Therefore, the amount of capital depends on prices and income distribution and any attempt to use the amount of capital to determine income distribution is circular reasoning. This result constitutes a criticism to the logic of the neoclassical theory of income distribution, which calls for a measure of capital independent of distribution in order to determine labor and capital factor prices r , w as indexes of their relative scarcity.

One important implication of Sraffa's model is that, under the considered set of assumptions, prices of production, the profit rate and in general, the value of any commodity aggregate could have a considerable nonlinear behavior as income distribution changes, even if the technique of the system l,A remains unchanged. This type of behavior poses additional problems to the neoclassical construction of macroeconomic production functions and to its theory of income distribution. To see this, consider the profit rate and not the wage rate as the given distributive variable.

Equations [3] and [4] represent the price and wage-profit curves, respectively. Equations [3] and [4] could have a considerable non-linear behavior or curvatures in the face of changes in the profit rate. Each technique l,A gives a particular wage-profit curve. Hence, theoretically it is possible for the curvatures of the wage-profit functions from different techniques to have multiple intersections among them, implying that one or more techniques be selected from different segments of the profit rate range if the choice of technique is based on the highest wage rate for a given profit rate.

Finally, another implication of the possible behavior of prices of production in [3] concerns the relationship between prices and the total amount of labor embodied in commodities v.

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- Theory of production.

This relationship constitutes an important element of the so-called debate on the transformation problem. Following Sraffa's developments, since the end of the s an increasing number of scholars have empirically estimated price of production models, the study of which had only been done theoretically before this period. Some of their work calculated prices of production at the observed income distribution and studied the relation between these prices, direct prices and market prices.

Other scholars have studied the effects that changes in income distribution have on the relation between wages and profits and on standard prices prices of production measured in terms of the standard commodity, a composite commodity the value of which does not change when income distribution changes.

There are two important results from this broad literature that continues up to now. On the one hand, prices of production, direct prices and market prices are considerably close to each other. On the other hand, standard prices and the wage rate are simple, nearly linear functions of the profit rate.

These results constitute a puzzle for the implications derived from Sraffa's work discussed above. As more countries and time periods are studied, more evidence piles up into these type of results. However, what has only been considered marginally in the literature is the explanation of the empirical regularities in these estimations. What are the economic forces that produce these regularities and what are their corresponding mathematical representations or constraints in price of production models?

Therefore, little attention has been paid to why actual economies allocate labor in such proportions and have such a means of production commodity structure that produces direct prices, prices of production, and market prices to be close to each other. By the same token, why do observed economies have labor and output proportions and an input commodities structure that generates nearly linear behavior in standard price and wage-profit curves under hypothetical changes in income distribution?

The book's main objective is the systematic study of prices of production and the profit rate in linear production models.

### Product description

This represents a contribution not only in the generation of new knowledge, but also in the formation of a new generation of scholars interested in these relevant topics in political economy. Of particular interest is the study of how relative prices and the profit rate behave in the face of hypothetical changes in income distribution.

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This task is based on a rich mathematical exposition of linear production models. There is a considerable effort to identify the algebraic structure of the models and to untangle their properties. The authors study in depth price of production models that only consider single commodity industries and circulating capital, like equations [1] and [2]. However, they also address several variants of this battle horse model, like fixed capital, joint production, the quantity system, etc.

The economic and mathematical material in the book is presented at an intermediate and advanced level and therefore assumes that the reader has a knowledge of price of production models equivalent to Pasinetti's or Vegara's textbooks. However, Modern Classical Economics and Reality contains a set of features not shared by the previously mentioned classic textbooks and other books on prices of production.

These characteristics arise from the series of theoretical and empirical contributions that the authors have produced.

Two unique features in this book stand out and make it a mandatory reference for research on the topic. First, empirical evidence plays a key role in the exposition. The book contains an extensive and systematic account of the empirics of prices of production. It reviews the empirical work from the literature and reports the empirical contributions for several countries and years done by the authors. Most of the presented theoretical concepts have an empirical counterpart.

In addition, the authors conduct an analysis on the different empirical results. Second, and in accordance with the subtitle of the book A Spectral Analysis of the Theory of Value and Distribution , Mariolis and Tsoulfidis dedicate a great deal of research effort and book space to the theoretical and empirical study of the spectrum of the input matrix and the role it plays in linear production models.

