Tag Archives: Example in Mathematical Economics

Figure 1: Wage Frontier for a Fixed Capital Example1.0 Introduction I continue to explore the simplest multisector model of the production of commodities by means of commodities in which circulating and fixed capital is used in both sectors. In previous explorations, I locate a four-technique pattern, observe recurrence of truncation, and provide an example in which truncating all machines is infeasible. I think my taxonomy of fluke switch points and methods of visualizing the effects of...

Figure 1: Factor Wage Curves For Feasible Techniques There are 12 coefficients that can be varied in my minimum multisector model in which production in all sectors can require both fixed and circulating capital. I do not think I am being very orderly in exploring this twelve-dimensional space. This is a fluke case in which the maximum rate of profits is zero for both the Alpha and the Beta techniques. If only new machines are used as means of production in producing new machines and in...

Figure 1: Variation of Choice Of Technique with a Coefficient of Production This post continues the analysis of this example. The coefficients of production and the techniques are the same as in the linked post, except here I consider the results of varying a1, 2, the amount of corn needed as circulating capital in operating Process II at unit level. Figure 1 above shows how the choice of technique varies with this parameter. This is a two-sector model, in which new machines and corn are...

Figure 1: A Wage Frontier1.0 Introduction This post presents a numberic example of a non-interlocked system with fixed capital and no superimposed joint production. This seems to be the minimum multiple-sector model: Of the production of commodities by means of comodities With both circulating and fixed capital, In which the fixed capital consists of machines of non-constant efficiency with a physical lifetime of more than one period. This is a step in my research agenda of exploring...

Figure 1: Prices of Production1.0 Introduction This post presents a new kind of fluke case in the analysis of the choice of technique, at least new to me. I call this a pattern for requirements for use, and it can arise only in a case of joint production. My graphs in this post have some incomprehensible notation, since I am currently exploring perturbing parameters, in line with my research agenda. I know that perturbing the requirements for use removes the indeterminancy in this example....

Figure 1: A Pattern Diagram This post illustrates the numeric example used here. The example is of an economy in which two commodities, iron and corn, are produced by workers from inputs of iron and corn. Two processes are available for each industry, leading to a choice among four techniques. I analyze stationary states. I look at prices of production, with a bushel corn as numeraire and wages paid out of the surplus at the end of the year. Prices of production are defined so as to allow...

I have a working paper. Abstract: This article extends to unequal rates of profits a derivation of prices of production from a linear program. A partition of the price-wage space is illustrated in an example with two produced commodities. The variation in the solution of the LP with perturbations of relative markups is illustrated. This analysis provides an intuitive explanation of how the reswitching of techniques and of how capital reversing can emerge in non-competitive markets.

1.0 Introduction Piero Sraffa wrote down his 'first equations' in 1927, for an economy without a surplus. D3/12/5 starts with these equations for an economy with three produced commodities. I always thought that they did not make dimensional sense, but Garegnani (2005) argues otherwise. This post details Garegnani's argument, albeit with my own notation. There are arguments about how and why Sraffa started on his research project I do not address here. The question is how did he relate...

1.0 Introduction One inspiration for this post is stumbling across this abstract 2.0 Marx Start with labor coefficients and a Leontief input/output matrix, in physical terms. You can construct this from make and use tables for your country, given price indices by sectors. For any existing capitalist economy, I expect that matrix to characterize a more than viable economy. After all the capital goods used up in producing the final demand in, say, a year are reproduced, some commodities...

I have defined patterns of switch points in considering perturbations of examples of the choice of technique. For example, I have defined three-technique and four-technique patterns. An obvious extension is to consider how these patterns arise in models of joint production. A simplification is to only consider models of fixed capital without superimposed joint production. This post lays out an example in which, maybe, some parameter values can lead to a three-technique pattern. I am...