Location and the theory of production Clarifications and extensions

This paper has attempted to clarify some weaknesses and flaws contained in Miller and Jensen's analysis. In particular, we have demonstrated that in Miller and Jensen's model, if the production function is homogeneous of degree one and the transport rate functions are independent of quantities shipped, it is impossible to have an interior solution. In addition, we have evaluated the role of the generalized transport rate functions in the profit-maximization location model with and without a prescribed level of output and shown that if transport rates depend on quantities shipped and have constant elasticities, then a linearly homogeneous production function is not sufficient to insure that optimum location is independent of output or the demand function. This result clearly invalidates Miller and Jensen's assertion.     

Transportation rates, market structure and the production-location decision : A note

This note examines the effects of market structure on production and location decisions of an oligopolistic firm. It shows that if transportation rates are a function of quantity shipped and distance traveled, a linearly homogeneous production function is not sufficient to ensure independence between the optimum location and market structure unless (i) the elasticities of transportation rates with respect to quantity shipped are constant and identical, and (ii) the ratios of marginal products to the marginal transportation costs are equal for each input. This results is significantly different from Hwang and Mai's in the constant transportation rates case.     

Some unresolved issues in the location theory of the firm

This paper presents a generalized location theory of the firm in linear space. Location outcomes are examined by utilizing a general as well as a particular transport rate structure for output and inputs and using a general concave production as well as a homogeneous production function, of the firm. The effect of a change in demand on the location is also investigated.     

Monopsony and the production-location decision of the firm

This paper incorporates monopsony power in one of the input markets within the context of the Weber-Moses triangular framework and examines the effect of an increase in monopsony power on the production-location decision of the firm. In particular, this paper shows that the optimum location of the firm is independent of monopsony power if the production funstion is homogeneous of degree one. However, if the production function is not homogeneous of degree one, the firm possessing monopsony power will have an incentive to move its location away from the monopsonized input market towards other markets under certain reasonable assumptions. Finally, some important policy implications are generated from the analysis.     

On the Relationship between Input–Output Coefficients and Hanoch's Linear Homogeneous Constant Differences of Elasticities of Substitution Production Function

Tilanus's ‘mixed’ input–output coefficients are generalized and it is shown that the generalized coefficients stand in a fixed proportion to each other if and only if the technology is described by Hanoch ‘s linear homogeneous constant differences of elasticities of substitution production function.     

Production location and random input price

The purpose of this paper is to develop systematically the theory of plant location for a competitive firm facing random input price. It will be shown that the impact of input price uncertainty on the firm's optimum location depend crucially upon (i) the firm's attitude toward risk, (ii) the characteristics of the production function, (iii) the structure of transport costs on inputs and output, and (iv) the type of input usages. Moreover, and more importantly, some conclusions obtained by prior studies on location theory in a certainty world can also be shown to be special cases of our more general results, but some are not justifiable in a world with random input price.     

Transport rates structure,optimum location,and theory of production: Reexamination

The two-stage approach consistently to present a generalized location theory of the firm in linear space is employed. It is shown that the second-order sufficient condition for the profit-maximizing and/or cost-minimizing location problem requires that transport rates increase with distance. In the process, it is demonstrated that this approach provides a compact way to analyze the location and production decisions separately and to avoid the errors made by Mathur and others.     

Stochastic comparisons of coherent systems

The study of stochastic comparisons of coherent systems with different structures is a relevant topic in reliability theory. Several results have been obtained for specific distributions. The present paper is focused on distribution-free comparisons, that is, orderings which do not depend on the component distributions. Different assumptions for the component lifetimes are considered which lead us to different comparison techniques. Thus, if the components are independent and identically distributed (IID) or exchangeable, the orderings are obtained by using signatures. If they are just ID (homogeneous components), then ordering results for distorted distributions are used. In the general case or in the case of independent (heterogeneous) components, a similar technique based on generalized distorted distributions is applied. In these cases, the ordering results may depend on the copula used to model the dependence between the component lifetimes. Some illustrative examples are included in each case.     

Alternative functional forms for production,cost and returns to scale functions

We consider generalized production functions, introduced in Zellner and Revankar (1969), for output y=g(f) where g is a monotonic function and f is a homogeneous production function. For various choices of the scale elasticity or returns to scale as a function of output, differential equations are solved to determine the associated forms of the monotonic transformation, g(f). Then by choice of the form of f, the elasticity of substitution, constant or variable, is determined. In this way, we have produced and generalized a number of homothetic production functions, some already in the literature. Also, we have derived and studied their associated cost functions to determine how their shapes are affected by various choices of the scale elasticity and substitution elasticity functions. In general, we require that the returns to scale function be a monotonically decreasing function of output and that associated average cost functions be U- or L-shaped with a unique minimum. We also represent production functions in polar coordinates and show how this representation simplifies study of production functions' properties. Using data for the US transportation equipment industry, maximum likelihood and Bayesian methods are employed to estimate many different generalized production functions and their associated average cost functions. In accord with results in the literature, it is found that the scale elasticities decline with output and that average cost curves are U- or L-shaped with unique minima. © 1998 John Wiley & Sons, Ltd.     

