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

Operations Research and Operations Management

By Xie, Y., L. Xie, M. Lu, and H. Yan

Published in Production and Operations Management, November 2020

“Performance-price ratio” (PPR) has become a keyword for both suppliers and sellers in promoting their products. As these are prime customer concerns, customer choice, centered on product performance and price, has received much recent attention in the literature via a number of utility-based discrete choice models. 

Based on a rich data set from the TV market in China, Professor Houmin Yan of the Department of Management Sciences and his co-authors set up a research agenda to ask: 
1) How customers behave under the performance-price ratio choice criterion? 
2) How this behaviour is linked with a retailer’s revenue in a competitive market? 
3) Whether this modelling approach derives analytical results that are able to assist retailers in developing their products and winning market share? 
4) Whether this theoretical model is supported by data observed in practice? 

Starting from deriving the customer choice probability under the PPR maximization criterion, Yan and his co-authors characterize the equilibrium for the pricing game between oligopoly retailers. The state of equilibrium depends on the retailers’ price sensitivities: high sensitivity brings a price war; low sensitivity leads to a subgame with one less player; in between, a closed-form solution is obtained by transferring the first-order condition into a linear equation system with respect to the PPR vector. With the closed-form solution and assuming a positive correlation between price sensitivity and performance, which is the case in the China TV market, they find that releasing a better product makes customers more sensitive to the retailer’s price changes and helps in winning market share. 

Following the theoretical analysis, they carry out empirical calibrations on the PPR model
with real data from the China TV market. Yan and his co-authors make the following observations: 
1) In terms of interpreting the variance of the data points, the PPR model is better than the surplus model at both the product and brand levels. 
2) In the product-level regression, the functionality coefficients for the PPR model are positive, whereas all of the functionality coefficients for the surplus model are negative, which is inconsistent with intuition. 
3) In the brand-level regression, the PPR model are statistically significant, whereas the surplus model sometimes are not statistically significant. 

The above observations indicate that the PPR model fits the China TV market data better than the surplus model.