Quadratic Production Research Articles

An interval multi-objective fuzzy-interval credibility-constrained nonlinear programming model for balancing agricultural and ecological water management

This study presents an interval multi-objective fuzzy-interval credibility-constrained nonlinear programming (IMFICNP) model combined with spatial water requirement of ecological vegetation (SEWR) estimation for solving the problem of allocation of agricultural and ecological water in irrigation districts under uncertainties. Through techniques of remote sensing (RS) and geographic information system (GIS), the ecological vegetation is subdivided into three types including forest land, grassland and shrubland and the water requirement of ecological vegetation is extended from site-specific sample to spatial decision-making unit (DMU), which provides a set of spatial data for input parameters of constraints. The IMFICNP model can be formulated through combination of interval parameter programming, multi-objective programming and fuzzy-interval credibility-constrained programming, which can handle the conflicts of multiple objectives under uncertainties such as single uncertainty (interval and fuzzy parameters) and dual-uncertainties (fuzzy-interval sets), and finally generate optimal water allocation schemes for crop and ecological vegetation under different credibility levels. The interval quadratic crop water production functions (IQCWPFs) are introduced to express the nonlinear relationships between crop yield and irrigation amount. Then, this model is applied to a case study of Huangyang Irrigation District (HID) in Shiyang River Basin to demonstrate its applicability. The results indicate that a higher credibility level is accompanied by less amount of water allocation and lower system benefit. The amount of water allocation at the DMU is dominated by planting area of crops and ecological vegetation, but there are few exceptions that optimal solutions are determined by the economic value. In addition, SEWR enables to reflect spatial heterogeneity of the DMU at a larger scale. IMFICNP model can coordinate conflicts among multiple objectives and it can tackle the violation of system constraints with fuzzy-interval sets. Therefore, these results can effectively balance the agricultural and ecological water management in irrigation districts, and provide valuable basis for the sustainable development of arid and semi-arid areas.

Comparison of two finite element schemes for a chemo-repulsion system with quadratic production

In this paper we propose two fully discrete Finite Elements (FE) schemes for a repulsive chemotaxis model with a quadratic production term. The first one, which corresponds to the backward Euler in time with FE in space, is energy-stable in the primitive variables of the model, under a “compatibility” condition on the FE spaces. The second one, which is obtained modifying the scheme proposed in [13] by applying a regularization procedure, has an “approximated positivity” property which is obtained from discrete energy estimates and an additional estimate for a singular functional. These properties are not available in previous approaches. Additionally, we study the well-posedness and the long time behaviour of the schemes, obtaining exponential convergence to constant states as in the continuous problem. Finally, we compare the numerical schemes throughout several numerical simulations, which are in agreement with the theoretical results.

Dynamic wage bargaining and labour market fluctuations: the role of productivity shocks

In this paper, we explore the way in which different bargaining settings affect labour market fluctuations by means of an analytical apparatus that has never been used for this purpose. Specifically, modelling wage negotiations as a problem of stochastic optimal control, we analyze how productivity disturbances shape the dynamics of output, employment, and wages by focusing on the way in which firms’ technology and workers’ preferences interact with the adjustment rules of employment underlying the bargaining process. With a quadratic production function and risk averse workers, we show that wage negotiation outcomes whose employment adjustments go in the direction of the labour demand of the firms match the cyclical behaviour of the involved variables but fail to replicate the observed wage rigidity. By contrast, we show that wage bargaining outcomes whose employment adjustments target the contract curve of two negotiating parties are also able to deliver a strong degree of wage stickiness.

Predicting Immediate Marginal Milk Responses and Evaluating the Economics of Two-Variable Input Tactical Feeding Decisions in Grazing Dairy Cows.