The spectrum of the input matrix and its use to make an alternative representation of the linear production models require some lines of explanation. The spectrum of matrix A is constituted by the set of its different eigenvalues.

## Long run and short run

If we assume that matrix A is diagonalizable and for simplicity, that it has n distinct eigenvalues, then it has the following spectral decomposition:. Substituting equation [5] in the price and wage-profit curves [3] and [4], they can alternatively be represented as:. The book is comprised of six chapters. Chapter 1 describes how relative prices, the rate of profit, and the value of capital respond to changes in income distribution according to the classical political economists, neoclassicals, Dmitriev, and Sraffa.

Chapter 2 focuses on the properties of prices of production and the profit rate in systems like equations [1] and [2]. It is important to mention that throughout the book, wages are sometimes part of the capital advanced and sometimes they are not. However, there is no clear justification for this back and forth treatment of wages nor a discussion of the economic implications of this.

This chapter presents equation's [1] general characteristics and also particular cases representing hypotheses from different schools of thought. In spite of this emphasis, the chapter also considers more general relative price models and the study of the quantity system the study of growth and output allocation.

There are two aspects that the authors wish to deepen: the existence of upper and lower bounds in price and wage-profit curves as income distribution changes; and the effects of changes in income distribution and total productivity shifts on price-profit curves. Chapter 3 provides estimations and evaluations from the models and propositions discussed in the previous chapters for a variety of countries and years.

## Neoclassical Theories of Production - Selected References

However, it begins with a simple three industry example constructed from actual data which, together with the appendix of the chapter, gives a useful introduction and guide to the realm of empirical research on prices of production. They find the following main results, which are consistent for all countries and years considered within the meaningful profit rate not too close to its extreme values :. Direct prices, prices of production, and market prices are close to each other. The theory involves some of the most fundamental principles of economics.

These include the relationship between the prices of commodities and the prices or wages or rents of the productive factors used to produce them and also the relationships between the prices of commodities and productive factors, on the one hand, and the quantities of these commodities and productive factors that are produced or used, on the other. The various decisions a business enterprise makes about its productive activities can be classified into three layers of increasing complexity.

### Theory of Production: Short-Run Analysis

The first layer includes decisions about methods of producing a given quantity of the output in a plant of given size and equipment. It involves the problem of what is called short-run cost minimization. The second layer, including the determination of the most profitable quantities of products to produce in any given plant, deals with what is called short-run profit maximization.

The third layer, concerning the determination of the most profitable size and equipment of plant, relates to what is called long-run profit maximization. However much of a commodity a business firm produces, it endeavours to produce it as cheaply as possible. This task is best understood in terms of what is called the production function , i. It states the amount of product that can be obtained from each and every combination of factors. Here, y denotes the quantity of output.

The firm is presumed to use n variable factors of production; that is, factors like hourly paid production workers and raw materials, the quantities of which can be increased or decreased. In the formula the quantity of the first variable factor is denoted by x 1 and so on. The firm is also presumed to use m fixed factors, or factors like fixed machinery, salaried staff, etc. What Is the Long Run? A long run is a period of time in which all factors of production and costs are variable. When the long-run average cost LRAC falls, is means output is increasing.

If it rises, the firm experiences a diseconomy of scale. Firms will search for the production technology that allows it to produce the desired level of output at the lowest cost. Compare Investment Accounts. The offers that appear in this table are from partnerships from which Investopedia receives compensation. Related Terms Why Minimum Efficient Scale Matters The minimum efficient scale MES is the point on a cost curve at which a company can produce its product cheaply enough to offer it at a competitive price.

Understanding Diseconomies of Scale Diseconomies of scale occur when a business expands so much that the costs per unit increase. It takes place when economies of scale no longer function for a firm. What You Need to Know About Economies of Scale Economies of scale are cost advantages reaped by companies when production becomes efficient.

Law of Diminishing Marginal Productivity Explains the Decay of Cost Advantages The law of diminishing marginal productivity states that input cost advantages typically diminish as production levels increase. Partner Links. Related Articles.