Tag Archives: Example in Mathematical Economics

Figure 1: The Wage Frontier And Rent1.0 Introduction This post is another worked homework example, problem 7.8 in Chapter 10 of Kurz and Salvadori (1995). The example illustrates the possible non-existence of a cost-minimizing technique with intensive rent. I once looked at an example from J. E. Woods of joint production. I claim that that example does not make the desired point, given the possibility of a price of zero for some produced good. I do not think this example of rent can be...

Figure 1: The Wage Frontier And Rent This post is merely a worked homework example, problem 7.10 in Kurz and Salvadori (1995). I have not considered yet which parameters I want to explore perturbing. As a matter of history, Anderson, West, Malthus, and Ricardo took extensive rent as the paradigm case, and confined it to land. They imposed no limit on the production of industrial commodities. Ricardo, at least, also discussed the case of intensive rent. The marginalists, on the other hand,...

Figure 1: Three Patterns Across The Wage Axis And One Three-Technique Pattern This post continues the approach in this post and in this post. As previously stated, I consider the same two examples. In both examples, three processes are known for producing the numeraire, called "corn". In the example for the left panel, corn is a non-basic commodity, and a different basic commodity is used in each of the three techniques. In the example for the right panel, all three corn-producing processes...

Figure 1: Three Patterns Across The r Axis And One Three-Technique Pattern This post continues the approach in this post. I consider the same two examples. In both examples, three processes are known for producing the numeraire, called "corn". In the example for the left panel, corn is a non-basic commodity, and a different basic commodity is used in all three techniques. In the example for the right panel, all three corn-producing processes require inputs of labor power, corn, and labor (in...

Table 1: A Common Structure Example1.0 Introduction This post presents partitions of (a part of) parameter space for two examples of models of prices of production with a choice of technique. The examples have a different structure and are parametrized differently. Yet, I want to argue, the partitions are the same, at some level of abstraction. 2.0 Thing 1 The first example is an instance of the Samuelson-Garegnani model. Table 1 presents the coefficients of production for this example....

Figure 1: Convergence to a Pattern of Switch Points over the Axis for the Rate of Profits1.0 Introduction This post illustrates how to find fluke switch points. As usual, I proceed by example, in this case, as taken from my paper in Structural Change and Economic Dynamics. 2.0 Technoplogy In this example of a capitalist economy, two commodities, iron and corn, are produced. One process is known for producing iron. In the iron industry, workers use inputs of iron and corn to produce an...

Figure 1: A Pattern Diagram1.0 Introduction Aside, perhaps from the above visualization, nothing novel is presented in this post. It follows an example presented by Freni (1991). I know of this example from problems 7.7 and 7.29 in Kurz and Salvadori (1995). The oddities of this example can be seen in an earlier and more complicated example from D'Agata (1983). This is an example of intensive rent. When the requirements for use are large enough, capitalists will use more than one process...

Figure 1: Wage Curves and Rent1.0 Introduction I might as well illustrate an example with extensive rent and reswitching. I find it incredible that the agents in these sorts of models understand the implications of, say, a variation of the distribution of income for their self-interests. Nevertheless, I try to note the consequences of variation in the distribution of income and perturbations of model parameters on prices of production. And I do not worry too much about disequilibria. 2.0...

Figure 1: Variation in Switch Points with Time1.0 Introduction This post continues my effort to understand how fluke cases can partition parameter spaces in models of prices of production with extensive rent. Some background for this post is here, here, and here. 2.0 Technology The technology is described by the coefficients of production in Table 1. I assume that requirements for use are such that they cannot be satisfied by cultivating only two types of land. After fully cultivating...

Figure 1: Wage Curves for Fluke Case for r-Order of Fertility1.0 Introduction This post illustrates two fluke cases that can arise in a model with land and extensive rent. I call these a pattern of switch points for the r-order of fertility and a pattern of switch points for the w- order of fertility. I have previously described a fluke case in the order of rentability, which can be either over the wage axis or over the axis for the rate of profits. These fluke cases can arise in an...