Nonlinear Demand Research Articles

Nonlinear demand response programs for residential customers with nonlinear behavioral models

To mitigate environmental issues of the thermal power plants, their greenhouse gas emissions are factored into the unit commitment (UC) problem. Moreover, demand side management as an effective strategy can relieve the energy security and environmental issues. Thus, the residential customers as one of the major groups of the customers, should be incorporated in the UC and generation scheduling problems. In this study, implementation of demand response (DR) programs in the UC problem are modeled. Herein, the implemented DR programs are entitled nonlinear DR (NDR) programs because nonlinear behavioral models for the residential customers are considered. In addition, the value of cost correlated with the implementation of the NDR programs in the UC problem (UC-NDR) are modeled. It is demonstrated that cooperation of the residential customers in the UC-NDR problem can be beneficial in decreasing cost and greenhouse gas emissions of the thermal power plants. In addition, it is concluded that comprehensive studies are needed to realistically model the residential customers behavior, since the different behavioral models result in different solutions and outcomes for the UC-NDR problem.

Rapid Economic Growth in India

We explore till 2040 the role of technical change in agriculture, irrigation and concern for food security in rapid economic growth in India. India aspires to achieve double-digit growth. For a densely populated country of 1.2 billion people with growing incomes meeting its increasing and diversifying food needs will be a challenge. We explore this using a multi-sector, inter-temporal optimising model with 20 expenditure classes, 10 rural and 10 urban, each with its own linear expenditure system derived from an underlying non-linear demand system. We also assess the diversification of demand that is likely to occur and impact on poverty under different alternatives. At least a 4 per cent growth rate of agricultural gross domestic product (GDP) is needed to support GDP growth rates in excess of 8 per cent for which a slightly optimistic agriculture TFPG growth rate of 2 per cent along with a slightly optimistic development of irrigation potential to 90 million hectare (Mha) (net) is needed. JEL Classification: C61, C67, O13, O21, O33

Memory, market stability and attractors coexistence in a nonlinear cobweb model

We investigate the dynamics of a cobweb type model with nonlinear demand and supply curves in which producers make forecasts on future prices with a backward looking expectation formation mechanism: the expected price for the next period is obtained by a weighted average of the prices observed in the last two periods. The study herewith presents aims at confirming the existence of a locally stabilising effect due to the presence of memory, but an increase of memory in price expectations can be globally qualitatively destabilising, in the sense that it leads to coexistence of different attractors with their respective basins of attraction.

How Meat Demand Elasticities Vary with Price, Income, and Product Category

As US beef and pork prices approached record high levels in 2014, industry analysts expressed surprised at consumer response. Because the relative price swings have occurred only recently, traditional approaches to demand analysis that rely on historical data series may be less useful than is typically the case. Employing one of the largest and longest‐running choice experiments, we analyze data on 110,295 choices made by 12,255 consumers observed over a year‐long time period coinciding with historically high meat prices. Our findings reveal nonlinear demands for meat products, with demand being more inelastic at higher prices. Ground beef, steak, and pork chop demands are more sensitive to changes in chicken breast price than the reverse. Moreover, cross‐price elasticities between disaggregate meat products shrink as prices rise. Consumers' incomes significantly affect demand inter‐relationships. Higher income consumers are more likely to choose steak and chicken breasts and are less likely to choose ground beef, chicken wings, and deli ham than are lower income consumers. High‐income consumers tend to be less responsive to own‐price changes and more responsive to cross‐price changes than lower income consumers. This analysis provides estimates of structural demand parameters that help explain current meat expenditure patterns, and the results have implications for the assumption of linearity often invoked in policy analyses.

Optimal product pricing and lot sizing decisions for multiple products with nonlinear demands

Most manufacturing firms consider product pricing as a key strategic decision. Production planning and scheduling, on the other hand, are mostly treated as a non-strategic decisions. Most businesses, therefore, follow some sequential decision-making process; where product prices are determined first and then operational plans are made to fulfill the resulting demand at the lowest possible cost. In this paper, we present a coordinated decision model approach for multi-product pricing and lot sizing decisions for a manufacturer who has limited production capacity. Although the presented model is specific to demands that follow constant elasticity of the price, it can easily be extended to other convex demand functions. We show that a coordinated decision-making process where price and production plans are determined simultaneously may lead to substantially higher profits. We propose an efficient solution methodology for finding optimal prices and product quantities and use real-world data to demonstrate the applicability of this research.

