Tag Archives: Example in Mathematical Economics

Figure 1: Bifurcation Diagram1.0 Introduction This post continues my exploration of the variation in the number and "perversity" of switch points in a model of prices of production. This post presents a case in which one switch point replaces two switch points on the wage frontier. 2.0 Technology The example in this post is one of an economy in which four commodities can be produced. These commodities are called iron, steel, copper, and corn. The managers of firms know (Table 1) of one...

Figure 1: Bifurcation Diagram1.0 Introduction I have been exploring the variation in the number and "perversity" of switch points in a model of prices of production. I conjecture that generic changes in the number of switch points with variations in model parameters can be classified into a few types of bifurcations. (This conjecture needs a more precise statement.) This post fills a lacuna in this conjecture. I give an example of a case that I have not previously illustrated. 2.0...

This post states a mathematical conjecture. Consider a model of prices of production in which a choice of technique exists. The parameters of model consist of coefficients of production for each technique and given ratios for the rates of profits among industries. The choice of technique can be analyzed based on wage curves. A point that lies simultaneously on the outer envelope of all wage curves and the wage curves for two techniques (for non-negative wages and rates of profits not...

Table 1: Distribution of Votes Among Parties and Districts DistrictToriesWhigsTotalI5149100II5149100III3367100Total1351653001.0 Introduction This post, amazingly enough, is on current events. Stephanopoulos and McGhee have developed a formula, the efficiency gap, that measures the partisanship of the lines drawn for legislative districts. In this post, I present a numerical illustration of this formula and connect it to current events. I conclude with some questions. 2.0 Numerical Example...

I have organized a series of my posts together into a working paper, titled Bifurcations and Switch Points. Here is the abstract: This article analyzes structural instabilities, in a model of prices of production, associated with variations in coefficients of production, in industrial organization, and in the steady-state rate of growth. Numerical examples are provided, with illustrations, demonstrating that technological improvements or the creation of differential rates of profits can...

Figure 1: Bifurcation Diagram I have presented a model of prices of production in which the the rate of profits differs among industries. Such persistent differential rates of profits may be maintained because of perceptions by investors of different levels of risk among industries. Or they may reflect the ability of firms to maintain barriers to entry in different industries. In the latter case, the model is one of oligopoly. This post is based on a specific numeric example for...

Figure 1: Bifurcation Diagram This post is a continuation of the analysis in this reswitching example. That post presents an example of reswitching in a model of the production of commodities by means of commodities. The example is one of an economy in which two commodities, iron and corn, are produced. Managers of firms know of two processes for producing iron and one process for producing corn. The definition of technology results in a choice between two techniques of production. The...

1.0 Introduction Consider a partial equilibrium model in which: Consumers demand to buy a certain quantity of a commodity, given its price. Firms produce (supply) a certain quantity of that commodity, given its price. This is a model of perfect competition, since the consumers and producers take the price as given. In this post, I try to present a model of the supply curve in which the managers of firms do not make systematic mistakes. This post is almost purely exposition. The...

Figure 1: Price Wicksell Effects in Example1.0 Introduction This post presents another example from my on-going simulation experiments. I am still focusing on simple models without the choice of technique. The example illustrates an economy in which price Wicksell effects are positive, for some ranges of the rate of profits, and negative for another range. 2.0 Technology I used my implementation of the Monte-Carlo method to generate 20,000 viable, random economies in which three...

Figure 1: Blowup of Distribution of Maximum Distance of Frontier from Straight Line1.0 Introduction This post is the third in a series. Here is the first, and here is the second. In this post, I am concerned with the probability that price Wicksell effects for a given technique are negative, positive, or both (for different rates of profits). A price Wicksell effect shows the change in the value of capital goods, for different rates of profits, for a technique. If a (non-zero) price...