Elastic Demand Function Research Articles

Study on the pricing and replenishment of vegetable commodities based on the optimization model

Based on the problems of short shelf life, inventory control and pricing management, marketing, economics, operation research, and the control optimal theory, this paper establishes the regression prediction analysis model; establish the optimization model, formulate the total amount of daily replenishment; analyze the deficiencies of the model. Finally, the combination of the research results gives the replenishment and pricing decision to improve the revenue of the supermarket. In this study, the correlation degree between the two variables of each vegetable category and the single product sales volume was measured, and the time series analysis was used to identify the sales trend. Then according to the correlation analysis of descriptive statistics, using cosine similarity formula, analyze the data units, the total sales dimension normalization, using the method of standardize the correlation between item and category, using pearson correlation coefficient and Spearman correlation coefficient to study the relationship between category and sales, establish Spearman correlation coefficient to determine the final correlation coefficient, cluster analysis of each category, analysis of the correlation. By processing the relevant data, establish the ARIMA time series model, forecast on July 1,2023-July 7, the relevant data, using the adftest function time series stability test, fit the ARIMA time series model, using differential sequence to time series analysis, calculate vegetable sales and sales price of elastic demand function, finally find the optimal solution through the particle swarm algorithm.

Joint Optimization of Distance-Based Fares and Headway for Fixed-Route Bus Operations

This paper proposes a profit maximization problem designed for fixed-route bus operations, optimizing two key variables: distance-based fares and headways. This study formulates a profit maximization problem while considering the dynamic nature of transit ridership influenced by various demand elasticities. The elasticity of demand is modeled using parameters such as onboard time, waiting time, and fare. Three primary constraints are considered: (1) a financial constraint ensuring the profit (including government subsidy) is non-negative, (2) a demand constraint that ensures actual demand is non-negative (i.e., elastic demand function value is between zero and one, and (3) a maximum headway constraint that limits passenger waiting times to half the headway duration, so that no passengers wait more than one bus. Notably, this research goes beyond the existing literature, which predominantly focuses on average fares, by exploring the implications of a distance-based (user-based) fare structure. A genetic algorithm is used to find solutions. The study employs numerical analyses to verify the solution method and conducts sensitivity analyses on critical input parameters. This study is suitable for one time block (e.g., multiple hours) for a steady demand, and can be extended into multiple time periods to reflect demand changes with the time of day.

Bimodal transit design with heterogeneous demand elasticity under different fare structures

The study develops a new optimisation model to design a bimodal transit system from a microeconomic view to maximise the profit of a transit agency considering heterogeneous demand elasticity and different fare structures. Bimodal transit network parameters are optimized to better serve passenger demand. An elastic demand function is devised to include various time components and incorporate flat, distance-based, and hybrid fares. A nested iterative procedure is developed to find a near-optimal solution. Numerical experiments reveal the following interesting findings. First, the increase in elasticity parameters has a knock-on effect on the financial performance, consequently leading to a net profit reduction. Second, a distance-based fare scheme brings in the least actual demand but makes the most profit, compared with the flat and hybrid fare schemes. Third, passengers prefer using a rail-bus system to a BRT-bus system, especially at a higher demand level.

A Planning Model for Flexible-Route Bus Operations with Financial Constraints

In suburban areas where the demand is not high enough, the fixed-route buses usually operate with infrequent services, which increase the cost of waiting transit services for fixed-route service users. For those low demand regions, flexible-route bus operations with doorstep services, which operate with flexible routes, flexible schedules, and smaller vehicles, can be a feasible alternative. This study formulates the social welfare for flexible-route bus operations under various financial constraints, seeking to jointly optimize the headway, fare, and zone size. Elastic demand functions are constructed as a part of problem formulations. Unlike many previous studies, this study does not presume the shape of the zone, so that the flexible-route bus services can be designed according to the geographical conditions in the regions. Moreover, the amount of subsidy for financially constrained policy is calculated based on the actual demand although many previous studies used the potential demand to calculate the subsidy amount. Numerical analyses are explored to evaluate and compare system-wide welfares for different financial perspectives, i.e., no financial constraint, break-even policy, and subsidized policy. The solution optimality for constrained nonlinear optimization problems is verified using analytical optimization or the Karush-Kuhn-Tucker (KKT) conditions. It is found that the welfare of subsidized transit operations is located between the welfare amounts of unconstrained and break-even cases; this finding of welfare variations over subsidy amounts can be a helpful resource for transportation mobility analysts in determining the appropriate service quality and the corresponding amount of subsidy. Sensitivity analyses are presented to explore the system-wide welfare with respect to critical input parameters, including a comprehensive analysis of the unit cost of bus operations, which offers implications toward Mobility-as-a-Service (MaaS) planning.