Stochastic volatility demand systems

ABSTRACTWe address the estimation of stochastic volatility demand systems. In particular, we relax the homoscedasticity assumption and instead assume that the covariance matrix of the errors of demand systems is time-varying. Since most economic and financial time series are nonlinear, we achieve superior modeling using parametric nonlinear demand systems in which the unconditional variance is constant but the conditional variance, like the conditional mean, is also a random variable depending on current and past information. We also prove an important practical result of invariance of the maximum likelihood estimator with respect to the choice of equation eliminated from a singular demand system. An empirical application is provided, using the BEKK specification to model the conditional covariance matrix of the errors of the basic translog demand system.

Oligopolistic interacting markets

A model of several interacting Cournot markets is considered. The markets are named interacting because the same number of producers act on each of them. Every producer chooses his own supply volumes on every market using the price situations, his own costs, and production and delivery limitations. It is proved that in the case of linear demand functions the problem of finding the Nash equilibria in the model of interacting Cournot markets represents a potential game, i.e., it is equivalent to a mathematical programming problem. Nonlinear demand functions linearization procedures and preferences of initial problem reduction to the potential game are discussed.

Four Express Service Cooperation Modes for B2C E-Commerce

The express service quality becomes a dominant factor along with the price of product affecting consumer's purchasing decision. This paper investigates how the express service quality affects the demand of online purchasing, and how to improve the express service quality and supply chain's performance through cooperation. The authors consider an online supply chain and utilize a nonlinear demand model by incorporating the express service quality as a decision variable and propose four express service cooperation modes, i.e. (1) the retailer offering subsidy to the express provider, (2) the integration between the retailer and the express provider, (3) the manufacturer offering subsidy to the express provider and (4) the integration between the manufacturer and the express provider. In each cooperation mode, they derive the equilibrium pricings, service levels, demands and profits. By comparison, the authors explore which one is appropriate for chain members to implement.

Probabilistic Seismic Assessment of RC Bridges: Part II — Nonlinear Demand Prediction

One of the most determinant components of any seismic safety assessment procedure is the estimate of the nonlinear seismic demand, particularly if such procedure is probabilistic rather than deterministic. Indeed, the prediction of the seismic demand of RC structures is dictated by a number of variables, related to the seismic action or to the geometrical and material properties, with different relevancy and uncertainty levels. From a macro-viewpoint one can distinguish the different approaches for nonlinear demand prediction in two major groups: nonlinear static and dynamic. Whereas the latter is widely recognised as the most accurate approach, the former, particularly by means of nonlinear static procedures (NSPs), represents a valid alternative tool for performance-based seismic assessment of structures, quite accepted among the scientific community worldwide. Significant effort has therefore been made, over the past few years, to improve those simplified methods and several different proposals in terms of application methodology have come up. Simultaneously, validation studies have thoroughly been carried out, even though focusing mainly on regular, building structures, rather than typically irregular bridges, and have focused the validation through the direct comparison of response prediction. The capability of such procedures within a probabilistic framework that yields the collapse probability of randomly sampled RC viaducts is herein investigated. A commonly employed nonlinear static procedure (N2) is further validated against nonlinear dynamic analysis using two distinct probabilistic procedures, described and tested in a companion paper, which account differently for the uncertainty of the concerned variables (geometry, material properties, earthquake records, intensity level). A case study of seven bridge configurations, with different (ir)regularity levels, is considered together with a relatively large set of real earthquake records and random simulation is carried out using the Latin Hypercube Sampling scheme. The conclusions have further probed the suitability of nonlinear static analysis in estimating seismic demand by leading, under probabilistic conditions, to slightly conservative probabilities of collapse of RC bridges with respect to nonlinear dynamic analysis.

Two different routes to complex dynamics in an heterogeneous triopoly game

We study a triopoly game with heterogeneous players. The market is characterized by a nonlinear (isoelastic) demand function and three competitors. The main novelty is the double route to complex dynamics that we find and is quite rare in heterogeneous triopoly models. We show that the two routes have important implications for the economic interpretation of the dynamics emerging when the Cournot–Nash equilibrium becomes locally unstable. Moreover the model displays multistability of different attractors, requiring a global analysis of the dynamical system.

Spatial Cournot competition in a linear–circular market

This paper explores a linear and circular model with spatial Cournot competition. It is shown that agglomeration of firms at the center of the main street is the equilibrium when the demand density on the main street (linear market) is high, and there exists a unique separated location equilibrium when the density is moderate. Moreover, the socially desirable interior locations are more dispersed than the equilibrium ones. Finally, extensions on tax policies, nonlinear demand, non-uniform distribution, and others are also discussed.

