| 1 |
Invariant Relationships for Homothetic Production Functions |
Martin J. Beckmann |
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Abstract
An operational approach to production functions must recognize the limitations imposed on our knowledge by the observability and measurability of variables and of the relationships defining production functions. One important limitation on our knowledge arises through the presence of technical change, another through the difficulty of measuring the marginal product of capital or even the capital stock itself. Depending on what we assume to be observable we find ourselves restricted to a smaller or broader class of admissible production functions. Further restrictions are imposed by the limitations of statistical technique. Thus in practice most estimated relationships are assumed linear either in the variables or in some suitable transformation, usually a logarithmic one.
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| 2 |
Characterization of the CES Production Functions by Quasilinearity |
Wolfgang Eichhorn |
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Abstract
It is well-known .) that a linearly homogeneous production function . with CES (constant elasticity of substitution), σ, is a CD (COBB-DOUGLAS [1928]) production function . for σ = 1, or an ACMS (ARROW-CHENERY-MINHAS-SOLOW [1961]) production function
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| 3 |
Technical Progress, Neutral Inventions, and Cobb-Douglas |
Wolfgang Eichhorn,Serge-Christophe Kolm |
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Abstract
In 1961, H. Uzawa [5] showed that Hicks neutrality .) of inventions (or technical progress) together with Harrod neutrality imply that the underlying production function Φ is Cobb-Douglas. His proof requires differentiability up to the second order and, clearly, the linear homogeneity of Φ. W. Krelle, 1969, in a similar context [3, pp.123ff], also assumes both differentiability and linear homogeneity.
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| 4 |
A Characterization of Hicks Neutral Technical Progress |
Rolf Färe |
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Abstract
In this paper a characterization of Hicks-neutrality is given in terms of output augmenting technical progress. Compared to Sato-Beckmann (2), who characterize Hicksneutrality with marginal productivities, differentiability is not assumed here. Similar problems are considered in Eichhorn-Kolm (1).
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| 5 |
On Linear Expansion Paths and Homothetic Production Functions |
Rolf Färe |
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Abstract
In economic theory of production, homothetic production functions, introduced by Shephard in (5) and extended in (6), play an important role. Shephard has shown (see (6)) that such a production structure is a necessary and sufficient condition for the related cost function to factor into a product of an output and a factor price index. Subsequently in (3) homothetic production functions, strictly increasing along rays in the input space, were characterized by a functional equation. Furthermore, it was shown in (4), that homothetic production functions are a sufficient condition for, what might be called, a strong Law of Diminishing Returns.
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| 6 |
Neutral Inventions and CES Production Functions |
Frank Stehling |
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Abstract
In the literature of economic theory the most frequently used classes of (macroeconomic) production functions with completely substitutable factors are the CD functions .) and ACMS functions .) defined respectively (for two arguments, usually interpreted as capital and labour) by .and .or, if a time variable t is involved., by . and ..
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| 7 |
Production Duality and the von Neumann Theory of Growth and Interest |
S. N. Afriat |
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Abstract
Production relations, which generalize the concept of a production function, have a duality theory based on their connection with similar relations defined in the dual space of prices. A classical homogeneous relation is a special type which, when the input and output goods are the same, is illustrated by that introduced by von Neumann as the basis for his economic model. For this type the connection with the dual is symmetrical, the typical properties are preserved in products, and the dual of a product is the corresponding product of the duals. Two further properties, introduced by D. Gale for a production relation, appear as dual properties, since either one on a production relation is equivalent to the other on the dual. Another kind of result which, as with several general features here, is reflected also in the extensive work of R.T. Rockafellar, shows a duality between cost and return functions with an exchange of role between a correspondence and its dual.
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| 8 |
A Note on a Production Problem in a Multisectoral Economic Model |
Klaus Hellwig,Otto Moeschlin |
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Abstract
The multisectoral economic model, considered here, was suggested in [4]. We start with the definition of an equilibrium solution to this model. An economic interpretation of it may be found in [4].
