Nonlinear Pricing Research Articles

Naming Matters: Prompting Smaller Portions in an Online RCT

Large portions, which can lead people to eat more, are becoming increasingly common in U.S. restaurants. This study tested whether portion-size descriptions on menus and different pricing strategies influence the selection of smaller portion sizes. This was a 4×2 between-subjects online randomized controlled experiment. This was an online simulated menu-ordering study conducted in 2021 among 2,205 U.S. adults. Adults viewed a fast-casual and full-service menu with entrées available in 2 sizes and ordered an entrée from each. Participants were randomized to view 1 of 4 portion-size descriptors (smaller/larger portion): (1) no descriptor/large (control), (2) standard/large, (3) just right/large, and (4) no descriptor/hearty. Participants were also randomized to either linear (i.e., reduced price=50% larger portion's price) or nonlinear pricing (i.e., reduced price=70% larger portion's price) (4×2 factorial design). In 2022, logistic regression models were used to analyze whether the interventions increased the likelihood of choosing a reduced portion. Regardless of pricing scheme, participants in the standard/large condition selected reduced portions by 10 (95% CI=0.04, 0.16) and 13 (95% CI=0.07, 0.18) percentage points more than those in the control condition (fast-casual and full-service menus, respectively). Selection of reduced portions in the just right/large condition increased by 9 (95% CI=0.04, 0.15) and 8 (95% CI=0.02, 0.14) percentage points. For the fast-casual menu, keeping portion-size descriptors constant, participants ordered a reduced portion by 5 percentage points more with nonlinear pricing than with linear pricing. Portion-size descriptions on restaurant menus, even with nonlinear pricing, are a low-cost strategy to promote the selection of lower-calorie, smaller portions without restricting choice.

Spot–Futures Price Adjustments in the Nikkei 225: Linear or Smooth Transition? Financial Centre Leadership or Home Bias?

This paper studies price discovery in Nikkei 225 markets through the nonlinear smooth transition price adjustments between spot and future prices and across all three futures markets. We test for smooth transition nonlinearity and employ an exponential smooth transition error correction model (ESTECM) with exponential generalised autoregressive conditional heteroscedasticity (EGARCH), allowing for the effects of transaction costs, heterogeneity, and asymmetry in Nikkei price adjustments. We show that the ESTECM-EGARCH is the appropriate model as it offers new insights into Nikkei price dynamics and information transmission across international markets. For spot–futures price dynamics, we find that futures led spot prices before the crisis, but spot prices led afterwards. This can be explained by the lower level of heterogeneity in the underlying spot transaction costs after the crisis. For cross-border futures prices, the foreign exchanges (Chicago and Singapore) lead in price discovery, which can be attributed to their roles as global information centres and their flexible trading conditions, such as a more heterogeneous structure of transaction costs. The foreign leadership is robust to the use of linear or nonlinear models, the time differences between Chicago and the other markets, and the long-run liquidity conditions of the Nikkei futures markets, and strongly supports the international centre hypothesis.

A general revealed preference test for quasilinear preferences: theory and experiments

We provide a generalized revealed preference test for quasilinear preferences. The test applies to nonlinear budget sets and non-convex preferences as those found in taxation and nonlinear pricing contexts. We study the prevalence of quasilinear preferences in a laboratory real-effort task experiment with nonlinear wages. The experiment demonstrates the empirical relevance of our test. We find support for either convex (non-separable) preferences or quasilinear preferences but weak support for the hypothesis of both quasilinear and convex preferences.

A Stackelberg game scheme for pricing and task offloading based on idle node-assisted edge computational model

Mobile edge server (MES) can meet the low latency requirements of End user (EU) tasks, but the MES computing resources are limited. This paper proposes an IDs-assisted MES (MES-IDs) computing model to expand MES. However, how to find a task offload strategy to minimize EU calculation costs and improve MES and ID benefits on a task completion basis. This paper proposes a three-way optimization calculation method based on the Stackelberg game to reduce the problem complexity, which decomposes into EUs-BS and BS-IDs problems. The EUs-BS problem design pricing scheme obtains the EU task optimal offload rate. The BS-IDs problem uses nonlinear pricing methods to find the optimal task offload problem between MES and ID on the resource unit price, a multi-constrained nonlinear convex optimization problem. We propose an immune Metropolis-based particle swarm loss optimization algorithm (PIMA) to obtain an approximate optimal solution for the nonlinear convex optimization problem by adjusting the resource price. Numerical simulation results show that compared with GSP and PSI algorithms, the PIMA algorithm shows more robust stability and can effectively reduce task completion delay and computational cost.

