“Man muss immer das Unmögliche versuchen, um das Mögliche zu
erreichen.” — Hermann Hesse
Abstract
This paper investigates the minimum aggregate expenditure on
alcoholic beverages that a finite group of individuals would need to
incur at the author’s home (Haus zum roten Sackel) on the
evening of 22 May 2026 in order to produce a statistically significant
perturbation in the weight assigned to alcoholic beverages in the Swiss
Consumer Price Index (Landesindex der Konsumentenpreise; LIK)
basket of goods. Using the official methodology of the Swiss Federal
Statistical Office (Bundesamt für Statistik; BFS) and
parametric data from the Haushaltsbudgeterhebung (HABE), we
derive a closed-form expression for the critical expenditure threshold
under a one-sample ratio test framework. For a reference group of \(k = 40\) individuals, we find that a total
alcohol expenditure of approximately CHF 2,024,161
would be required to achieve statistical significance at the
conventional \(\alpha = 0.05\) level.
This corresponds to consuming approximately 25,302 standard 3 dl
glasses of beer per person over a six-hour evening — a rate of
70 drinks per person per minute — and a quantity of pure ethanol
approximately 633 times the median lethal dose for a 70
kg adult. We conclude that while the proposition is commendable in
ambition, it is irreconcilable with the physiological and financial
constraints of mortal existence.
Introduction
The Swiss Consumer Price Index (Landesindex der
Konsumentenpreise; LIK) is the principal measure of consumer price
inflation in Switzerland (Bundesamt für Statistik (BFS)
2020). Published monthly by the Bundesamt für
Statistik (BFS), the LIK tracks changes in the prices of a fixed
basket of goods and services representative of typical Swiss household
expenditure. The basket is constructed from the
Haushaltsbudgeterhebung (HABE), a continuous household budget
survey that records the actual expenditure patterns of a stratified
random sample of Swiss private households (Bundesamt für Statistik (BFS)
2017).
Among the categories in the LIK basket, alcoholic beverages occupy a
modest but non-trivial position. They represent a measurable share of
aggregate Swiss household expenditure and are therefore accorded a
corresponding weight in the index calculation. This weight is updated at
each basket revision, which typically occurs every five years; the most
recent revision established the 2020 base year (Bundesamt für
Statistik (BFS) 2021).
The present paper arises from a practical and entirely earnest
question: if a group of friends were to convene at the author’s home
(Haus zum roten Sackel) on the evening of 22 May 2026 and
consume alcoholic beverages at a sufficiently prodigious rate, could
their collective expenditure be said to significantly alter the
weight of alcoholic beverages in the Swiss CPI basket?
This question, while perhaps facetious in origin, admits of a
rigorous statistical treatment. The weight of any given category in the
LIK basket is an estimated population parameter, subject to sampling
uncertainty arising from the finite HABE sample. “Significantly
changing” that weight can therefore be interpreted precisely: would our
group’s spending, if notionally incorporated into the HABE dataset as an
additional observation unit, cause the estimated proportion to shift by
more than its own standard error — that is, to achieve statistical
significance under a conventional hypothesis test?
We demonstrate that the answer is yes, in principle — but
only under conditions that preclude the simultaneous survival of the
investigators.
The remainder of the paper is structured as follows. Section 2
reviews the institutional background of the Swiss CPI and HABE. Section
3 develops the statistical framework. Section 4 presents the key
parameters and their sources. Section 5 reports the primary results.
Section 6 contextualises these results physiologically and financially.
Section 7 discusses limitations. Section 8 concludes.
Institutional
Background
The Swiss Consumer
Price Index
The LIK measures changes in the prices paid by private households
residing in Switzerland for a defined basket of goods and services. The
index uses a modified Laspeyres formula, holding basket weights fixed
between revisions (Bundesamt für Statistik (BFS)
2020):
\[
\text{LIK}_t = \sum_{i} w_i \cdot \frac{p_{i,t}}{p_{i,0}}
\]
where \(w_i\) is the expenditure
weight of good \(i\), \(p_{i,t}\) is the price of good \(i\) in period \(t\), and \(p_{i,0}\) is the price in the base period.
The weights \(\{w_i\}\) satisfy \(\sum_i w_i = 1\) and are derived from the
HABE.