On Joan Robinson’s Output Symmetry Theorems with Various Taxations under Third-Degree Price Discrimination: A Generalization

This paper incorporates more general cases with a new class of constantly adjusted concavity demand curves and includes three types of taxes. To verify the output symmetry under various forms of taxation, we simulate both linear and constant elasticity demand functions under the unit, demand ad valorem, and cost ad valorem taxes. If all the demand functions in the submarkets are linear, the total outputs are identical under both uniform pricing and third-degree price discrimination. Furthermore, if all the weak market demand curves are strictly “Robinson-concave” and all the strong market demand curves are strictly “Robinson-convex” or linear, then the total output under price discrimination exceeds that under uniform pricing, and vice versa. While different taxes lead to higher costs, the cost pass-through changes the prices of the products, and the change of total output still depends on the curvature of the demand curve. Therefore, the curvature of the demand curve remains the main determinant of changes in output. Our study provides a theoretical basis for market intervention in price discrimination.

Robust market equilibria under uncertain cost

This work studies equilibrium problems under uncertainty where firms maximize their profits in a robust way when selling their output. Robust optimization plays an increasingly important role when best guaranteed objective values are to be determined, independently of the specific distributional assumptions regarding uncertainty. In particular, solutions are to be determined that are feasible regardless of how the uncertainty manifests itself within some predefined uncertainty set. Our mathematical analysis adopts the robust optimization perspective in the context of equilibrium problems. First, we present structural insights for a single-stage, nonadjustable robust setting. We then go one step further and study the more complex two-stage or adjustable case where a part of the variables can adjust to the realization of the uncertainty. We compare equilibrium outcomes with the corresponding centralized robust optimization problem where the sum of all profits are maximized. As we find, the market equilibrium for the perfectly competitive firms differs from the solution of the robust central planner, which is in stark contrast to classical results regarding the efficiency of market equilibria with perfectly competitive firms. For the different scenarios considered, we furthermore are able to determine the resulting price of anarchy. In the case of non-adjustable robustness, for fixed demand in every time step the price of anarchy is bounded whereas it is unbounded if the buyers are modeled by elastic demand functions. For the two-stage adjustable setting, we show how to compute subsidies for the firms that lead to robust welfare optimal equilibria.

Effects of built environment and weather on demands for transportation network company trips

This paper investigates the effects of the built environment and weather on the demands for transportation network companies (TNC) in Toronto. The research is based on a historical dataset of Uber trips from September 2016 to September 2018 in Toronto. A wide range of built environments, sociodemographic, and weather data are generated at the dissemination area-level and fused with the monthly aggregated Uber dataset. To provide insight into the underlying factors that affect TNC demand, a series of aggregate demand models are estimated using log-transformed constant elasticity demand functions, with consideration of the seasonal lag effect. To capture the weather effect, an autoregressive moving average model is estimated for the downtown core of Toronto. The model results show that the influence of lagged ridership and seasonal lag effect have a positive correlation with TNC demand. The trip generation and attraction models reveal that TNC trips increase where when the commuting trip duration is longer than 60 min. It is found that the number of apartments in a dissemination area is positively correlated with TNC trip generation, while the number of single-detached houses has a negative correlation. The time-series model indicates that temperature and total daily precipitations are positively correlated with TNC demand. Due to the lack of comprehensive data sources on the Uber and Lyft ridership, the policymakers often struggle to make evidence-based policy recommendations to regulate such disruptive technologies. The series of models presented in this study will help us better understand the potential users of transportation network companies (TNC) and the effects of land use, built environment and weather on transportation network company trips.