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| 9 |
A Dynamic Input-Output Model with Variable Production Structure |
Hartmut Kogelschatz |
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Abstract
The closed dynamic input-output model introduced by Leontief is given by the following system of difference equations.where A = (a.) and B = (b.) denote the nxn matrices of current input coefficients and capital coefficients, respectively; x. is the nx1 vector of outputs in period t. From the point of view of growth theory one has been interested in the question whether this production model admits proportional growth of outputs at a constant rate, i.e. whether there exists a real number λ such that.From (1.1) and (1.2) with x:= x...
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| 10 |
Disaggregated Production Functions |
Wilhelm Krelle |
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Abstract
Neoclassical production functions are a useful concept in macroeconomics. But as soon as it comes to disaggregation and as soon as current input and investment decisions have to be explained simultaneously as in disaggregated econometric forecasting systems they cannot be used directly. Of course, there is always the last resort to the Walras-Leontief-type fixed input and capital coefficients. But they do not allow for price substitution and technical progress and therefore can only be applied for short term economic analysis, i.e. for time horizons not exceeding about 4 years.
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| 11 |
Balanced Growth of Open Economies under Variable Degree of Homogeneity |
Frank Stehling |
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Abstract
Production processes of closed economies which can be described by possibly non-linear systems of first order difference equations.were analysed by R.M. Solow and P.A. Samuelson [7]; their results, concerning existence and behavior of so-called balanced growth solutions have been generalized by J.F. Muth [4], D.B. Suits [9], M. Morishima [3], H. Nikaido [5] and [6], and the author [8]. H. Nikaido was the first who examined production processes of open economies which can be described by a non-autonomous system of (possibly non-linear) first order difference equations.where aεℝ.. is a constant vector, a̱ ≥ 0̱ ., and K is a real-valued function satisfying K(t) > 0, K(0) = 1; x.(t) is the income of sector i in period t. For a detailed representation of the underlying model, in which are involved assumptions about production techniques and consumption behavior, see Nikaido [3].
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| 12 |
On Weak Homogeneity |
Richard Vahrenkamp |
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Abstract
In the sectoral analysis of an economy the non-negative matrices play an important role. Given such a matrix A in the Leontief model, to each gross-output-vector x there corresponds the input-vector xA. The matrix A gives rise to a non-negative matrix H, describing a growing economy, which relates the income-vector y(t) at period t to the income-vector y(t+1) at period t+1 by.as shown e.g. by Nikaido [2, p.98]. In the past 20 years some work has been done to drop some of the properties of the mapping H: R.. → R.., which involves linearity, homogeneity of degree 1, and monotonicity. But in these weakened assumptions on H, always homogeneity of some fixed degree has been retained [2, Part III].
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| 13 |
Continuity of Production Correspondences and a Relation between Efficient Input and Output Vectors |
Georg Bol |
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Abstract
This paper deals with the description of multi-commodity production by the concept of production correspondences. As in the papers of Shephard [8], Jacobsen [5] etc., we use two correspondences, the “production correspondence”, denoted by P and its “inverse” correspondence denoted by L — we call the pair (L,P) a production system -; as initial concept we use that given by Opitz [6,7], which, in particular, means, that there are no assumptions about convexity (resp. concavity).
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| 14 |
On Efficient Points of a Stochastic Production Correspondence |
Rudolf Henn,Eugen Krug |
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Abstract
In his book “Theory of Cost and production Functions” Shephard has introduced the concept of production correspondences. Such a correspondence assigns to each combination of inputs the possible outputs. Of course, this connection is not always deterministic. For example, the weather or the development of interest have great influence in some sectors of economy. Hence we shall try in the following to stochasticize this concept of production correspondence..
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| 15 |
Production Correspondences and Convex Algebra |
Pieter H. M. Ruys |
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Abstract
The production technology is usually represented in the quantity space by production sets, or by production functions and correspondences. Shephard [4] showed that in many cases production functions can be obtained from cost functions of a given technology and Uzawa [6] argued the 1–1 correspondence between these production functions and cost functions. These results have been generalized to production correspondences by Shephard [5]. He also showed that there exists a dual relation between cost structures (resp. output revenue structures) in the price space and production-input structures (resp. production-output structures) in the quantity space.
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发表于 2025-3-21 19:48:31