Dynamic Cournot duopoly games with nonlinear demand function

In this paper, dynamic duopolistic Cournot models are investigated with discrete time scales under the assumption of unknown inverse demand function and linear cost. With this motivation, we consider different types of models: bounded rational duopoly, Puu’s duopoly, bounded rational duopoly with delay, and bounded rational multi-team model. In these models, the firms use two important adjustment mechanism, the bounded rationality and Puu’s approach, to update their quantity in each period. The locally asymptotic stability of the fixed point of each model is investigated and complex dynamic characteristics including period doubling bifurcation, strang attractors and chaotic phenomena are also discussed. Numerical simulations are carried out to show such complex behavior of the four models and to point out the impact of the models’ parameters on the stability of the fixed points.

Demand Uncertainty and the Bayesian Effect in Markdown Pricing with Strategic Customers

This paper studies the role of demand uncertainty in temporal discrimination when the retailer applies markdown pricing facing strategic customers. We consider a model in which a retail firm announces a pair of declining prices for two selling periods, and customers with heterogeneous valuations each decide whether to buy a unit early, later or never. In this model, if the demand function is linear and its parameters are common knowledge, there never exist any markdown prices that achieve temporal discrimination for any feasible model parameters. Either all buying customers wait, or all buy early. By contrast, if the demand level is unknown, there always exists a temporally discriminating markdown pricing scheme for all feasible model parameters. We derive qualitative insights to the way demand uncertainty and Bayesian updating contribute to temporal discrimination, which broadly apply to nonlinear demand functions as well. We also show that in case of demand uncertainty, there always exists a temporally discriminating pricing scheme that yields a strictly higher profit to the retailer than the optimal static pricing scheme. Ironically, however, the retailer cannot implement the optimal scheme due to the same demand uncertainty.

Coordination contracts for competitive two-echelon supply chain with price and promotional effort sensitive non-linear demand

In this study, our objective is to analyse the effects of a competitive supply chain with single commodity, multiple retailers and a common supplier when there is a rivalry among the retailers. The market demand of the product is assumed to be price dependent and to be enhanced by providing effective promotional effort. We also assume that the supplier's wholesale price is the same for all retailers. The retailers determine their market sales price(s) and promotional efforts to optimise the profit from the perspectives of the individual and the whole supply chain. We also analyse the coordination mechanisms among the members of the chain with several contracts and find the optimal range for the contract parameters. Finally, we investigate the model by the collective numerical data and also provide the graphical illustration of the comparison among the coordination mechanisms by the contracts.

Non-linear Demand and Price: An Empirical Analysis of the Brazilian Industrial Electricity Consumption

In this paper we proposed an econometric model for industrial electricity demand in Brazil. Differently from residential customers, industries in Brazil, in addition to purchasing energy and capacity, also face a tariffmenu with Time of Use pricing. Each item in this menu also has different components and price discrimination structure. All these characteristics pose an empirical problem that, so far, has not been faced together in the literature. This methodology was applied in a non-experimental micro data sample of 646 large Brazilian industrial customers (with demands over 300 KW) between January 2002 and December 2006. The results indicate demands for the various services (capacity and energy, separated between peak and non-peak hours) are price elastic, and at least in the AZUL tariff, there is complementarity between energy and capacity in the different periods. Thus, policies on tariff structures based on assumptions of an inelastic aggregate electricity demand could have effects that are quite different from what was intended.

Properties of instrumental variables estimation in logit-based demand models

Purpose – This paper aims to investigate the effects of using poor-quality instruments to remedy endogeneity in logit-based demand models. Endogeneity problems in demand models occur when certain factors, unobserved by the researcher, affect both demand and the values of a marketing mix variable set by managers. For example, unobserved factors such as style, prestige or reputation might result in higher prices for a product and higher demand for that product. If not addressed properly, endogeneity can bias the elasticities of the endogenous variable and subsequent optimization of the marketing mix. In practice, instrumental variables (IV) estimation techniques are often used to remedy an endogeneity problem. It is well-known that, for linear regression models, the use of IV techniques with poor-quality instruments can produce very poor parameter estimates, in some circumstances even worse than those that result from ignoring the endogeneity problem altogether. The literature has not addressed the consequences of using poor-quality instruments to remedy endogeneity problems in non-linear models, such as logit-based demand models. Design/methodology/approach – Using simulation methods, the authors investigate the effects of using poor-quality instruments to remedy endogeneity in logit-based demand models applied to finite-sample data sets. The results show that, even when the conditions for lack of parameter identification due to poor-quality instruments do not hold exactly, estimates of price elasticities can still be quite poor. That being the case, the authors investigate the relative performance of several non-linear IV estimation procedures utilizing readily available instruments in finite samples. Findings – The study highlights the attractiveness of the control function approach (Petrin and Train, 2010) and readily available instruments, which together reduce the mean squared elasticity errors substantially for experimental conditions in which the theory-backed instruments are poor in quality. The authors find important effects for sample size, in particular for the number of brands, for which it is shown that endogeneity problems are exacerbated with increases in the number of brands, especially when poor-quality instruments are used. In addition, the number of stores is found to be important for likelihood ratio testing. The results of the simulation are shown to generalize to situations under Nash pricing in oligopolistic markets, to conditions in which cross-sectional preference heterogeneity exists and to nested logit and probit-based demand specifications as well. Based on the results of the simulation, the authors suggest a procedure for managing a potential endogeneity problem in logit-based demand models. Originality/value – The literature on demand modeling has focused on deriving analytical results on the consequences of using poor-quality instruments to remedy endogeneity problems in linear models. Despite the widespread use of non-linear demand models such as logit, this study is the first to address the consequences of using poor-quality instruments in these models and to make practical recommendations on how to avoid poor outcomes.