Impact of inflation and discount on optimum ordering and preservation technology expenses scheme of perishable inventory model

This study coins an inventory model for deteriorating articles. The work devises an optimal approach of expenditure on preservation technology to attenuate the degradation process. The demand in the inventory model is both price and stock level sensitive. Demand in the form of price dependence is again a convex combination of linear and nonlinear prices. The investigation proliferates state-of-the-art strategy by presenting the concept of discount if payment is done in advance. The suggested model scrutinises the impact of inflation on optimality plan as well. The object of this exercise is to find optimal cycle length and preservation technology expenses to minimise the total cost per unit time. Stock is backlogged partially. Solution methodology of nonlinear minimisation problem embodies derivation of theorems and propositions. The final results are validated with the help of three examples, convexity of graphical schemes and sensitivity analysis. The paper also outlines the managerial point of view.

A Transactions Cost Analysis of the Welfare and Output Effects of Rebates and Non-Linear Pricing

A Transactions Cost Analysis of the Welfare and Output Effects of Rebates and Non-Linear Pricing

Electric Vehicle Charging Pricing Design for Agent-Based Traffic Microsimulation

Over the past few years, electric vehicles (EVs) have become a popular mode of individual transportation due to their significant benefits over internal combustion engine vehicles, resulting in significant growth in their penetration rate. However, the current flat electricity charging pricing and rapid diffusion of EVs may impose challenges to both transportation systems and power grids. It is well-accepted that the implementation of charging pricing schemes is a promising solution for changing and controlling EV users’ charging behavior. Nevertheless, in most research studies that have examined pricing schemes, the charging logic is defined in a way that agents will charge their vehicles while performing their daily activities. This will make the application of pricing schemes unfeasible, as agents will not have the freedom to unplug their EVs whenever they want, to reduce their billing costs. Accordingly, this paper provides an agent and activity-based framework for charging pricing schemes by decoupling activity and charging start and end times. Following this, three different charging pricing schemes have been introduced, including time of use (TOU), non-linear and zonal pricing and tested on the Montreal scenario.

Joint Scheduling of Proactive Pushing and On-Demand Transmission Over Shared Spectrum for Profit Maximization

Proactive pushing has emerged as a promising solution to scale the service capacity by utilizing idle spectrum resources when on-demand transmission cannot fully exploit the spectrum resources during off-peak times. How to schedule both pushing and on-demand transmission jointly to meet a higher spectrum efficiency becomes a critical issue. Moreover, efficient and fair spectrum sharing among multiple resource schedulers remains open. In this paper, we introduce virtual network operators (VNOs) as schedulers that pay for consumed bandwidth and jointly schedule pushing and on-demand services. We adopt nonlinear spectrum pricing schemes with a convex and increasing price function enabling each VNO to share spectrum resources appropriately and independently. Considering the revenue from users and the cost for spectrum, we formulate a Markov decision process (MDP) to maximize the profit of VNO. A modified value iteration algorithm is applied to solve the MDP with reduced computational complexity. Furthermore, we show the structure of the optimal policy and provide the upper and lower bounds for the optimal performance. We present a low-complexity heuristic policy that can scale in practice with large state spaces and action spaces.

Stress Testing Structural Models of Unobserved Heterogeneity: Robust Inference on Optimal Nonlinear Pricing

Stress Testing Structural Models of Unobserved Heterogeneity: Robust Inference on Optimal Nonlinear Pricing

Tackling Nonlinear Price Impact with Linear Strategies

Tackling Nonlinear Price Impact with Linear Strategies

Carbon price prediction based on multi-factor MEEMD-LSTM model

China’s national carbon market has already become the largest carbon market in the world. The prediction of carbon price is extremely important for policymakers and market participants. Therefore, the prediction of carbon price in China is of great significance. To achieve a better prediction effect, a multi-factor hybrid model combined with modified ensemble empirical mode decomposition (MEEMD) and long short-term memory (LSTM) neural network optimized by machine reasoning system on the basis of production rules is proposed in this paper. In addition to historical carbon price, other factors, such as energy, macroeconomy, environmental condition, temperature, exchange rate which affect carbon price fluctuation, are formed as multi-factor. The change characteristics of carbon price time series data and other associated factors are extracted in the carbon price prediction. The MEEMD is used to decompose data which is taken as potential input variables into LSTM neural network for prediction and the machine reasoning system based on production rules can automatically search and optimize the parameters of LSTM to further improve the prediction results. The experimental results demonstrate that the proposed method has better prediction effect, robustness and adaptability than the LSTM model without MEEMD decomposition, the single factor MEEMD-LSTM method and other benchmark models. Overall it seems that the proposed method is an advanced approach for predicting the non-stationary and non-linear carbon price time series.

