Optimizing the Spatial Structure of the Agricultural Production Function

Important characteristics of spatial agricultural production functions are derived by introducing a non‐negative curvilinear spatial demand function for production input intensities. Given the usual neoclassical rationale assumptions of spatial demand for capital and labor inputs under competitive environment of farming in developing agricultural economies, the optimal production levels are determined by optimizing spatial demand for production inputs. Decreasing price‐to‐transport costs ratio (that is, decrease in the prices of capital goods or increase in freight rates) and increasing wage‐to‐travel costs ratio (that is, increase in labor wages or decrease in the travel rate) expand the limits of the (spatial) optimal boundary of the demand for agricultural capital goods and labor input respectively. These effects occur on account of the operation of (positive) spatial price gradient and (negative) wage‐gradient in the market region. It may be noted that elasticities of demand for production factors are spatially variant and have significant effects on the alterations in the structure of agricultural production. However, the spatial optimal solution of production has a complicated relationship with them. The price elasticity has negative and wage elasticity has positive spatial gradients in the market region. Farmers located in the periphery of the market region are not much affected by the proportionate changes occurring in the prices of agricultural capital goods but are more sensitive to the proportional changes in labor wages. Because of a decreasing trend in capital input demand and increase in labor input with distance from the market, capital‐product diminishes with a decreasing rate and labor‐product increases with an increasing rate in the spatial structure of agricultural production. As a result, capital‐labor ratio falls toward zero, which raises profit rate per unit of capital investment especially in the outer part of the market region. The equilibria of optimal production with price elasticity as well as of capital intensity with labor employment (that is, capital‐labor ratio as unity) determine spatial limits of the optimal production zone which is shifted outward subject to the provision of cheap transportation, stabilizing market prices and/or increasing wage rate at the market center. It will help in extending outwardly the optimal spatial limits of capital investment and will mobilize capital resources of farmers in the periphery for efficient and competitive capital‐dominated farming.     

SPATIAL ENTRY DETERRENCE UNDER OLIGOPOLY*

ABSTRACT. This paper examines colluding, oligopolistic firms in a linear market. By assuming that rivals do not compete for consumers at their market boundaries, it is shown that an equilibrium exists without adopting a convex transportation cost function. Two price profiles are derived. The first describes firm prices in the absence of threatened entry. The second details profit-maximizing prices which forestall entrants. Given infinite relocation costs, threatened entry leads to price adjustments by the incumbent firms.     

Optimal Facility Location in a One-Dimensional Spatial Market

This paper analyzes properties of the optimal spatial arrangement of what may be interpreted as a class of public facilities. Optimality is defined as cost minimization. Three different optimality criteria are considered, and for each, the necessary and, sufficient conditions, market area size, and production levels, are derived. The relationship between optimal production levels and number of facilities needed is also considered. Next the results of implementing various pricing strategies are analyzed with emphasis given to marginal and uniform pricing. It is shown that, given certain conditions, all facilities incur operating deficits, given marginal pricing. Estimates on the level of the deficits are derived in terms of location rents. Finally, in the appendix, several important results from other studies are derived as special cases of the basic model.     

Modeling Residential and Business Telecommunication Flows: A Regional Point-to-Point Approach

Regional telecommunication flows, measured in terms of numbers of messages and conversation minutes, are analyzed with a systematic random sample of toll calls characterized by their timing, duration, cost, and origin-destination (O-D) locations. Point-to-point models are econometrically estimated, with such independent variables as destination market size, O-D distance, and average and time-of-day (TOD) prices, for the residential and business sectors separately. The results indicate that (1) the demands for calls and conversation minutes are price-inelastic and slightly elastic, respectively, (2) business demand is relatively more price-elastic than residential demand, (3) distance is a strong determinant of telephone demand, and (4) most TOD demand substitutions resulting from TOD price changes would take place between the daily and evening rate periods. Several areas for further research are outlined.     

Fluctuation in the Random Spatial Economy and The Control of Inflation

A self-contained spatial economy is set out as the steady-state of a harmonic oscillator under Gaussian excitation. A dollar bill performs a random walk on a line with elastic barriers at each end and represents payments for traded goods. Diffusive surges of money and the fluctuations in zonal incomes are examined. The center, being less dependent on extra-zonal trade, has fewer brakes on price levels and can more easily begin “inflation.” Imposing a uniform deflationary policy would cause the periphery to be squeezed without reason while the center would be affected too little and too late. The organization of a futures market in construction is analyzed as a spatially discriminating form of control.     