The location theory of firm revisited impacts of rising energy prices

The impact of rising energy prices on the locational pattern of industries is analyzed by a simple two-firm straight line location model. The concavity of average cost function of final consumer's good with respect to locational variables is proved for the case of linear homogeneous Cobb- Douglas production functions and this leads to the possible three cases of end-point location. The rise in energy prices induces ‘double location at the market’ or ‘double location at the port’ instead of separate location of two industries, i.e., intermediate good industry and consumer's good industry.     

Revisiting the decomposition of cost efficiency for non-homothetic technologies: a directional distance function approach

In the early 1980’s Kopp and Diewert proposed a popular method to decompose cost efficiency into allocative and technical efficiency for parametric functional forms based on the radial approach initiated by Farrell. We show that, relying on recently proposed homogeneity and duality results, their approach is unnecessary for self-dual homothetic production functions, while it is inconsistent in the non-homothetic case. By stressing that for homothetic technologies the radial distance function can be correctly interpreted as a technical efficiency measure, since allocative efficiency is independent of the output level and radial input reductions leave it unchanged, we contend that for non-homothetic technologies this is not the case because optimal input demands depend on the output targeted by the firm, as does the inequality between marginal rates of substitution and market prices—allocative inefficiency. We demonstrate that a correct definition of technical efficiency corresponds to the directional distance function because its flexibility ensures that allocative efficiency is kept unchanged through movements in the input production possibility set when solving technical inefficiency, and therefore the associated cost reductions can be solely—and rightly—ascribed to technical-engineering-improvements. The new methodology allowing for a consistent decomposition of cost inefficiency is illustrated resorting to simple examples of non-homothetic production functions.     

Effective Rates of Sectoral Productivity Change

In effective rates of sectoral productivity change, some of the inputs are treated as produced. Here, this is extended to cover all the inputs. All the sectoral rates of productivity growth based on a static input–output (IO) framework are shown to be equal to the corresponding rates of decrease in the production price. For the direct rate, all the input prices are treated as exogenous constants. For the effective rates, prices of the inputs, which are treated as produced, are determined by production technology. The fully effective rate is derived from the price equations of the closed dynamic IO model. It is equal to the rate of decrease in the production price when the prices of all inputs, human capital and human time included, depend on production technology. The overall rate, obtained as a weighted sum of the fully effective sectoral rates, is equal to the rate of growth in the growth potential of the economy.     

Unbiased determination of production technologies

To determine whether an industry exhibits constant returns to scale, whether the production function is homothetic, or whether inputs are separable, a common approach is to specify a cost function, estimate its parameters using data such as prices and quantities of inputs, and then test the parametric restrictions corresponding to constant returns, a homothetic technology, or separability. Statistically, such inferences are valid if the true cost function is a member of the parametric class considered, otherwise the inference is biased. That is, the true rejection probability is not necessarily adequately approximated by the nominal size of the statistical test. The use of fixed parameter flexible functional forms such as the Translog, the generalized Leontief, or the Box-Cox will not alleviate this problem.The Fourier flexible form differs fundamentally from other flexible forms in that it has a variable number of parameters and a known bound, depending on the number of parameters, on the error, as measured by the Sobolev norm, of approximation to an arbitrary cost function. Thus it is possible to construct statistical tests for constant returns, a homothetic technology, or separability which are asymptotically size α by letting the number of parameters of the Fourier flexible form depend on sample size. That is, the true rejection probability converges to the nominal size of the test as sample size tends to infinity. The rate of convergence depends on the smoothness of the true cost function; the more times is differentiable the true cost function, the faster the convergence.The method is illustrated using the data on aggregate U.S. manufacturing of Berndt and Wood (1975, 1979) and Berndt and Khaled (1979).     

Combining Probability Distributions by Multiplication in Metrology: A Viable Method?

In measurement science quite often the value of a so‐called ‘output quantity’ is inferred from information about ‘input quantities’ with the help of the ‘mathematical model of measurement’. The latter represents the functional relation through which outputs and inputs depend on one another. However, subsets of functionally independent quantities can always be so defined that they suffice to express the entire information available. Reporting information in terms of such a subset may in certain circumstances require aggregating probability distributions whose arguments are interrelated quantities. The option of aggregating by multiplication of distributions is shown to be susceptible of yielding inconsistent results when the roles of inputs and outputs are assigned differently to the quantities. Two alternatives to this practice that do not give rise to such discrepancies are discussed, namely (i) logarithmic pooling with weights summing to one and (ii) linear pooling, of which the former appears to be slightly more favourable for applications in metrology. An example illustrates the inconsistency of results obtained by distinct ways of multiplying distributions and the manner in which these results differ from a logarithmically pooled distribution.     