Nonlinear pricing, biased consumers, and regulatory policy

Recent empirical analyses show consumers in electricity and water markets respond to average price rather than marginal price, calling for information provision policies that help correct the consumers’ bias. This paper characterizes the regulated tariff if the regulator is informed about the average-price response of consumers. I find the regulated tariff for biased consumers promotes equity gains by featuring quantity premia and providing access to utility consumption for a larger population than in the world of rational consumers. The world of biased consumers can also yield higher total welfare. These results bring up the opportunity costs of the information provision programs that help consumers correct the bias.

Efficient public good provision by lotteries with nonlinear pricing

In this paper, we introduce nonlinear pricing of lottery tickets to the mechanism of Morgan (2000), in which a lottery is used to finance the public good. In a model with n symmetric agents, we find that incorporating this instrument fully achieves the efficient provision of public good when each agent’s initial wealth is sufficiently high. In a model with two asymmetric agents, there exists a nonlinear lottery mechanism that induces efficient public good provision provided that agents are not too heterogenous. Intuitively, the proposed nonlinear pricing rule leads to a decreasing marginal cost for ticket purchase, which provides stronger incentives for agents to make contributions, compared with Morgan (2000).

Solitary Wave and Singular Wave Solutions for Ivancevic Option Pricing Model

The nonlinear option pricing model presented by Ivancevic is investigated. By using travelling wave transforming method, the nonlinear option pricing equation is transformed into a differential equation with constant coefficients. By solving the differential equation with F-expansion method, a series of exact solutions have been obtained for the Ivancevic option pricing model. By choosing appropriate parameter values, the dark-soliton and dark-soliton-like solutions, periodic wave solutions, and rogue wave solutions are obtained. These solutions will enrich the types of exact waves in the existing literature of the Ivancevic option pricing model. Furthermore, they may have potential uses in describing the possible physical mechanisms for wave phenomenon in financial markets.

Equity premium prediction using the price of crude oil: Uncovering the nonlinear predictive impact

Highly cited studies, such as Mork (1989), Hamilton (1996), Hamilton (2003) and Kilian and Vigfusson (2013) establish a nonlinear connection between movements in the real (nominal) price of crude oil and the real gross domestic product (GDP) growth rate. Based on the observation that crude oil price increases have a different impact on the real GDP growth rate than crude oil price decreases, the authors introduce various nonlinear transformations of the price of crude oil to account for the nonlinear predictive impact. Using predictive regressions à la Goyal and Welch (2008), a growing number of studies in recent years have conditioned on these nonlinear crude oil price measures to predict equity premium out-of-sample. By applying the dynamic rotation rule suggested in Zhu and Timmermann (2021), we demonstrate that the form of nonlinearity that helps improve relative out-of-sample point prediction accuracy the most does not have to do with crude oil price increases (decreases) relative to recent prices as perceived by the current literature, but with connecting the relative out-of-sample point prediction performance between the benchmark and the crude oil price-based model with movements in economic variables measuring equity market volatility, economic activity, uncertainty and financial conditions. The statistical evidence of out-of-sample equity premium predictability also translates to economic gains.

Commercial consumers pay attention to marginal prices or average prices? Implications for energy conservation policies

Any energy conservation policy intervention associated with energy price variation needs to consider whether consumers respond to marginal or average pricing. To the best of our knowledge, there is no such evidence for commercial electricity consumers (such as office buildings and malls), although commercial consumers are responsible for nearly 18% of electricity consumption in the United States. This study examines a four-tiered decreasing-block pricing schedule for commercial consumers. Based on individual-consumer-level data, we analyze the daily electricity consumption of 597 commercial accounts in Phoenix metropolitan, Arizona, from May 1, 2013, to December 31, 2016. We run 2SLS models with policy-induced price variation as instrumental variables to estimate the effects of marginal and average prices on commercial electricity consumption at each cutoff point. We also study the heterogenous response across industry sectors. Our analysis shows that commercial consumers respond to both marginal and average prices, but have different responses with respect to how much electricity they consume. Higher-usage consumers tend to respond more to average prices, whereas lower-usage consumers are more sensitive to marginal prices. Our findings indicate that conservation policies should be tailored differently for commercial electricity consumers. Nonlinear electricity pricing structures can reduce energy consumption, particularly for commercial consumers who have lower energy demand if the pricing structure shifts from decreasing to increasing blocks. In contrast, a flat rate with a higher price level can limit the electricity consumption of high-use consumers. As for an industry-wise policy design, nonlinear pricing can be effectively used to reduce aggregate consumption in the construction, manufacturing, real estate, and rental and leasing industries, professional, scientific, and technical services, other services (except public administration), and public administration industries.