TWO-DIMENSIONAL BERTRAND COMPETITION: BLOCK METRIC,EUCLIDEAN METRIC,AND WAVES OF ENTRY*

This paper examines two-dimensional spatial competition, with Bertrand price determination. With a block metric, equilibrium prices are significantly lower when market areas are squares than when they are diamonds (rotated squares) of the same size. If demand density grows, waves of entry occur, and the shapes of market areas change from squares to diamonds and back to squares again. The former change leaves prim unchanged, whereas the latter cuts prices in half. Results are also derived for a Euclidean metric, with square and hexagonal market areas. Optimal waves of entry are examined with the block metric. With either metric, the socially optimal market shape becomes suboptimal if market areas are constrained to be of the zero-profit size.     

The Location Invariance Theorem in Weberian Space Under Uncertainty

This paper examines the validity of the location invariance theorem in Weberian space under various types of uncertainty. The main results are: Given that the firm's location is constrained to remain at a specified distance from the output market, the optimal location is invariant to any change in product demand if and only if the production function is homothetic for a firm facing demand price uncertainty, or if the production function is homothetic and both inputs are risk-neutral for a firm facing technological uncertainty. Alternatively, given that the distance from the firm's location to the output market is a variable, location invariance occurs for a firm facing demand price uncertainty if the production function is linear homogeneous. In the presence of input price uncertainty the optimal location always varies with a change in product demand. The results can include those previously obtained for linear stochastic location models as special cases and some are new contributions to the literature.     

VALUING ENVIRONMENTAL QUALITY: A SPACE‐BASED STRATEGY*

ABSTRACT This paper develops and applies a space‐based strategy for overcoming the general problem of deriving the implicit demand for nonmarket goods. It focuses specifically on evaluating one form of environmental quality, distance from Environmental Protection Agency designated environmental hazards, via the single‐family housing market in the Puget Sound region of Washington State. A spatial two‐stage hedonic price analysis is used to: (i) estimate the marginal implicit price of distance from air release sites, hazardous waste generators, hazardous waste handlers, superfund sites, and toxic release sites; and (ii) estimate a series of implicit demand functions describing the relationship between the price of distance and the quantity consumed. The analysis, which represents an important step forward in the valuation of environmental quality, reveals that the information needed to identify second‐stage demand functions is hidden right in plain sight—hanging in the aether of the regional housing market.     

ZONE PRICING*

ABSTRACT. Our purpose is to study a spatial price policy often encountered in the real world, known as zone pricing. This price policy consists in determining simultaneously several delivered prices together with the geographical zones in which they apply. It is shown that zone pricing approximates perfect spatial price discrimination and that the firm's profit increases with the number of zones. Furthermore, the number of markets supplied by the firm rises with the number of zones. Finally, zone pricing is compared to other standard spatial price policies and possible extensions are discussed.     