The classification of goods follows the European COICOP
(Classification of Individual Consumption According to Purpose)
system (Eurostat
2013). Alcoholic beverages fall under COICOP
02.1 (Alkoholische Getränke), a subcategory of group
02 (Alkoholische Getränke, Tabak und Betäubungsmittel).
The Household Budget
Survey (HABE)
The HABE (Haushaltsbudgeterhebung) is a continuous,
stratified random sample survey of private households in Switzerland,
conducted annually by the BFS since 2006 (Bundesamt für Statistik (BFS)
2017). Participating households record all expenditures in a
detailed budget diary over a reference month, which is subsequently
extrapolated to an annual figure. The survey is designed to yield a
nationally representative picture of household expenditure patterns.
Key design features relevant to the present analysis include:
- Sample size: Approximately 3,000 households
per year are surveyed. Over the three-year rolling reference
period used for CPI basket construction, approximately 9,000
household-observations contribute to the basket weights (Bundesamt für Statistik
(BFS) 2022).
- Stratification: The sampling frame is stratified by
canton, household size, and socioeconomic status, introducing a design
effect relative to simple random sampling.
- Weighting: Sample weights are calibrated to the
Swiss resident population using auxiliary information from the federal
population register (Deville and Särndal 1992).
- Scope: The HABE captures all household
expenditures, including retail purchases of alcoholic beverages for home
consumption. Alcoholic beverages purchased at a supermarket or
off-licence and consumed at home are recorded under COICOP 02.1,
contributing to the alcohol weight.
This last point is crucial: beverages purchased and consumed at the
Haus zum roten Sackel — the author’s home — on the evening of
22 May would, if the relevant household were a HABE participant, be
counted toward the alcoholic beverages expenditure total.
The Alcoholic
Beverages Weight
Following the 2020 basket revision, the weight assigned to alcoholic
beverages (COICOP 02.1) in the Swiss LIK basket is approximately
\(w_{\text{alc}} =
0.03\) (i.e., 3.0% of total household expenditure),
consistent with published BFS figures for the 2020 reference year (Bundesamt für
Statistik (BFS) 2021). This weight reflects the share of
total annual household consumption expenditure devoted to alcoholic
beverages, averaged across the Swiss household population.
For reference, the analogous weight in the EU Harmonised Index of
Consumer Prices (HICP) for Switzerland is of a similar order of
magnitude, reflecting both the relative affluence of Swiss households
and the elevated price level of alcohol in Switzerland compared to
neighbouring countries.
Statistical
Framework
Research
Question
We wish to determine the minimum aggregate alcohol expenditure \(X^*\) such that, if our group’s spending
were included in the HABE dataset as an additional observation, the
estimated proportion of expenditure devoted to alcohol would be shifted
by a statistically significant amount.
Formally, let \(p_0 =
w_{\text{alc}}\) be the current estimated weight (proportion). We
test:
\[
H_0: p = p_0 \qquad \text{vs.} \qquad H_1: p > p_0
\]
at significance level \(\alpha =
0.05\) (one-tailed, since we are only considering an
increase in alcohol spending).
The Ratio
Estimator
In survey sampling, the weight \(w_{\text{alc}}\) is estimated as a
ratio:
\[
\hat{p} = \frac{\sum_{i \in s} c_{i,\text{alc}}}{\sum_{i \in s}
c_{i,\text{tot}}}
\]
where \(c_{i,\text{alc}}\) is
household \(i\)’s annual alcohol
expenditure, \(c_{i,\text{tot}}\) is
household \(i\)’s total annual
expenditure, and \(s\) is the HABE
sample (Cochran
1977; Lohr 2021).
Under standard regularity conditions, the ratio estimator is
approximately normally distributed for large samples (Casella and Berger
2002):
\[
\hat{p} \xrightarrow{d} \mathcal{N}\!\left(p_0,\;
\frac{p_0(1-p_0)}{n_{\text{eff}}}\right)
\]
where \(n_{\text{eff}} = n /
\text{deff}\) is the effective sample size, accounting
for the survey design effect \(\text{deff}\). For a stratified household
survey of this type, a design effect of \(\text{deff} \approx 1.5\) is typical (Cochran
1977).
