Basic food and drink price distributions transcend time and culture

The study investigates whether a simple function of basic food and drink prices—specifically, the dispersion (width) of their logarithms—has remained stable across vastly different contexts and eras. Although food prices are reported in heterogeneous quantity units (counts, weights, volumes, package sizes) and consumers often rely on posted prices rather than unit-price calculations, the authors deliberately use prices as reported in historical records to encompass periods when consumers likely could not compute unit prices. Using the German hyperinflation as a motivating case, they observe that despite price levels changing by factors exceeding ten million within months, the relative price dispersion remains narrow and forms a band of approximately constant width when plotted in log terms. This observation motivates a focus on the sample standard deviation of log prices at a given time as a robust summary of the distribution of relative prices, independent of currency or units.

Prior research has documented regularities in pricing independent of product attributes (Schindler and Kibarian, 1996) and emphasized that price metrics and package sizes affect consumer behavior (Jones and Monsivais, 2016; Yonezawa and Richards, 2016). Consumers typically rely on posted prices unless unit prices are available or easily computed (Granger and Billson, 1972; Yan et al., 2014; Çakır and Balagtas, 2014). Hyperinflation dynamics can decouple nominal prices from real factors (Keynes, 1919; Cagan, 1956). Work on food price volatility highlights substantial fluctuations in levels (Gilbert and Morgan, 2010). Classical analyses of price behavior (Mills, 1927; Keynes, 1928) and modern studies of price dispersion typically examine individual-item dispersion across sellers (Lach, 2002) rather than the cross-item dispersion within a market basket at a point in time. Broader pricing theory and behavioral pricing provide context (Weber, 2012; Koschate-Fischer and Wüllner, 2017). Econophysics offers scale-invariant frameworks and has found power laws in price-related data (Stanley et al., 1999; Ishikawa, 2009; Blackwell, 2018). Cognitive research on logarithmic mental number representations suggests potential behavioral underpinnings for log-based invariances (Dehaene, 2003; Cheng and Monroe, 2013).

• Quantity of interest: For each time point with N≥2 positive prices P1,...,PN (in any common currency/units for that dataset and date), compute the base-b (b>1) logarithms of prices. Compute the sample mean A_b = (1/N) Σ log_b(P_j) and the sample standard deviation (width) B_b = sqrt( Σ (log_b(P_j) − A_b)^2 / (N−1) ). No assumption is made about the underlying distribution of log prices.
• Scale invariance: If the log-price distribution were Gaussian, approximately 68% of prices would lie between A_b ± B_b. The implied raw-price ratio spanning this ±1 standard deviation band is R = b^(2B_b), which is base-invariant.
• Empirical benchmark: Historical evidence consistently indicates B_10 ≈ 0.5, implying R ≈ 10 (i.e., most prices fall within one order of magnitude of each other at a given time).
• Data selection and processing: The study compiles cross-sectional price lists of basic food and drink items at various dates from diverse regions and eras, respecting original item definitions and units. For Fig. 2, a conservative approach was used: only items with prices reported at all selected dates within a dataset were included to ensure comparability. Fig. 3 uses a single long English series with minimal filtering, computing B_10 whenever at least two prices are available. Organizational bulk purchases (e.g., monasteries, hospitals) were excluded due to non-household quantities.
• Datasets and periods: Ancient Egypt (1135 and 1113 BCE; spelt, barley, bread, fats, cream, beer, honey, salt, vegetables); Hellenistic Babylon (292–78 BCE; barley, dates, mustard, cress, sesame); Delhi under Firoz Shah Tughlaq (1351–1388 CE; grains, clarified butter, sesame oil, salt); Istanbul under the Ottoman Empire (1489–1770 CE; wheat, flour, bread, rice, butter, olive oil, mutton, honey, sugar, coffee, chickpeas) including periods with price ceilings; Germany (1850–2000 CE); USA (1920–1942 CE); UK (1960–2004 CE); Tokyo (1957–2001 CE; specific branded items); Chilean supermarket scraped data (2007–2010 CE; 39 categories with full daily coverage); long English series (1209–1914 CE) including saffron (1265–1570 CE). Also included for comparison: Diocletian’s maximum price edict (301 CE) and Soviet state-store and market prices (1950, 1958).
• Computation: For each chosen date and dataset, compute B_10. For visualization (e.g., Fig. 1, Fig. 4), plot log10 prices with interpolated bands A_10 ± B_10. Sensitivity analyses include excluding outliers/items (e.g., saffron) and using all available data versus conservative subsets.

