Tag Archives: Example in Mathematical Economics

Figure 1: Real Factor Price Frontier1.0 Introduction I am planning on posting at an even slower rate for a while. This post continues my exploration of a way of visualizing the choice of technique proposed by Carlo Milana. In this post, I show how to correctly apply his visualization to an example from my 2017 ROPE paper. 2.0 Technology Two techniques are available for producing corn, the consumption good. Each technique consists of a flow-input, point-output technology, with a finite...

Maybe this post should be titled "Erratum" or "corrigendum". I have an example in my paper last year in which wage frontiers are supposed to vary with two parameters. One is the markup in the "iron" industry. And the other is σ t. The example should be as in Table 1. All the theory and the visualizations in the paper work out with this example. Table 1: Technology for Producing Steel and Corn InputIndustryIronCornAlphaBetaLabora0,1 = 1aα,0,2(t) = (5191/5770) e(1/10) - σ taβ,0,2 =...

Figure 1: Two Dimensional Pattern Diagram1.0 Introduction This post extends an example from Bertram Schefold. It presents markup pricing in an example with a machine that can be operated for two years or junked after one year. This is a case of joint production in which, unlike in some cases, the choice of technique can still be analyzed by the construction of the wage frontier. Also, I do not think the question of requirements for use enter in here, and all matrices are square. As usual,...

I have a new working paper. Abstract: Does the Cambridge equation, in which the rate of profits in a steady state is equal to the quotient of the rate of growth and the savings rate out of profits, hold in an economy with widespread non-competitive markets? This article presents a multiple-good model of markup pricing in an attempt to answer this question. A balance equation is derived. Given competitive conditions, this model can be used to derive the Cambridge equation. The Cambridge...

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...