Simple SummaryIn Australia, feeding grazing dairy cows concentrate and forage supplements is common. Dairy farmers face the challenge of profitably feeding their cows in situations where there is significant variation in feed costs and milk price. We used the results of grazing experiments to develop equations that predict the yield of milk fat and milk protein when different combinations of concentrates and pasture + forage are fed to grazing lactating dairy cows. We applied economic principles to these predictions to estimate the optimal combination of these feeds for given costs and prices. Feed is the largest variable cost in dairying. The allocation of pasture and supplements that are based on better estimates of milk responses to supplements should lead to increased profit for farmers.Feed is the largest variable cost for dairy farms in Australia, and dairy farmers are faced with the challenge of profitably feeding their cows in situations where there is significant variation in input costs and milk price. In theory, the addition of 5.2 MJ of metabolisable energy to a lactating cow’s diet should be capable of supporting an increase in milk production of one litre of milk of 4.0% fat, 3.2% protein and 4.9% lactose. However, this is almost never seen in practice, due to competition for energy from other processes (e.g., body tissue gain), forage substitution, associative effects and imbalances in rumen fermentation. Pasture species, stage of maturity, pasture mass, allowance and intake, stage of lactation, cow body condition and type of supplement can all affect the milk protein plus fat production response to additional feed consumed by grazing dairy cows. We developed a model to predict marginal milk protein plus fat response/kg DM intake when lactating dairy cows consume concentrates and pasture + forages. Data from peer reviewed published experiments undertaken in Australia were collated into a database. Meta-analysis techniques were applied to the data and a two-variable quadratic polynomial production function was developed. Production economic theory was used to estimate the level of output for given quantities of input, the marginal physical productivity of each input, the isoquants for any specified level of output and the optimal input combination for given costs and prices of inputs and output. The application of the model and economic overlay was demonstrated using four scenarios based on a farm in Gippsland, Victoria. Given that feed accounts for the largest input cost in dairying, allocation of pasture and supplements that are based on better estimates of marginal milk responses to supplements should deliver increased profit from either savings in feed costs, or in some cases, increased output to approach the point where marginal revenue equals marginal costs. Such data are critical if the industry is to take advantage of the opportunities to use supplements to improve both productivity and profitability.

Cultivating marine macroalgae in CO2-enriched seawater: A bio-economic approach

By the end of the current century atmospheric CO2 concentration may reach 1000 ppm, more than twice the present level set at ca. 400 ppm. Marine macroalgae (seaweeds) contribute to global primary production and by taking up CO2 they may ameliorate and regulate global climate change. Seaweeds also have direct and indirect economic importance by providing food and bioactive compounds for human benefit. Nonetheless, all these benefits could be jeopardized by the ongoing pressures, both local and global, on marine environments. In this study we examine the effects of dissolved CO2 and seasonal seawater temperature on the growth rates (measured weekly changes in biomass and expressed on a daily basis) of two model species, Ulva rigida (Chlorophyta) and Gracilaria conferta (Rhodophyta), which are common in the intertidal zone of the Israeli Mediterranean Sea, and cultivated by the local seaweed industry. The seaweeds were grown in land-based 40 L fiberglass tanks fertilized with sufficient N and P, supplied with running seawater and continuous air bubbling to keep equal exposure of the seaweeds to nutrients and light. The tanks were also provided with aeration with regular air (ambient CO2, ~ 400 ppm) or CO2-enriched air (~780 ppm). Seaweeds exposed to CO2–enriched seawater grew faster, 32.5 and 8.5% growth per day for U. rigida and G. conferta, respectively. Following calculations of productivity rates, market price, and input cost, we estimate production and show a quadratic production function with respect to temperature for each CO2 concentration. Thus, there is an optimal temperature that maximizes seaweed output. Based on the production function estimates and using market prices, maximal short-run profits were obtained at ca. 22.5 °C and 27.5 °C for U. rigida and G. conferta, respectively. These results may provide useful information for seaweed growers on what and where to grow seasonally, and how farming activities should adapt to external changes in temperature and CO2 concentration.

134 Meta-analysis to Determine the Effects of Particle Size on Nursery and Finishing Pig’s Growth Performance and Stomach Morphology