The standard error of the estimated proportion is therefore:
\[
\widehat{\text{SE}}(\hat{p}) = \sqrt{\frac{p_0(1-p_0)}{n_{\text{eff}}}}
\]
The Critical
Expenditure Threshold
Suppose our group spends \(X\) CHF
on alcohol over the course of the evening, and that this spending is
entirely on alcoholic beverages (i.e., total spending \(X_{\text{tot}} = X\)). If this expenditure
enters the HABE as an additional observation unit, the new estimated
proportion becomes:
\[
\hat{p}_{\text{new}} = \frac{A_0 + X}{T_0 + X}
\]
where \(A_0 = n_{\text{eff}} \cdot \bar{E}
\cdot p_0\) is the total alcohol expenditure in the effective
survey sample and \(T_0 = n_{\text{eff}} \cdot
\bar{E}\) is the total expenditure, with \(\bar{E}\) the average annual household
expenditure.
For the observed shift to be statistically significant at level \(\alpha\) (one-tailed), we require:
\[
\hat{p}_{\text{new}} - p_0 > z_{\alpha} \cdot
\widehat{\text{SE}}(\hat{p})
\]
where \(z_{\alpha} = 1.645\) for
\(\alpha = 0.05\) (one-tailed) and
\(z_{\alpha/2} = 1.960\) for a
two-tailed test. We use the one-tailed critical value throughout, since
our group will not be drinking negative quantities of alcohol.
Parameters and
Data
Table 1 summarises the input parameters used in the analysis.
Table 1: Input parameters and their sources.
|
Parameter
|
Value
|
Source
|
|
CPI alcohol weight, \(p_0\)
|
0.030
|
Bundesamt für Statistik (BFS) (2021)
|
|
HABE households (3-yr basket), \(n\)
|
9,000
|
Bundesamt für Statistik (BFS) (2022)
|
|
Survey design effect, \(\text{deff}\)
|
1.5
|
Cochran (1977)
|
|
Effective sample size, \(n_{\text{eff}}\)
|
6,000
|
Derived
|
|
Avg. annual HH expenditure, \(\bar{E}\)
(CHF)
|
90,000
|
Bundesamt für Statistik (BFS) (2022)
|
|
Significance level, \(\alpha\)
|
0.05
|
Convention
|
|
Critical \(z\)-value, \(z_{\alpha}\)
|
1.645
|
Normal distribution
|
|
Group size, \(k\)
|
40
|
Author’s social circle
|
|
Price per standard drink (CHF)
|
2.00
|
Swiss supermarket survey (pre-study)
|
|
Volume per standard drink (dl)
|
3
|
Established practice
|
|
Alcohol by volume (ABV)
|
5%
|
Label inspection
|
|
Session duration (hours)
|
6
|
Author’s optimism
|
The price per drink (\(\bar{q}\))
introduces some uncertainty. The group will purchase alcohol at a Swiss
supermarket; a 33 cl bottle of beer retails in the range of CHF
1.50–3.00 depending on brand and retailer, with CHF 2.00 adopted as the
baseline central estimate.
Results
Primary Result:
Critical Expenditure Threshold
Substituting the parameters from Table 1 into the closed-form
expression derived in Section 3.4:
\[
X^* = \frac{\Delta \cdot T_0}{1 - p_0 - \Delta}
= \frac{0.003622 \times 5.4e+08}{1 - 0.03 - 0.003622}
\approx CHF 2,024,161
\]
The group of \(k = 40\)
individuals must collectively spend approximately CHF 2,024,161 on
alcoholic beverages at the Haus zum roten Sackel on
the evening of 22 May 2026 for the resulting shift in the estimated CPI
alcohol weight to achieve statistical significance at \(\alpha = 0.05\) (one-tailed).
The corresponding new proportion would be:
\[
\hat{p}_{\text{new}} = \frac{A_0 + X^*}{T_0 + X^*} = 0.033622
\]
which exceeds the critical threshold \(p_0
+ \Delta = 0.033622\) by construction.
Per-Person
Breakdown
Table 2 disaggregates the total requirement across the \(k = 40\) members of the group.
Table 2: Per-person requirements for statistical significance.
|
Quantity
|
Value
|
|
Required total expenditure
|
CHF 2,024,161
|
|
Required expenditure per person
|
CHF 50,604
|
|
Standard drinks per person (@ CHF 2.00)
|
25,302
|
|
Volume per person (litres of beer)
|
7,591
|
|
Pure ethanol per person (litres)
|
379.5
|
|
Pure ethanol per person (kg)
|
299.4
|
|
Drinks required per person per hour
|
4,217
|
|
Drinks required per person per minute
|
70.3
|
|
Multiples of LD50 (pure ethanol, 70 kg adult)
|
633
|
The Proportion Shift
as a Function of Expenditure
Figure 1 illustrates the trajectory of the estimated CPI alcohol
proportion \(\hat{p}_{\text{new}}(X)\)
as a function of total group alcohol expenditure \(X\), alongside the significance threshold
and the critical value \(X^*\).
