Performance‐Price‐Ratio Utility: Market Equilibrium Analysis and Empirical Calibration Studies

Abstract

In this study, as an alternative to the surplus utility, we propose a performance‐price‐ratio (PPR) utility and specialize the customer choice model with a PPR maximization criterion. With the PPR‐based choice model, we investigate a pricing game between retailers in a competitive market. Through transferring the decision variable from price to performance‐price ratio, the first‐order condition of the game becomes a linear equation system, which enables us to develop a closed‐form equilibrium solution. The solution reveals how product performance and price sensitivity affect equilibrium pricing, market share, and revenue. With the developed theoretical results, we carry out empirical studies with a rich data set obtained from the China TV market. At the individual product level and the brand level, we calibrate the PPR‐based choice model and the widely used surplus‐based model with a Bayesian information criteria‐based stepwise multivariate regression method. The regression results suggest that the PPR‐based model fits both the product‐level and brand‐level data better than the surplus‐based model. Through the stepwise selection of independent variables, we find that the leading features affecting a TV’s performance are 3D TV functionality and its screen size. Moreover, we explore how the market equilibrium evolves with the game decision sequence, market structure, and new product entry.

Insight into China's Economically Motivated Adulteration Risk in Online Agricultural Product Sales

“…(Quality-price-ratio utility, Xie et al, 2021) The QPR of seller 𝑖's products can be defined by 𝑉 𝑖 = 𝛼 ̂𝑖𝛿 𝑝 𝑖 𝛾 , where 𝛾 > 1 measures the price sensitivity of consumers on the EP. Furthermore, the QPR utility of seller 𝑖's products can be defined by 𝑈 𝑖 = 𝑉 𝑖 𝜉 𝑖 , where the random variable 𝜉 𝑖 reflects the consumers' heterogeneous tastes for seller 𝑖's products.…”

“…Denote 𝑈 0 = 𝑉 0 𝜉 0 the consumers' reservation utility. Similar to Xie et al (2021) and Liu (2022), we assume that (𝜉 0 , ⋯ , 𝜉 𝑛 ) are i.i.d. and follow the Frechet distribution (Type II extreme value distribution), which is equivalent to assuming a Gumbel distribution (Type I extreme value distribution) random variable that yields the well-known MNL model.…”

“…Moreover, the EP will decide the take rate charged from its sellers to maximize its expected profit. By modeling the two stakeholders' decisions a three-stage Stackelberg game, we first analyze the sellers' equilibrium selling prices for their adulterated products by using the quality-price-ratiobased (QPR-based) choice model under the QPR maximization consumer choice criterion (Xie et al, 2021). Second, we derive their equilibrium adulteration decisions under the preemptive EMA scenario.…”

“…Xie et al (2021), we treated the other sellers' (whose sales volumes are smaller than 10) products as the outside option in the QPR-based consumer choice model. Then, we have 𝑛 = 31.…”

“…Furthermore, to satisfy Assumption 1(i), we set 𝛾 = 𝑛−0.1 𝑛−1 = 1.03. According toXie et al (2021), for the QPR model, given any seller's selling price 𝑝 𝑖 , the quality of his products can be derived by…”