Abstract A meta-analysis was conducted to determine grain particle size (PS) effects on pig growth performance and stomach morphology. Data from 29 trials (11 in the nursery and 18 in the finisher) published from 1986 to 2016 for a total of 140 observations were recorded in a database. The response variables were average daily gain (ADG), average daily feed intake (ADFI), gain-to-feed ratio (G:F), ulceration and keratinization scores. Tested predictors included the interactions between PS linear and quadratic effects, production phase, diet form, and main effects of grain type, ingredient inclusion, and mill type. Trial was included as a random effect. Data were analyzed with the lmer function from the lme4 package in R. Significant predictors (P < 0.05) and with improved model fit remained in the final model. Results indicated a significant interaction (P < 0.05) between diet form and quadratic PS for ADFI and G:F. Nursery and finishing pigs fed meal diets linearly reduced ADFI and improved G:F as PS reduced. Nursery pigs fed pelleted diets had reduced ADFI and improved G:F with PS reduced to 500–600µ, with increased ADFI and poorer G:F at lower PS. Finishing pigs fed pelleted diets had reduced ADFI and improved G:F with PS reduced to 500–600µ, with no further changes at lower PS. Regardless of diet form and production phase, ADG increased (quadratic, P < 0.05) as PS reduced until approximately 600µ and decreased at lower PS. There was no evidence of PS effect on ulceration score (P = 0.12). Keratinization score increased (P < 0.05) as PS decreased. Reducing PS in meal diets linearly increased keratinization scores, reduced ADFI, and improved G:F. However, no further benefits in performance were observed at grain PS below 500–600µ in pelleted diets.

Robust Model for the Quadratic Production Function in Presence of High Leverage Points

Robust Model for the Quadratic Production Function in Presence of High Leverage Points

Tax competition and club goods

We augment the traditional model of tax competition with spillovers in public good provision. In our model, identical countries compete for mobile capital. A subset of these countries can coordinate their taxes and provide a public good that generates international spillovers. This subset forms a club of high taxes. Adopting a utility function that is linear for the public good and a quadratic production function, we calculate the equilibrium tax rates and capital allocation. The partial tax equilibrium is analogous to size differences. We show that the utility of both club and non-club countries increases with the number of participating members. We also demonstrate that an increase in the degree of spillovers benefits all, including countries outside the club, even though outsiders do not directly benefit from the spillovers. We show that in a world with many tax competitors, spillovers can restore the stability of cooperation and compensate for incentives to exit the club to win the tax competition.

Irrigation water resources management under uncertainty: An interval nonlinear double-sided fuzzy chance-constrained programming approach

An interval nonlinear double-sided fuzzy chance-constrained programming (INDFCCP) approach is formulated to effectively allocate irrigation water among competing water users. The INDFCCP approach is formulated by combining inexact quadratic programming (IQP) and double-sided fuzzy chance-constrained programming (DFCCP) within a general optimization framework. This approach has the following features. (1) It’s able to handle interval and fuzzy uncertainties, and nonlinearity existing in the objective functions. (2) It’s capable of addressing these fuzzy constraints and fuzzy variables where different confidence levels and satisfaction degree levels should be satisfied. (3) Each fuzzy chance-constraint can be further analyzed with the maximum and minimum reliability scenarios, which makes it possible to reflect variations of system conditions. (4) Interval quadratic crop water production functions (IQCWPFs) are employed in place of deterministic ones to quantitatively describe the mathematical relationships between crop yields and actual crop evapotranspiration (or irrigation water applied). Then, to demonstrate its applicability and feasibility, the INDFCCP approach is applied in the Yingke Irrigation District (YID), northwest China for allocating irrigation water to three crops in three subareas under uncertainty. Finally, more flexible decision solutions regarding optimal irrigation water allocation have been generated and analyzed under different predetermined confidence levels, showing several advantages of the INDFCCP approach with respect to the deterministic one. Under the same confidence level, system benefits under the minimum reliability scenario (e.g. [499.6, 909.7] × 106 Yuan, α = 0.5) are higher than that under the maximum reliability scenario (e.g. [498.7, 908.9] × 106 Yuan, α = 0.5). From above outcomes, the INDFCCP approach provides more appropriate results and reliable scientific bases needed for better managing irrigation water in irrigated agricultural areas.

