1\section{Related literature}\label{sec:lit}23\paragraph{Price dispersion and search.} That identical goods sell at different prices in the same market is the oldest puzzle of the economics of information \citep{stigler1961}. Equilibrium dispersion arises when some consumers are informed and others are not \citep{salop1977}, or when consumers sample a small number of prices \citep{burdett1983}; \citet{baye2006} survey the theory and the evidence. Empirically, dispersion is large and persistent even for homogeneous products \citep{sorensen2000,lach2002}, and most of it is \emph{relative} dispersion---the same store is cheap for some goods and expensive for others---rather than a stable store-level ranking \citep{kaplan2015,kaplan2019}. Our H1 tests whether the Quebec banner-level posted prices display economically meaningful and persistent gaps on exactly matched items; the within-banner store mixture we uncover connects directly to the store-level dispersion these papers measure with scanner data.45\paragraph{Sales, high--low pricing and reference prices.} \citet{varian1980} rationalises temporary sales as a mixed strategy that price-discriminates between informed shoppers and loyal customers; \citet{pesendorfer2002} and \citet{hendel2006,hendel2013} show how storable-goods demand accumulation generates sale cycles; \citet{hosken2004} document the empirical regularities of retail price variation; \citet{chevalier2003} and \citet{macdonald2000} show prices falling at demand peaks; \citet{chevalier2019} measure how consumers exploit ``best prices''. The macro literature treats sales as distinct from regular-price changes: regular prices are sticky, sales are frequent, temporary and return to the reference \citep{bils2004,nakamura2008,klenow2008,eichenbaum2011,kehoe2015}, sales respond weakly to aggregate shocks \citep{guimaraes2011,coibion2015,anderson2017,gagnon2020}, and menu-cost models with multi-product firms reproduce the size distribution of changes \citep{golosov2007,midrigan2011,nakamura2013,anderson2015}. Our H2 and H3 are the posted-price implications of this literature: volatility with and without sales, and whether the reference price moves after a sale.67\paragraph{Retail competition and chain pricing.} Retailers choose between every-day-low-price and high--low formats \citep{hoch1994,lal1997,ellickson2008}; large chains price nearly uniformly across their stores \citep{dellavigna2019,hitsch2019,hitsch2021}, with zone pricing as the main exception \citep{adams2024}; entry of mass merchants lowers measured prices \citep{hausman2007}. The Canadian retail grocery market is concentrated among three national chains plus Walmart and Costco \citep{competitionbureau2023}. We map Food-Ka's 54 feeds to 26 companies and show that most exactly matched comparisons are \emph{within} company (Metro vs.\ Super~C; Maxi vs.\ Provigo vs.\ Club Entrepôt)---format differentiation inside a chain---rather than across chains.89\paragraph{Scraped and online prices.} The Billion Prices Project established that online prices are a valid high-frequency source for inflation measurement and that online and offline prices coincide for most items of multi-channel retailers \citep{cavallo2016,cavallo2017}; scraped data reveal more frequent price changes and stockouts than official collections \citep{cavallo2018,cavallo2023,gorodnichenko2017}. Our contribution to this literature is cautionary: when a retailer's site serves store-specific prices and the scraper does not pin the store, the ``online price'' is a draw from the chain's store-price distribution.1011\paragraph{Price indices, substitution and shrinkflation.} Matched-model and multilateral methods address chain drift and assortment change \citep{feenstra1994,ivancic2011,dehaan2011,melser2018,diewert2022,redding2020}; price measurement during the pandemic highlighted the role of changing baskets \citep{diewert2020}; household-level differences in inflation arise from product-level heterogeneity \citep{jaravel2019,argente2021,beck2024,hottman2016}. Package downsizing is a hidden price increase to which demand is less sensitive than to list-price increases \citep{gourville2004,cakir2014,cakir2021,hoppe2024}. Our H5 compares naive average posted prices with matched-model indices on the same data; we cannot observe within-listing package changes and say so.1213\paragraph{Shopping effort, store choice and access.} Paid prices fall with shopping time and store switching \citep{aguiar2007,griffith2009,kaplan2016,nevo2019}; private labels and brand premia reflect information as much as quality \citep{bronnenberg2015,dube2018}; spatial access and assortment shape effective prices \citep{handbury2015,allcott2019,atkin2018}. Our H6 computes the posted-price savings frontier under a banner-count constraint; because store geography is unobserved, travel costs enter only as an illustrative sensitivity.1415\paragraph{Record linkage.} Probabilistic matching of product listings is a record-linkage problem \citep{fellegi1969,christen2012}; recording error in scanner panels is itself a research topic \citep{einav2010}. We treat matching as a measured component of the design, with tier-specific precision estimates propagated to the results.1617The evidence matrix in the replication package (\texttt{literature/evidence\_matrix.csv}) links each theoretical claim used in this paper to these sources, states the limitation for our setting, and identifies where WP37 adds something.18