Optimal Design for Demand Responsive Connector Service Considering Elastic Demand

Differing from the conventional fixed-route transit, Demand Responsive Connector (DRC) is scheduled to pick up passengers based on requests, and delivers them to a common destination (e.g., a metro station). The demand for DRC is affected by not only the fare and travel time, but also time reliability. The latter' impact is non-negligible because of the uncertainty nature of DRC on collecting the temporally and spatially distributed passengers. This paper explicitly introduces an elastic demand function embedded with a time deviation penalty model. Based on that, one-vehicle and two-vehicle DRC models are formulated to maximize the social welfare. The decision variables include fare, service area, and operating cycle time. Augmented Lagrange Multiplier Method is applied to solve the optimization problem. Simulation is performed to verify the validity of the models. In numerical studies, sensitivity analysis unveils the influences of several key parameters, e.g., potential demand density, vehicle capacity, line-haul distance and elasticity factors. By comparison, threshold values of demand density are revealed for the applicability of the one-vehicle and two-vehicle schemes. The proposed model provides a decision-making tool for DRC operators considering local conditions.

Pipes, Taps and Vendors: An Integrated Water Management Approach

This paper applies a microeconomic-based stylized model to identify the optimal modal split of water supply infrastructure in regions of the Global South against the background of the Sustainable Development Goal (SDG) No. 6. We assume a linear city, with some plausible assumptions on income and willingness-to-pay, and then calculate the optimal tap density, leading in turn to an optimal modal split between piped and unconnected water consumption. From an economic perspective, not all water users need to be connected to a centralized, pipeline infrastructure, and the non-connected households should be served by non-mobile or mobile vendors. The analysis is firstly made for the case of totally inelastic demand functions for simplification reasons and afterwards the analysis becomes more complicated and realistic by addressing elastic demand functions which are based on a simplified version of the Stone-Geary utility function. In terms of policy implications, the paper suggests a role for decentral, offgrid solutions to generalized water supply, with a certain role for water vendors.

Airline network competition in inter-continental market

As the number of countries liberalizing their skies increases, some airlines, notably carriers in the Middle East, have extended their hub-and-spoke networks beyond domestic borders. This allows them to serve international destinations without the need to go through traditional gateway hubs, so that they can compete with airline alliances relying on the traditional dual-gateway, or the so-called “dog-bone” networks. This paper proposes a stochastic optimization model to address the location choice issue of additional gateway airports, with a consideration of the competition between airlines running traditional dog-bone networks and hub-and-spoke networks in a liberalizing inter-continental market. A two-stage approach is adopted to model the effects of demand uncertainty. In the first stage, the future passenger demand is not observable and thus airlines or airline alliances aim to maximize their own expected profit by choosing additional gateway airports from the set of candidate gateway airports pre-specified by the regulator. In the second stage, with the passenger demand observed and the gateway scheme fixed, airlines determine their aircraft sizes and service frequencies to maximize their own profit, and air passengers choose routes that minimize their own travel disutility. Based on a calibration of the demand dispersion parameters in elastic demand function, the proposed model is applied to the China-Europe aviation market, which includes the inter-continental international market and the associated Chinese and European domestic markets, so that to ascertain the comparative advantages of different network configurations. The social welfares of the system under different demand scenarios and different gateway schemes are compared, and the sensitivity analyses of some parameters are also implemented.

The Optimal Taxation of Air Travel Under Monopolistic Dynamic Pricing

This article re-examines the question of how to optimally tax air travel within the model from Gallego and van Ryzin (1994), in which a monopolistic airline chooses its dynamic pricing policy to sell tickets to randomly arriving consumers over a finite time horizon until the plane departs. In general, the profit maximizing policy differs from the welfare maximizing policy. However, for a certain class of demand functions that includes constant elasticity and exponential demand functions, a simple policy instrument, namely a tax on vacant seats is sufficient to perfectly align profit maximization incentives with welfare maximization. Calibrating the model to predict a load factor of 80% (the current global average), the welfare maximizing tax on vacant seats leads to load factors of 97% for the constant elasticity demand function and 98% for the exponential demand function. These results suggest that club mechanisms for financing Global Public Good Institutions via aviation taxes will create stronger participation incentives if they do not constrain countries to use passenger taxes but instead allow them to use emissions taxes and even taxes on vacant seats.