A THEORETICAL FRAMEWORK FOR SMALL BUSINESS POLICY

A number of public policy issues have been discussed in this article, the most important of which are: 1. Small business would not need special consideration if our economy were basically a competitive one. 2. A large and growing segment of our economy has sufficient market and political power to make our economy basically non-competitive. 3. Small firms tend to provide price competition, to lead in the development of new products and processes, and to generate new innovations and new employment. 4. Government policy tends to create artificial economies of scale, giving an unwarranted advantage to the very large firm. As a first approximation, a policy of government neutrality on firms of varying size is needed. But, because of discriminations which already exist which favor large firms over small firms, special small business programs may be necessary to provide an equitable policy base. Unfortunately, programs designed to benefit all business, like the investment tax credit, tend to primarily benefit larger firms (Berney, 1979). This is the case for two reasons. First, there is a basic difference in production relationships: large firms tend to be more capital intensive and small firms more labor intensive. Second, the more complex a rule or regulation, the more costly it is for small business to use it. Consequently, even the employment tax credit, which should benefit the small firm is not used by them. Instead, it tends more to benefit the larger firm. Neutrality, as a governmental policy, would appear to demand different treatment for firms of varying size. As an example, the “regulatory flexibility” concept applies different standards to different sized firms so that the burden of regulation is more equitably distributed. The concept of encouraging or requiring financial institutions and other lenders to establish “dual prime rates” is a further example. Since small firms appear to have much higher debt to equity ratios and rely more heavily on shorter-term bank credit, they are more heavily burdened by a tight money policy which forces increases of interest rates. Thus, dual prime rates help to spread the burden of rising interest costs more equally. As many people prefer to work for themselves, equalizing the burden of government policy could only serve to increase the basic growth rate for small business, thus providing an easier start for entrepreneurs and would encourage a more rapid rate of economic growth. None of these discussions, however, argues that small business should be protected from failure. The more efficient firms will succeed and prosper, and the least efficient will not. Many currently successful entrepreneurs learn how to improve their production processes or managerial skills from their failures. What is being recommended as a first step is that government should concentrate on equalizing burdens and benefits in order to achieve true neutrality. If private economies of scale do indeed exist, new firms must grow to survive; what the government should not create are artificial economies of scale with public policy. A strong argument for further action can also be made: it appears that significant external benefits are produced by an economic system with a dynamic small business sector. Since these benefits go to society as a whole rather than entrepreneurs alone in the form of increased profits, a freely operating market without government assistance does not generate as many new small businesses as would be optimal for our society. To internalize the benefits that come from small business, governmental programs need to be devised to increase the rate of return on new, innovative small businesses. Should this happen, we could then anticipate increased rapid rates of innovation and technological change, more rapid rates of employment growth, expanded price competition in all sectors of the economy, and improved export capabilities, in short, true flexibility in our capitalistic system.     

城市住宅市场价格系统动力学模型实证研究

城市住宅市场价格影响因素复杂,必须用系统思想才能准确预测模拟其发展趋势。文章结合对兰州市住房市场的实证研究,从理论和实践两方面构建了城市住宅市场价格系统动力学仿真模型,并借助计算机利用系统动力学软件对模型进行了调试和分析,得到了比较令人满意的结果。认为,城市住宅价格系统动力学模型在以下三方面有较大的推广应用价值:①房地产市场趋势仿真模拟;②房地产政策研究和决策分析;③城市住宅市场系统内在机制研究。     

LOCATION,THEORY OF PRODUCTION,AND VARIABLE TRANSPORTATION RATES*

ABSTRACT. The question of what conditions insure independence between location and output decisions is investigated within the context of triangle space. Assuming that transportation rates vary with quantity and distance, it is shown that this independence is insured if the production function generates a linear expansion path and the following are all constant: transportation rate elasticities with respect to distance and quantity, and the price elasticity of demand for inputs.     

SPATIAL PRICING IN INTERDEPENDENT MARHETS*

ABSTRACT. Conditions for spatial price equilibrium are derived for a set of firms in oligopolistic spatial competition, distributed at fixed locations in a heterogeneous region where consumer purchasing patterns are a probabilistic function of the price distribution rather than a deterministic function of proximity to firms. The resulting prices vary with accessibility to consumers or with the degree of local spatial monopoly, and result in non-zero profits for firms. Conditions describing the existence and stability properties of this spatial price equilibrium are defined, and are shown to be equivalent for two different hypotheses concerning disequilibrium pricing behavior: a partial price adjustment model and a Bertrand game. For two different profit goals, total profit maximization and profit rate maximization, it is shown that a spatial price equilibrium exists and is at least locally quasi-stable.     

Spatial Price Discrimination in Two-Dimensional Competitive Markets

Intuition suggests that firms that can apply price discrimination make higher profits than firms that are restricted in their pricing policy. In this paper, we show that, in general, this is not the case. In the framework of a two-dimensional spatial model with elastic demand à la Lösch, we further investigate the interplay of transport costs, competition, and price policy. One of our results is that under realistic specifications of parameters each firm gains a monopolistic area in the center of its market that has the same shape as the entire market, but with a convexly or concavely distorted separating line, depending on the extension of the market.     

Housing Price Gradients: The Intersection of Space and Built Form

A hedonic housing price model, implemented for the Dallas region, reveals a housing market structured around multiple nodes, some of which give rise to positive and others to negative externalities. The utility/disutility derived from relative location is capitalized into the size and quality of the housing stock and the nature of neighborhood amenities. The result is a convergence of space and built form.     