The Microcosmic Mechanism and Empirical Test of Uncertainty on the Non-Linear Fluctuation of Chinese Grain Prices-Based on the Perspective of Global Economic Policy Uncertainty

The dramatic fluctuations in grain prices and the threat to grain security caused by global economic policy uncertainty have been a social concern and a challenging area for price management authorities to regulate. Based on general equilibrium analysis in microeconomics, this paper constructs a mathematical model of the impact of global economic policy uncertainty on grain price fluctuation. It then examines the micro mechanism of non-linear grain price fluctuation under the dominant market mechanism and measures the non-linear shock effect of global economic policy uncertainty on grain prices using a threshold regression model. The results show that soybean and corn prices are subject to a two-zone fluctuation pattern due to global economic policy uncertainty. The impact has significant non-linear characteristics and is significantly greater in the high zone than that in the low zone. Accordingly, this paper offers government departments advice on better regulating and managing the market supply and demand and smoothing out sharp fluctuations in grain prices caused by changes in global economic policies.

Pricing American options with stochastic volatility and small nonlinear price impact: A PDE approach

In this paper, transaction costs as small nonlinear price impact are introduced into American option pricing under the Heston stochastic volatility model, forming a gap between option prices of the holder and writer. Through the use of a dynamic hedging strategy together with a known option independent of transaction costs, we derive two different nonlinear pricing partial differential equation systems for the holder and writer, respectively. A numerical algorithm is designed to solve the systems so that American option prices as well as the optimal exercise boundary can be simultaneously obtained. Examples are presented to illustrate the effect of transaction costs on both option prices and optimal exercise prices.

Nonlinear pricing for yield management and countering strategic consumer behavior

Many models assume that faced with excess inventory, retailers offer price discounts to increase sales. This discount is assumed to be a certain dollar amount or a certain percent of the regular price. However, many retailers use nonlinear pricing, e.g., “Buy one, get one for 50% off,” which we refer to as BOGO. We analyze BOGO within the newsvendor model and identify the reasons for its popularity. We describe the type of products for which BOGO is suitable, identify the optimal BOGO discount, and its effect on the retailer’s profit. We compare BOGO to straight price reduction and analyze the newsvendor’s optimal choice between them. We also examine the two promotions in the presence of strategic consumers. We find that for reasonable values of consumer marginal utility and a given order quantity, BOGO reduces strategic consumers’ chances of obtaining a unit at a discount and their incentive to wait. Therefore, the newsvendor orders a larger quantity with BOGO than with a price reduction. Thus, BOGO can be used to counter strategic consumer behavior. Also, we find that in the presence of strategic consumers, there are cases where it is optimal for the retailer to wait and offer a straight discount at the end of the season. However, with BOGO, it is always optimal to offer a BOGO at the start of the season if realized demand is low. We examine the robustness of our results to different arrival rates and positive salvage value and find that they qualitatively hold.

Cost-effective stochastic resource placement in edge clouds with horizontal and vertical sharing

To support distributed upper-level services such as those in edge or fog computing, a hierarchical and distributed multicloud architecture is introduced to replace the traditional centralized cloud architecture. The intra-time slot demand fluctuation with corresponding multidimensional resource sharing are neglected for efficiency reasons in the existing algorithms. By considering them, the service provider has the potential to obtain better solution, but also makes the scheduling problem a highly complicated stochastic optimization one. To effectively and efficiently solve the problem containing a nonlinear objective and constraints with heterogeneous nonlinear pricing functions, the general stochastic scheduling problem is formulated and its structure is exploited to obtain the base solution quickly, which is further applied with solution closure for fast convergence in the following configurable metaheuristic searching phrase. The experiments with many different problem settings show its superiority over existing algorithms with more than 30% revenue improvement. Therefore, the proposed algorithm can be used as a good supplement to the existing methods.