As is evident from Figure 1, the proportion curve is steeply concave:
the initial effect of spending on the proportion is negligible because
the additional expenditure constitutes a vanishingly small perturbation
to the total survey denominator \(T_0\). Only at expenditure levels of order
CHF 2 million does the curve begin to diverge
meaningfully from \(p_0\), and only at
\(X^* \approx\) CHF 2,024,161 does it
cross the significance threshold.
Physiological and
Financial Context
The figures derived above are most readily appreciated against two
anchoring benchmarks: the human body’s capacity to metabolise ethanol,
and the typical financial resources of a Swiss resident.
Physiological
Constraints
The average adult human eliminates pure ethanol at a rate of
approximately 0.10–0.20 litres per hour (roughly 7–14
g/hour), depending on body composition and enzyme activity (Jones 2010). Each
person in our group would need to consume 379.5 litres of pure ethanol
over six hours — a rate of 63.3 litres per hour, or approximately
422 times the human elimination rate.
The median lethal dose (LD50) of ethanol for a 70 kg adult is
estimated at approximately 0.5–0.8 litres of pure alcohol (World Health Organization
2024; Jones 2010), yielding a
central estimate of \(\text{LD}_{50}
\approx\) 0.6 litres. The required quantity of 380 litres
represents approximately 633 times the LD50 —
comfortably in the range associated with immediate and irreversible
termination of the investigator’s research career.
Were a hypothetical participant somehow physiologically immune to
ethanol toxicity and able to consume without limit, clearing the
required blood alcohol at the body’s natural rate would take:
\[
\frac{380 \text{ litres}}{0.15 \text{ litres/hour}} \approx 2530 \text{
hours} \approx 0.3 \text{ years}
\]
Financial
Constraints
The median gross annual income in Switzerland is approximately CHF
80,000 (Bundesamt
für Statistik (BFS) 2022). The required per-person
expenditure of CHF 50,604 represents approximately 0.6 years of
median gross income — before tax, and assuming no other
expenditures on food, housing, or other non-alcoholic essentials.
Table 3 presents a comparative financial perspective.
Table 3: Financial benchmarks.
|
Item
|
Amount (CHF)
|
|
Required per-person expenditure
|
CHF 50,604
|
|
Swiss median gross annual income
|
CHF 80,000
|
|
Swiss GDP per capita (2024, approx.)
|
CHF 95,000
|
|
Median Swiss home purchase price (2BR, Zurich)
|
CHF 1,200,000
|
|
Formula 1 racing licence (2024, approx.)
|
CHF 10,000
|
Calorific
Perspective
At approximately 45 kcal per dl for a 5% ABV beer, each person would
consume approximately 3,415,772 kilocalories —
equivalent to roughly 1366 days of the recommended
daily caloric intake.
Discussion
Assumptions and
Limitations
Several simplifying assumptions warrant acknowledgement.
Inclusion in the HABE sample. The analysis proceeds
under the counterfactual that our group’s expenditure is counted as an
additional household observation in the HABE dataset. In reality, the
probability of any given household being selected for the HABE is
approximately \(9,000{} / 3,700,000{} \approx
0.24\%\) per three-year cycle. Our spending will, with
overwhelming probability, never enter the dataset at all. This renders
the entire enterprise moot from a strict inferential standpoint, but
does not diminish its theoretical interest.
Single-period expenditure. The HABE records annual
household expenditure, extrapolated from a one-month diary. A single
evening’s expenditure would need to be annualised before inclusion,
reducing its effective contribution by a factor of approximately 365.
Under this annualisation, the required single-evening expenditure would
increase by a factor of 365, yielding a figure of approximately
CHF 738,818,739 — roughly 0.21% of total estimated
Swiss household consumption expenditure.
Homogeneous group expenditure. We assume all \(k\) members of the group contribute
equally. In practice, beverage distribution is subject to social
dynamics, turn-taking conventions, and the well-documented “last round”
phenomenon, introducing variance not captured in the present model.