ECONOMETRIC ANALYSIS OF HOUSING TRAIT PRICES IN A THIRD WORLD CITY*

ABSTRACT. A first step in the process of economic analysis of housing markets in Third World cities is the econometric analysis of housing trait prices. The information on market price of housing is basic to the derivation/estimation of other market parameters such as housing demand and supply elasticities. In addition, housing trait prices constitute invaluable inputs into the analysis of effects of government housing programs. This paper presents estimates of housing trait prices in a Third World city housing market, the city of Jos in Nigeria. Nonlinear stochastic specification of a policy constrained hedonic price function is presented as an unbiased estimator of housing trait prices. The Box-Cox statistical procedure was employed in the paper to obtain hedonic regression coefficients which are the parameters needed to compute the average prices evaluated both at the mean of each trait and at their margins. The potential uses of housing trait prices for policy analysis are discussed briefly.     

In Vindication of the Ghosh Model: A Reinterpretation as a Price Model

Ghosh's ‘supply-driven’ input-output model is a well-known alternative for Leontief's traditional ‘demand-driven’ input-output model. The Ghosh model calculates changes in gross sectoral outputs for exogenously specified changes in the sectoral inputs of primary factors. Typically, the model is interpreted so as to describe physical output changes as caused by changes in the physical inputs of primary factors. It has been convincingly argued, however, that this interpretation in terms of quantities is implausible. In the present paper it is shown that the supply-driven input-output model becomes plausible, once it is interpreted as a price model. That is, sectoral output values change due to price changes, which are caused by price changes for the primary inputs. Therefore the term Ghosh price model is adopted for the supply-driven model, whereas the demand-driven model is referred to as the Leontief quantity model. Dual to this Leontief quantity model is the standard Leontief price model. It is shown that the results obtained by the two price models are equivalent. Interpreting the supply-driven input-output model as a price model also allows for a meaningful interpretation of the inverse matrix in terms of multipliers. As the dual to the supply-driven (or Ghosh price) model the Ghosh quantity model is derived, which is equivalent to the demand-driven (or Leontief quantity) model.     

旅游景区一票制及其效率——基于产品捆绑定价模型的经济学分析

旅游景区一票制的理论基础是产品捆绑定价模型,但因为景区产品区别于其它一般产品,对景区进行捆绑定价时,不仅要考虑游客对景区的保留价格,还要考虑游客对景区时间消费量的预期（即保留时间）。本文通过只包含两个景区的保留价格一保留时间模型,对游客闲暇时间约束下的景区一票制定价及其绩效进行了分析,并推出了以下结论：（1）除了游客保留价格和保留时间,套票有效期的长短、参与一票制的景区数量的多少等也会影响一票制效率;（2）混合票制会增加效益,而纯一票制的效益不如非一票制的效益好。笔者在此基础上提出了一些建议。     

Collective Amnesia and the Mediation of Painful Pasts: the representation of France in the Second World War

This paper describes research that was designed to examine the assertion that historic designation of properties, under the heritage legislation in Canada's largest province, has a negative impact on the values of those properties. The actual selling price of subject properties was used to establish their value history trends, which were then compared to ambient market trends within the same communities. Almost 3,000 properties in twentyfour communities were investigated, in what is believed to be the largest study of its kind ever undertaken in North America. It was found that heritage designation could not be shown to have a negative impact. In fact there appears to be a distinct and generally robust market in designated heritage properties. They generally perform well in the market, with 74% doing average or better than average.The rate of sale among designated properties is as good or better than the ambient market trends and the values of heritage properties tend to be resistant to downturns in the general market.     

OPTIMALITY OF RECYCLING AND THE LOCATION OF A RECYCLING CENTER

ABSTRACT. Consider a community investigating the integration of recycling into its waste management program. Even if (1) the county's citizens do not gain utility from recycling, (2) landfill space is plentiful, and (3) the market price for recyclables is zero, recycling can still be optimal for a local government. By determining the relationship between the amount of recycling and the location of a recycling center, conditions are identified under which recycling will reduce total waste management costs enough that municipal recycling will be optimal. In addition, it is shown that the likelihood of municipal recycling increases with the size of the city.