Estimation and decomposition of inefficiency when producers maximize return to the outlay: an application to Norwegian fishing trawlers

This paper deals with estimation of a production technology where endogeneous choice of input and output variables is explicitly recognized. In particular, we assume that producers maximize return to the outlay (RO). For simplicity and tractability we start with a Cobb–Douglas transformation function with multiple inputs and outputs and show how the first-order conditions of RO maximization can be used to derive an estimating equation which is nothing but a partial input productivity equation. This equation does not suffer from the econometric endogeneity problem although the output and input variables are endogenous. First, we consider the case where producers are fully efficient allocatively but technically inefficient. The model is estimated using a single equation stochastic frontier approach. The model is then extended to allow allocative inefficiency and it is estimated as a system using generalized method of moment. Algebraic expressions are derived to decompose the effect of technical and allocative inefficiencies on RO. We also consider translog specifications that are estimated as (1) a single equation frontier model as well as (2) a system. We use a panel of Norwegian fishing trawlers data to estimate the model. Outputs are different species caught while inputs are labor and vessel size. We also control for number of days of operation, age of the vessel and year effects. Empirical results show that the average rate of RO is reduced by about 20 to 30 % due to technical inefficiency. On the other hand, average allocative efficiency is found to be about 78 %. The average overall efficiency is found to be around 60 %.     

LOCATION OF VERTICALLY LINKED OLIGOPOLISTS

This paper examines the geographical equilibrium of location of N vertically linked firms and its relation to the creation of an industrial cluster. In a two-region spatial economy, a monopolist firm supplies an input to N consumer goods firms that compete in quantities. When the transport cost of the input increases, downstream firms prefer to agglomerate where the upstream firm is located, to save in production cost. However, simultaneous increases in the transport cost of the input and of the consumer good or increases in the number of downstream firms lead to a relative dispersion of these firms, to reduce competition and locate closer to the local final consumer. In contrast to Mayer (2000) , when both transport costs increase, the location decision of downstream firms is based more on the geographical point that maximizes accessibility to the local final consumer than on the geographical point that minimizes the production cost.     

Unconventional government debt purchases as a supplement to conventional monetary policy

In response to the Great Financial Crisis, the Federal Reserve, the Bank of England and many other central banks have adopted unconventional monetary policy instruments. We investigate if one of these, purchases of long-term government debt, could be a valuable addition to conventional short-term interest rate policy even if the main policy rate is not constrained by the zero lower bound. To do so, we add a stylised financial sector and central bank asset purchases to an otherwise standard New Keynesian DSGE model. Asset quantities matter for interest rates through a preferred habitat channel. If conventional and unconventional monetary policy instruments are coordinated appropriately then the central bank is better able to stabilise both output and inflation.     

On Average Predictive Comparisons and Interactions

In a regression context, consider the difference in expected outcome associated with a particular difference in one of the input variables. If the true regression relationship involves interactions, then this predictive comparison can depend on the values of the other input variables. Therefore, one may wish to consider an average predictive comparison as a target of inference, where the averaging is with respect to the population distribution of the input variables. We consider inferences about such targets, with emphasis on inferential performance when the regression model is misspecified. Particularly, in light of the difficulties in dealing with interaction terms in regression models, we examine inferences about average predictive comparisons when additive models are fitted to relationships truly involving pairwise interaction terms. We identify some circumstances where such inferences are consistent despite the model misspecification, notably when the input variables are independent, or have a multivariate normal distribution.     

Spatial discrimination: Bertrand vs. Cournot with asymmetric demands

This paper develops a barbell model a la Hwang and Mai [Hwang, H., and C.C. Mai, 1990, Effects of spatial price discrimination on output, welfare, and location, American Economic Review 80, 567–575.] with homogeneous product and asymmetric demands to compare prices, aggregate profits and social welfare between Cournot and Bertrand competition, and to analyze the firms' equilibrium locations. It focuses on the impacts of the spatial barrier generated from transport costs, and the market size effect resulting from asymmetric demands. It shows that the market-size effect is crucial in determining firms' locations under Cournot competition, but insignificant under Bertrand competition. Moreover, the equilibrium price of the large market and the aggregate profits are lower but the social welfare is higher under Cournot competition than under Bertrand competition if one of the markets is sufficiently large and the transport cost is high.     

Location theory of the firm under price uncertainty

This paper presents a theory of location under price uncertainty employing a general utility and production function. The analysis is also conducted by incorporating a homogeneous production function. Risk preferences of the firm are treated as an integral part of the model.