Tag Archives: Example in Mathematical Economics

Figure 1: A Partition of Price-Wage Space for a Two-Commodity Reswitching Example1.0 Introduction This post generalizes my approach in Vienneau (2005). In that article, I present a Linear Programming (LP) problem for the firm. In the case of an economy that produces two commodities, one can present a graphical display that clarifies how Sraffa's equations arise. The dual LP is important in this development. Here, I show how that approach can work for a case in which rates of profits...

Figure 1: A Two-Dimensional Pattern Diagram The example in this working paper is of an economy in which two commodities are produced. Technical progress is modeled as decreasing the coefficients of production in one of the processes for producing corn. They decrease at a rate of σ of ten percent. Figure 2 shows how the pattern of switch points vary with technical progress. Initially, the Beta technique is cost-minimizing. Then it becomes a reswitching example. Around the switch point at...

I have uploaded another working paper: This article presents an example in which technical progress results in variations in the labor market. Around a switch point with a positive real Wicksell effect, a higher wage is associated with firms wanting to employer more labor per unit output of net product. Around a switch point with a reverse substitution of labor, firms in a particular industry want to hire more labor per unit output of gross product. Technical progress can bring about...

Figure 1: Regions for Basis Variables 1.0 Introduction I introduced a new way of visualizing the choice of technique for two-commodity models back in 2005. As far as I know, nobody has taken up this idea. I modify my method slightly by having labor advanced; wages are paid out of the surplus at the end of the year. I cite John Roemer in my paper linked previously. 2.0 Technology Table 1 specifies the technology I use for illustration. Each row lists the inputs needed to produce one...

I have been looking at the effects of perturbing parameters in models of the choice of technique. Now that I have one paper out of this research published, I thought I would recap where I am. I think I should be able to get at least another paper out of this. A challenge for me is to draw interesting economics out of these findings. In a sense, what I am doing is applied mathematics, albeit with more an emphasis on numerical exploration than proof of theorems. I claim that the development...

1.0 Introduction This post presents a model of a steady state with a constant rate of growth in which: Total wages and total profits grow at same rate. Neutral technical change increases the productivity of labor in all industries. The wage per hour increases with productivity. Each worker continues to consume the same quantity of produced commodities. But each worker takes advantage of increased productivity to work less hours per year. In these times, when concerns about global warning...

A Switch-Point Perturbation Diagram I have a new working paper at SSRN. Abstract: This article presents an analysis based on a comparison of stationary states. With technology and relative markups among industries taken as exogenous, the long-period trade-off between wages and rates of profits is determined. A long-period change in relative markups among industries can create a switch point exhibiting capital-reversing. Around such a switch point, a higher wage is associated with firms...

Figure 1: PPFs in Portugal1.0 Introduction This post continues these two posts. I change the model here to have wages advanced, not paid out of the surplus at the end of the year. I here consider an example of a model of stationary states in which two countries can trade in produced commodities to be used for consumption. The countries face given prices on international markets for traded commodities. (They are small open economies, in the jargon.) I take the rate of profits as given in...

Figure 1: Rates Of Profits for Specialization in Consumer Goods1.0 Introduction This post is a continuation of this example. How a country specializes in foreign trade depends on distribution. And foreign trade can reduce the consumption basket to be divided among the inhabitants of a country, as compared with autarky. 2.0 Patterns of Specialization Assume that the consumption basket in both countries contains both corn and linen. In a steady state, international prices and the...

Figure 1: Specialization In A Single Country1.0 Introduction This post considers how the firms in a small open economy will specialize, given prices on international markets and the domestic rate of profits. The example would only be interesting as part of a larger argument, which I have not yet worked out. 2.0 Technology Consider a small, open economy which has a flow-input, point-output technology for producing two consumption goods, corn and linen. Corn is manufactured from inputs of...