Land-sparing vs land-sharing with incomplete policies

This article analyzes the trade-off between yield and farmed area when a valuable species is affected by agricultural practices. Itrevisits, from an economic perspective, the ``land-sparing versus land-sharing'' debate elaborated in conservation biology using themethodology of the density-yield curve: The density of the species on farmland is a decreasing function of the yield. It is shown thatthe optimal yield is either increasing or decreasing with respect to the value of the species depending on the shape of the density-yieldcurve. Land-sparing and land-sharing are not necessarily antagonistic; for sufficiently elastic demand function, both the optimal yield andthe farmed area decrease with the value of the species. A general assessment of a second-best policy is performed, and several particularpolicies are considered, including a subsidy on biodiversity in farms, a tax or subsidy on farmland, and a tax or subsidy on a dirty input.In several cases, the first-best strategy and the second-best one induce contrasting effects on the yield.

Effective Risk Aversion in Thin Risk-Sharing Markets

We consider thin incomplete financial markets, where traders with heterogeneous preferences and risk exposures have motive to behave strategically regarding the demand schedules they submit, thereby impacting prices and allocations. We argue that traders relatively more exposed to market risk tend to submit more elastic demand functions. Noncompetitive equilibrium prices and allocations result as an outcome of a game among traders. General sufficient conditions for existence and uniqueness of such equilibrium are provided, with an extensive analysis of two-trader transactions. Even though strategic behaviour causes inefficient social allocations, traders with sufficiently high risk tolerance and/or large initial exposure to market risk obtain more utility gain in the noncompetitive equilibrium, when compared to the competitive one.

Dynamic Continuum Model with Elastic Demand for a Polycentric Urban City

This paper presents the development of a macroscopic dynamic traffic assignment model for continuum transportation systems with elastic demand. A reactive dynamic user equilibrium model is extended to simulate network equilibrium problems for an urban area with multiple central business districts (CBDs). Each copy of traffic flow reactively makes route choice decisions to minimize the total travel cost from origin to destination, based on instantaneous traffic information from a radio broadcasting service or route guidance system. The elastic demand function for each copy of flow is associated with its total instantaneous travel cost. The model is solved by a cell-centered finite volume method for conservation law equations and a fast sweeping method for Eikonal-type equations on unstructured grids. Numerical experiments for an urban traffic network with two CBDs are presented to verify the rationality of the model and the validity of the numerical method. The numerical results indicate that the model captures some macroscopic characteristics of two copies of flow interacting in time-varying urban transportation systems, e.g., the spatial distributions of the flow density and flux and the path choice behavior in response to elastic demand, and can describe traffic equilibrium phenomena, such as self-organization and traffic congestion build-up and dissipation.

A Spot Capacity Market to Increase Power Infrastructure Utilization in Multi-Tenant Data Centers

Despite the common practice of oversubscription, power capacity is largely under-utilized in data centers. A significant factor driving this under-utilization is fluctuation of the aggregate power demand, resulting in unused "spot (power) capacity". In this paper, we tap into spot capacity for improving power infrastructure utilization in multi-tenant data centers, an important but under-explored type of data center where multiple tenants house their own physical servers. We propose a novel spot capacity market, called SpotDC, to allocate spot capacity to tenants on demand. Specifically, SpotDC extracts tenants' rack-level spot capacity demand through an elastic demand function, based on which the operator sets the market price for spot capacity allocation. We evaluate SpotDC using both testbed experiments and simulations, demonstrating that SpotDC improves power infrastructure utilization and creates a "win-win" situation: the data center operator increases its profit (by nearly 10%), while tenants improve their performance (by 1.2{1.8x on average, yet at a marginal cost).

Shelf space re-allocation for out of stock reduction

A planogram is a detailed visual map that establishes product positions over a shelf in a retail store. It is designed to support an innovative merchandising approach, to increase sales and profits, to supply the best location of a product for suppliers and to better manage the shelves. Product selection and the shelf space reserved to each product is a central activity for retailers and Shelf Out of Stock (SOOS) events are often strongly related to planogram design. In this paper we present a solution to optimally re-allocate shelf space to minimize Out of Stock (OOS) events. The approach uses SOOS data coming in real time from a sensor network technology, named Shelf Detector System, and an Integer Linear Programming model that integrates a space elastic demand function. Experimental results, based on a real scenario in the diaper category in Belgium, have proved that the system can efficiently calculate a proper solution able to re-allocate space and reduce OOS events.