An Assessment of the Site-Specific Nutrient Management (SSNM) Strategy for Irrigated Rice in Asia

The site-specific nutrient management (SSNM) strategy provides guidelines for effective nitrogen, phosphorus and potassium management to help farmers make better decisions on fertilizer input and output levels in rice (Oryza sativa) production. The SSNM fertilizer recommendations are based on the yield goal approach, which has been frequently cited in empirical studies. This study evaluates the assumptions underlying the SSNM strategy for rice in the top rice-producing countries around the world, including India, Indonesia, the Philippines, Thailand, and Vietnam. Using a generalized quadratic production function, I explore whether major nutrients are substitutes as inputs and if there are complementarities between inorganic fertilizer and soil organic matter (SOM). The results suggest the relationships among major nutrients vary across sites—some inputs are complements, some are substitutes, and some are independent. The SOM also significantly affects the nitrogen fertilizer uptake. I conclude by suggesting that the SSNM strategy can be made to be more adaptive to farmer’s fields if these relationships are accounted for in the fertilizer recommendation algorithm.

Stability of cartels in Multimarket Cournot oligopolies

AbstractWe investigate the stability of cooperation agreements, such as those agreed by cartels, among firms in a Cournot model of oligopolistic competition embedded in a multimarket contact setting. Our analysis considers a broad array of 64 potential market structural configurations under linear demand and quadratic production costs. We establish that for an appropriate range of parameter values there exists a unique core stable market configuration in which an identical two‐firm cartel is sustained in both markets. Our result highlights the significance of multimarket presence for cartel formation in light of the well‐known result from the single‐market setting where cartels are non‐profitable.

Equilibrium existence in the Hotelling model with convex production costs

We revisit the spatial duopoly model à la Hotelling (1929), to show that, provided the parameter scaling marginal cost is sufficiently high, quadratic production costs guarantee equilibrium existence in presence of linear transportation costs and a uniform distribution, with minimum product differentiation and no undercutting. We also discuss the conditions under which partial coverage arises. Finally, we extend the duopoly game to generalise the condition for the existence of the pure-strategy equilibrium to a class of convex production cost functions.

Study of a chemo-repulsion model with quadratic production. Part I: Analysis of the continuous problem and time-discrete numerical schemes

We consider a chemo-repulsion model with quadratic production in a bounded domain. Firstly, we obtain global in time weak solutions, and give a regularity criterion (which is satisfied for 1D and 2D domains) to deduce uniqueness and global regularity. After, we study two cell-conservative and unconditionally energy-stable first-order time schemes: a (nonlinear and positive) Backward Euler scheme and a linearized coupled version, proving solvability, convergence towards weak solutions and error estimates. In particular, the linear scheme does not preserve positivity and the uniqueness of the nonlinear scheme is proved assuming small time step with respect to a strong norm of the discrete solution. This hypothesis is reduced to small time step in nD domains (n≤2) where global in time strong estimates are proved. Finally, we show the behavior of the schemes through some numerical simulations.

Study of a chemo-repulsion model with quadratic production. Part II: Analysis of an unconditionally energy-stable fully discrete scheme

This work is devoted to the study of a fully discrete scheme for a repulsive chemotaxis with quadratic production model. By following the ideas presented in Guillén-González et al. (2020), we introduce an auxiliary variable (the gradient of the chemical concentration), and prove that the corresponding Finite Element (FE) backward Euler scheme is conservative and unconditionally energy-stable. Additionally, we also study some properties like solvability, a priori estimates, convergence towards weak solutions and error estimates. On the other hand, we propose two linear iterative methods to approach the nonlinear scheme: an energy-stable Picard method and Newton’s method. We prove solvability and convergence of both methods towards the nonlinear scheme. Finally, we provide some numerical results in agreement with our theoretical analysis with respect to the error estimates.

The supermodularity of the tax competition game

Tax competition is often associated with the “race to the bottom:” a decrease in the tax rate of one jurisdiction (country, region or municipality) triggers similar reactions in neighboring jurisdictions. This race can be related to two properties of the tax competition game: positive tax spillovers and the strategic complementarity of tax rates. Using tools from generalized concavity, more precisely r-concavity, and supermodular games, this paper offers a simple yet unifying perspective on the fundamental forces that shape tax competition. The main results characterize sufficient conditions on the marginal productivity of tax competing jurisdictions to predict a “race to the bottom.” These conditions bind the curvature of the demand for capital of each tax-competing jurisdiction. Quadratic production function respects these, while Cobb–Douglas form requires an additional condition. We deduce several results: at least one pure-strategy Nash equilibrium exists and is unique. Going beyond our specific framework, we apply some results of supermodular games with positive spillovers: in case of multiple equilibriums, tax coordination is Pareto improving; but the coalition of a subgroup of countries does not achieve neither tax coordination, nor tax cooperation. Establishing similar sufficient conditions for the supermodularity of the tax competition game with welfare maximizers raises multiple issues. Besides the question of the nature of public spending, we discuss the role of capital by considering an elastic worldwide stock of capital, capital ownership, and offshore centers.