Price stationarity. We treat the per-drink price as
fixed. At the quantities implied by \(X^*\), one would expect significant upward
price pressure on Luzerner beer stocks, potentially triggering
inflationary effects in the very index we seek to perturb — a delightful
circularity that falls outside the scope of a partial-equilibrium
analysis.
Rational expectations. The model of Becker and Murphy (1988) suggests that rational addicts
will fully anticipate future consumption benefits when making current
investment decisions. Under this framework, agreeing to participate in
an evening at the Haus zum roten Sackel constitutes an
irreversible commitment to a consumption trajectory. We leave the
welfare analysis to subsequent work.
Group Size
Effects
Figure 2 demonstrates a key feature of the problem: while increasing
group size reduces the per-person burden linearly (since the total
requirement \(X^*\) is independent of
\(k\)), even a group of 40 individuals
requires CHF 50,604 each. No practically realisable group size renders
the task feasible.
Conclusion
We have derived and evaluated the minimum aggregate alcohol
expenditure required for a group of \(k\) individuals to produce a statistically
significant perturbation in the alcoholic beverages weight of the Swiss
Consumer Price Index basket.
The headline finding is unambiguous: if the 40 of us
collectively spend approximately CHF 2,024,161 — or
roughly CHF 50,604 per person — on alcoholic beverages
at the Haus zum roten Sackel on the evening of 22 May 2026, we
can indeed change the proportion of alcohol in the Swiss CPI basket by a
statistically significant amount at \(\alpha =
0.05\).
To be precise: the estimated CPI alcohol weight would shift from
\(p_0 = 0.03\) to \(\hat{p}_{\text{new}} = 0.03362\), a change
of 0.3622 percentage points, exceeding the critical threshold of 0.3622
percentage points.
Per person, this requires consuming:
- 25,302 standard 3 dl beers
- 7,591 litres of beer
- 379.5 litres of pure ethanol (approximately 633 ×
the lethal dose)
at a rate of 70 drinks per person per minute
sustained over a six-hour session.
We consider this an achievable and proportionate response to the
research question. We therefore recommend that the group proceed to the
Haus zum roten Sackel on 22 May 2026, place their order, and
contribute — however modestly — to Switzerland’s rich tradition of
empirical enquiry.
Whether the specific quantity demanded by statistical rigour can be
reconciled with continued biological function is a question we leave
open for future research.
Acknowledgements
The author thanks the friends who will accompany him on 22 May 2026
for their hypothetical willingness to contribute to this analysis. No
funding was received for this study; the author expects, however, that
the evening’s expenditure will significantly exceed his statistical
consulting budget.
Computational Reproducibility
All analyses were conducted in R (R Core Team 2024) with
the rmarkdown package (Allaire et al. 2023). The source
code is available upon request from the author, subject to his condition
that the requester buys the first round.
sessionInfo()
## R version 4.6.0 (2026-04-24)
## Platform: aarch64-apple-darwin23
## Running under: macOS Tahoe 26.4.1
##
## Matrix products: default
## BLAS: /Library/Frameworks/R.framework/Versions/4.6/Resources/lib/libRblas.0.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.6/Resources/lib/libRlapack.dylib; LAPACK version 3.12.1
##
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
##
## time zone: Europe/Zurich
## tzcode source: internal
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] kableExtra_1.4.0 knitr_1.51 ggplot2_4.0.3
##
## loaded via a namespace (and not attached):
## [1] vctrs_0.7.3 svglite_2.2.2 cli_3.6.6 rlang_1.2.0
## [5] xfun_0.57 stringi_1.8.7 textshaping_1.0.5 S7_0.2.2
## [9] jsonlite_2.0.0 labeling_0.4.3 glue_1.8.1 htmltools_0.5.9
## [13] sass_0.4.10 scales_1.4.0 rmarkdown_2.31 grid_4.6.0
## [17] evaluate_1.0.5 jquerylib_0.1.4 fastmap_1.2.0 yaml_2.3.12
## [21] lifecycle_1.0.5 stringr_1.6.0 compiler_4.6.0 RColorBrewer_1.1-3
## [25] rstudioapi_0.18.0 systemfonts_1.3.2 farver_2.1.2 digest_0.6.39
## [29] viridisLite_0.4.3 R6_2.6.1 magrittr_2.0.5 bslib_0.11.0
## [33] tools_4.6.0 withr_3.0.2 gtable_0.3.6 xml2_1.5.2
## [37] cachem_1.1.0
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