a capital good and a consumption good, are produced with constant technology. If one assumes workers spend all their wages and capitalists save a constant proportion of profits, one can derive the Cambridge equation in this model. The Cambridge equation shows that, along a steady state growth path, the economy-wide rate of profits is...

Figure 1: Rate of Profits Unequal to Scale Factor for Rate of Profits This post continues the example in the previous post. I modify the prices equations so that the rate of profits in producing corn is (s1 r̂), and the rate of profits in producing ale is (s2 r̂). The solution to the price equations are: pcorn = 16 [16 + (s1 - s2) r̂]/[204 + (3 s1 + 9 s2) r̂] pale = 32 [10 - (s1 - 3 s2) r̂]/[204 + (3 s1 + 9 s2) r̂] w = 4 [51 - (9 s1 + 5 s2) r̂ - s1s2 r̂2]/[204 + (3 s1 + 9 s2) r̂]...

Figure 1: Variation of Prices of Production with Wages and Markups1.0 Introduction This post documents an example in my working paper, The Labor Theory of Value and Sraffa's Standard Commodity with Markup Pricing. 2.0 Technology Consider a simple economy in which corn and ale are each produced from inputs of labor, corn, and ale. Inputs for unit outputs are shown in the columns in Table 1. Obviously, the units of measure should not be taken serious. Inputs are totally used up in the...

Figure 1: A Pattern Diagram with Joint Production1.0 Introduction This post completes an example. I analyzed bits of this example here and here. This post may make no sense if you have not read a long series of previous posts or, maybe, the papers highlighted here and here. I am interested in how and if my approach to analyzing and visualizing variations in the choice of technique with technical progress extends to joint production. The example suggests fake switch points do not pose an...

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 -...