Penentuan Umur Optimal Peremajaan Kelapa Sawit di Kabupaten Paser Kalimantan Timur

Determining of optimal replanting age of oil palm helps farm households to prepare replanting investment. This research was to detemine optimal age for replanting of oil palm and to evaluate the sensitivity of optimal replanting age when there are changes in output price, cost, interest rate, and yield. The number of samples are 268 oil palm farm household. The farmers, age of oil palm and location were taken based on purposive sampling. Data were analyzed using profit maximization concept with Comparison of Equivalent Annual Net Revenue (CEAN) method. The result showed that the optimal replanting age of oil palm with quadratic production function and cubic production function was between 33 and 35 years. The optimal replanting age was sensitive to changes on interest rate, price of fresh fruit bunch, farm cost, and productivity.

Farm Technologies and Production Risk in the Face of Climate Change in Tanzania

In countries where insurance and credit markets are thin or missing, production and consumption risks play a critical role in the choice and use of production inputs and adoption of new farm technologies. This paper investigated the effect of selected farm technologies and their risk implications in different rainfall patterns of Pangani river basin in Tanzania. Given the production risks posed by climate change, such information can be used by decision makers to identify appropriate agricultural practices that act as a buffer against climate change. Using a household and plot-level data set, Just and Pope framework was applied to using a quadratic production function to investigate the impact of selected farm technologies on average crop yields and the variance of crop yields, while controlling for several household and plot level factors. The results revealed that farm technologies perform differently in different rainfall areas, which underscores the importance of careful geographical targeting when promoting and up-scaling farm technologies adoption to climate change.

Manufacturing High-Tech Products Subject to Rapid Obsolescence

We formulate a production problem in high-tech industry as a free-final-time optimal control problem. The instance with linear production cost is equivalent to a problem proposed by Pangburn and Sundaresan. The instance with quadratic production cost allows us to find a solution which is closer to what is seen in the real world. In the latter instance, the optimal production rate is strictly decreasing in a neighborhood of the final time.

Dynamics of a Bertrand duopoly with differentiated products and nonlinear costs: Analysis, comparisons and new evidences

This paper studies mathematical properties and dynamics of a duopoly with price competition and horizontal product differentiation by introducing quadratic production costs (decreasing returns to scale), thus extending the model with linear costs (constant returns to scale) of Fanti et al. [11]. The economy is described by a two-dimensional non-invertible discrete time dynamic system. The paper first determines fixed points and other invariant sets, showing that synchronized dynamics can occur. Then, stability properties are compared in the cases of quadratic costs and linear costs by considering the degree of product differentiation and the speed of adjustment of prices as key parameters. It is also shown that synchronization takes place if products tend to be relatively complements and stressed similarities and differences between models with quadratic and linear costs. Finally, the paper focuses on the phenomenon of multistability thus underlying new evidences in comparison with the model with linear costs.

Competition and privatization policies revisited: the payoff interdependence approach

We investigate the relationship between competition and privatization policies. Existing studies measure the strength of competition based on the number of firms, and show that the optimal degree of privatization is higher in more competitive markets. We introduce an interdependent payoff structure into a mixed oligopoly and revisit this problem. Here, we assume that firms consider their own and other firms’ profits. In the model, competition increases when firms are negatively affected by rivals’ profits. We find that under the assumption of quadratic production costs, which is popular in mixed oligopolies, the optimal degree of privatization is higher when there is less market competition. This finding contrasts with those of prior studies. However, this result may be reversed when we adopt alternative model formulation. Furthermore, in the constant marginal cost case, the optimal degree of privatization is always lower when there is less market competition, which is opposite to the result in the quadratic cost case. Our results suggest that the relationship between an optimal privatization policy and the strength of competition crucially depends on the market structure, including the cost conditions.