UTILIZATION OF ARMA MODELS TO MEASURE DAMAGE POTENTIAL IN SEISMIC RECORDS

ARMA parameters are developed to assess the damage potential in seismic records. The parameters are chosen to fit acceleration time series of particular earthquake records using the maximum-likelihood method. For each event, a set of random accelerograms is generated and used to establish statistically-valid structural response spectra. Since the number of earthquake accelerograms in any seismic region is limited, non-stationary stochastic models are used to characterize earthquake ground motion. From a sample of earthquakes, the mean and variance of response spectral ordinates are obtained for damage predictors. Structural design spectra for earthquakes are based on smoothed linear response spectra obtained from different events scaled by their peak values. Such an approach does not incorporate other characteristics of the excitation represented by measured data. Samples of acceleration records are generated for each event. In this study, individual records for an earthquake are treated as one realization of an underlying non-stationary process that actually characterizes the earthquake. This research provides a reliable description of the information contained within acceleration records, and can also provide a reasonable estimate of the average nonlinear demand spectra.

Extended Brauer model for ferromagnetic materials: analysis and computation

Purpose – The purpose of this paper is to develop a fast and accurate analytic model function for the single-valued H-B curve of ferromagnetic materials, where hysteresis can be disregarded (normal magnetization curve). Nonlinear magnetoquasistatic simulations demand smooth monotone material models to ensure physical correctness and good convergence in Newton's method. Design/methodology/approach – The Brauer model has these beneficial properties, but is not sufficiently accurate for low and high fields in the normal magnetization curve. The paper extends the Brauer model to better fit material behavior in the Rayleigh region (low fields) and in full saturation. Procedures for obtaining optimal parameters from given measurement points are proposed and tested for two technical materials. The approach is compared with cubic spline and monotonicity preserving spline interpolation with respect to error and computational effort. Findings – The extended Brauer model is more accurate and even maintains the computational advantages of the classical Brauer model. The methods for obtaining optimal parameters yield good results if the measurement points have a distinctive Rayleigh region. Originality/value – The model function for ferromagnetic materials enhances the precision of the classical Brauer model without notable additional simulation cost.

A bioeconomic model of a multi-site fishery with nonlinear demand function: number of sites optimizing the total catch.

We present a mathematical model of a fishery on several sites with a variable price. The model takes into account the evolution during the time of the resource, fish and boat movement between the different sites, fishing effort and price that varies with respect to supply and demand. We suppose that the movements of the boats and resource as well as the variation of the price go on at a fast time scale. We use methods of aggregation of variables in order to reduce the number of variables and we derive a reduced model governing two global variables, respectively the biomass of the resource and the fishing effort of the whole fishery. We look for the existence of equilibria of the aggregated model and perform local stability analysis. Two main cases can occur. The first one corresponds to over-exploitation leading to fish extinction. At extinction, the fishing effort tends to a positive value. The second case corresponds to a durable fishery equilibrium which is globally asymptotically stable. In the later case, we show that there exists a number of fishing sites that optimizes the total catch of the fishery.

An iterative method for forecasting most probable point of stochastic demand

The demand forecasting is essential for all production and non-production systems. However, nowadays there are only few researches on this area. Most of researches somehow benefited from simulation in the conditions of demand uncertainty. But this paper presents an iterative method to find most probable stochastic demand point with normally distributed and independent variables of n-dimensional space and the demand space is a nonlinear function. So this point is compatible with both external conditions and historical data and it is the shortest distance from origin to the approximated demand-state surface. Another advantage of this paper is considering n-dimensional and nonlinear (nth degree) demand function. Numerical results proved this procedure is convergent and running time is reasonable.