Tag Archives: Example in Mathematical Economics

Figure 1: The Wage-Rate of Profits Frontier1.0 Introduction This post completes a demonstration that the economic life of a machine is independent of the capital-intensity of a technique. I here fill in the upper right of a two-by-two table. I have previously filled in the upper-left and lower right entries. And I also have an example for the lower left. 2.0 Technology Tables 1 and 2 present coefficients of production for processes which can be combined to produce a new output of corn....

1.0 Introduction I have been reading Robin Hahnel. Hahnel argues even more strongly than Steedman did that labor values are redundant. And he argues for the importance of the fundamental Sraffian theorem. I think this may be Hahnel's coinage. Anyways' this is my working my way through some of what I think he is saying. Hahnel has some interesting things to say, not discussed here, about analyzing environmental concerns in a Sraffian framework. I ignore the chapter in Hahnel (2017) on the...

Figure 1: The Wage-Rate of Profits Frontier This post continues a series of posts demonstrating that the change in the economic life of a machine at a switch point is independent of the change of the capital intensity of the technique at a switch point. I here fill in the lower left in a a two-by-two table. The wage curves above are for the an example with the same structure as in the previous post in this series.This is a 'one-good' model. The manager of firms know three processes to...

Figure 1: The Wage-Rate of Profits Frontier1.0 Introduction This is one in a series of posts demonstrating that the change in the economic life of a machine at a switch point is independent of the change of the capital intensity of the technique at a switch point. I want to illustrate each entry in a two-by-two table in a previous post. The example in this post has two switch points. One fits the traditional Austrian and neoclassical stories, as in the entry in the upper-left of the table....

1.0 Introduction This post is an attempt to work through some linear algebra that some have used to understand Karl Marx's Capital. I have recently explained how, in a simple model, prices of production are equal to labor values if the organic composition of capital does not vary among industries. That special case is the setting of volume 1. In capitalism, workers rent themselves out to their employers. They work longer, under the dominion of capital, than needed to produce the...

1.0 Introduction A simple labor theory of value holds in two special cases. The rate of profits in the system of prices of production is zero. The vector of direct labor coefficients is an eigenvector of the Leontief input-output matrix corresponding to the maximum eigenvalue. I do not know if I've worked through this alone before. A more rigorous approach would prove the uniqueness of the solution. 2.0 The Setting Suppose a capitalist economy is observed at a given point in time. n...

Figure 1: Variation in the Economic Life of a Machine with Technical Progress This post varies the coefficients of production in an example from Bertram Schefold. I wanted to have 'nice' fractions at a time of zero. Qualitatively, this looks like a previous post. Reviewers for a recent rejection of an article with another fixed capital example objected to this type of model. I need to relate technical progress to a well-known type (Harrod-neutral, Marx-biased, or whatever) or produce some...

Figure 1: A Two-Dimensional Parameter Space The above is for this example. I wish somebody would be inspired by this to write it up with mathematical proofs. What I see here is found by numerical methods. Figure 1 shows a partition of the parameter space based on fluke switch points. The dashed line shows the temporal path in the previous post. Each of the solid lines are parallel affine functions, with a slope of unity. A proof that these slopes are unity should be able to handle a model...

Figure 1: Variation in the Maximum Wage and the Cost-Minimizing Technique with Time This post presents an example in which some coefficients of production vary from those in example. Reswitching, capital reversing, and the reverse substitution of labor do not arise in this example. Table 1 shows the coefficients of production for this example. The labor coefficients vary identically with the the labor coefficients in the previous example. a2,1(a), a3,1(a), a2,1(b), a3,1(b), a1,2(c),...

Figure 1: Variation in the Maximum Wage and the Cost-Minimizing Technique with Time1.0 Introduction I thought I would revisit the application of my analysis of fluke switch points to an example of Harrod-neutral technical change. Two techniques are assumed to experience Harrod-neutral technical change. The same commodities are produced with both techniques. No capital goods are produced for one technique that are unproduced in the other. Consequently, the techniques have no processes in...