Cross-border externalities and cooperation among representative democracies

This paper analyzes the provision of public goods with cross-border externalities by representative democracies. The level of provision of each country is decided by a policy maker elected by majority rule at the country level. We compare the case in which policy makers set their policies noncooperatively with the case in which they set their policies through Coasian cooperation. Cooperation induces policy makers to internalize cross-border externalities, but it also induces strategic voters to elect a policy maker who cares less about the public good to reduce their public good contribution. The former effect increases public good provision while the latter reduces it. We show that once voters' incentives are taken into account, whether cooperation is beneficial depends neither on voters' preferences, nor on the magnitude of spillovers, nor on the size, bargaining power, or efficiency of each country. Instead, it depends only on the curvature of the demand for the public good: cooperation increases (decreases) public good provision when the demand function is more (less) convex than the unit elastic demand function. Hence, the desirability of international cooperation depends mostly on the type of public good considered.

Economic Analysis of Transmission Expansion Planning With Price-Responsive Demand and Quadratic Losses by Successive LP

The growth of demand response programs and renewable generation is changing the economics of transmission. Planners and regulators require tools to address the implications of possible technology, policy, and economic developments for the optimal configuration of transmission grids. We propose a model for economic evaluation and optimization of inter-regional transmission expansion, as well as the optimal response of generators' investments to locational incentives, that accounts for Kirchhoff’s laws and three important nonlinearities. The first is consumer response to energy prices, modeled using elastic demand functions. The second is resistance losses. The third is the product of line susceptance and flows in the linearized DC load flow model. We develop a practical method combining Successive Linear Programming with Gauss-Seidel iteration to co-optimize AC and DC transmission and generation capacities in a linearized DC network while considering hundreds of hourly realizations of renewable supply and load. We test our approach for a European electricity market model including 33 countries. The examples indicate that demand response can be a valuable resource that can significantly affect the economics, location, and amounts of transmission and generation investments. Further, representing losses and Kirchhoff’s laws is also important in transmission policy analyses.

Cross-Border Externalities and Cooperation Among Representative Democracies

This paper analyzes the provision of public goods with cross-border externalities by representative democracies. The level of provision of each country is decided by a policy maker elected by majority rule at the country level. We compare the case in which policy makers set their policies noncooperatively with the case in which they set their policies through Coasian cooperation. Cooperation induces policy makers to internalize cross-border externalities, but it also induces strategic voters to elect a policy maker who cares less about the public good to reduce their public good contribution. The former effect increases public good provision while the latter reduces it. We show that once voters' incentives are taken into account, whether cooperation is beneficial depends neither on voters' preferences, nor on the magnitude of spillovers, nor on the size, bargaining power, or efficiency of each country. Instead, it depends only on the curvature of the demand for the public good: cooperation increases (decreases) public good provision when the demand function is more (less) convex than the unit elastic demand function. Hence, the desirability of international cooperation depends mostly on the type of public good considered.

Inflation and the Exchange Rate: The Role of Aggregate Demand Elasticity

This paper examines the effect of aggregate demand elasticity on the exchange rate when inflation occurs. We discover that both the source of the inflation, whether demand-pull or cost-push, and the elasticity of aggregate demand with respect to the price level, are of consequence for the exchange rate. We obtain two primary conclusions. First, the effect on the exchange rate of cost push inflation is ambiguous and is partially determined by the price level elasticity of aggregate demand. In particular, and assuming that the two examined countries have equivalent aggregate supply elasticities, we conclude that the nation with the less elastic aggregate demand function will see its currency appreciate relative to the other. Second, demand-pull inflation results in an unambiguous increase in the exchange rate but the size of that increase is partially a function of aggregate demand elasticity. Assuming again that two countries have equivalent aggregate supply elasticities, that country with the more elastic aggregate demand will experience currency appreciation.