• The width (sample standard deviation) of log10 prices, B_10, is remarkably stable across time and cultures, typically lying between about 0.25 and 0.75, with a central tendency around 0.5. This implies that roughly two-thirds of basic food and drink prices at a given place/time fall within one order of magnitude (R ≈ 10) of each other.
• German hyperinflation case: Between April 1922 and November 1923, price levels for staple items rose by factors exceeding 10 million, yet at any given time the most expensive item was less than 250 times the cheapest. The range of relative prices was thus negligible compared to the absolute price level variation. Log-price plots show a band of near-constant width, with A_10 ± B_10 maintaining a difference near 1.
• Cross-cultural robustness: Data spanning ancient Egypt, Babylon, medieval Delhi, Ottoman Istanbul, Germany, USA, UK, Tokyo, and modern Chile all yield B_10 within the same narrow band, despite differences in institutions, technology, culture, and market regimes (including periods with price controls and hyperinflation). In Fig. 2, even the hyperinflation episode appears as a modest peak (height ≈ −0.3 relative to the band), despite underlying log-price levels changing by about 10.
• Long-run English series (1209–1914): Raw B_10 estimates over seven centuries are internally consistent and remain within the global band. Including saffron increases dispersion for dates where saffron is present, but widths still stay within the broader stability range; excluding saffron reduces B_10 as expected.
• Temporal variability: Short-term fluctuations in B_10 occur, but there are no persistent step changes; the width does not drift significantly from its long-term average and appears decoupled from inflation and general price volatility.

The findings address the central question by showing that the dispersion of relative prices (measured as the sample standard deviation of log prices) behaves as a near-constant, scale-invariant characteristic of food markets. This stability persists across extreme macroeconomic conditions (e.g., hyperinflation), institutional settings (from free markets to price ceilings), and vast differences in culture and technology. The decoupling of B_10 from inflation and price-level volatility suggests that the cross-item structure of relative prices is governed by constraints that keep prices neither too dispersed nor too concentrated. Prices of individual items move within an apparently fixed distribution, with items weaving around rather than the distribution widening or narrowing materially over time. The result contrasts with classical approaches focusing on rates of change and with modern price-dispersion studies that examine variation across sellers for a single item. Here, the within-market, cross-item dispersion at a point in time shows universality. The scale invariance (dependence on ratios) aligns with perspectives from econophysics, which may offer tools to model such constraints. The authors speculate that cognitive factors, such as a logarithmic mental number line, could contribute to stable perceptions and pricing heuristics. However, current economic theory does not readily explain the observed universality, indicating an opportunity for theoretical development that may integrate behavioral, nutritional economics, and complex-systems insights.

The width (sample standard deviation) of the distribution of logarithms of basic food and drink prices has remained essentially unchanged over three millennia and across diverse geographies and cultures. This width appears independent of the specific items consumed, average incomes and expenditures, and prevailing technologies, institutions, or political conditions. A plausible explanation may involve a regulatory mechanism that keeps relative prices from drifting too far apart or becoming overly similar, and that has operated consistently across time and space. The universality of this “standard” width invites extensions of price-distribution theory and interdisciplinary modeling (e.g., econophysics, behavioral economics) to explain the underlying mechanism. Future research could aim to identify the shape of the underlying distribution, test cognitive hypotheses about logarithmic price perception, and explore policy or market design implications of the stable dispersion.

• Ancient datasets often contain few items, limiting inference beyond estimating a dispersion measure; this constrains efforts to characterize the full form of the underlying distribution.
• Prices are used as reported without harmonizing quantities or units across items or datasets; while intentional, this heterogeneity could introduce measurement noise. Quantities and weightings are not explicitly modeled.
• Some datasets reflect non-free-market conditions (e.g., Ottoman price ceilings, Soviet state-store prices) which may affect dispersion; nonetheless, observed widths remain within the universal band.
• The study is observational and cross-sectional at each time point; causal mechanisms underlying the stability of B_10 are not identified.
• Selection for Fig. 2 is conservative (requiring items to be present at all selected dates), which may exclude items with intermittent reporting; Fig. 3 mitigates this by using all available dates with N≥2.
• The analysis does not determine the exact parametric form of the log-price distribution due to data limitations in historical lists.