Background & Literature

Current Pricing at Yankee Stadium (2025)¶

Observed Prices¶

• Beer: $10-15, average $12.50

• Tickets: Average $80

• Stadium capacity: 46,537

Consumer Behavior¶

• ~40% of attendees consume alcohol at games Lenk et al. (2010)

• Mean BAC among drinkers: 0.057%

• Average consumption: 2.5 beers among drinkers

• Overall average: 1.0 beers per attendee

Literature Review¶

Demand Elasticities¶

Ticket Demand (Inelastic)

Noll (1974) found ticket demand elasticity of -0.49 for MLB (1970-71 seasons), while Scully (1989) estimated -0.63 to -0.76 for the 1984 season.

Teams consistently price in the inelastic region of ticket demand Fort (2004).

Beer/Concessions Demand

Krautmann & Berri (2007) found that:

• Beer demand is relatively inelastic in MLB

• Teams price tickets below revenue-maximizing level to drive concession sales

• Concessions are high-margin complements to tickets

General alcohol demand elasticities range from -0.79 to -1.14, but stadium demand is more inelastic due to:

• Captive audience (no alternatives during game)

• Experiential consumption (part of stadium ritual)

• Social pressure and peer effects

Complementarity¶

Coates & Humphreys (2007) explain that tickets and concessions are complementary goods:

• Higher beer prices reduce attendance

• Lower ticket prices increase beer sales

• Teams jointly optimize across both revenue streams

This explains why teams price in the inelastic region of ticket demand - they’re maximizing total profit, not just ticket revenue.

Externalities from Stadium Alcohol Consumption¶

Crime & Violence¶

Carpenter & Dobkin (2015) found:

• 10% increase in alcohol consumption → 1% increase in assault

• 10% increase in alcohol consumption → 2.9% increase in rape

Rees & Schnepel (2009) documented that college football games increase assault, vandalism, and disorderly conduct, with effects concentrated on game days and in the immediate vicinity.

Stadium-specific evidence:

Luca & Sood (2018) provides the most directly relevant evidence using MLB data from Philadelphia (2006-2015). They exploit the natural experiment that baseball games vary in length while alcohol sales stop after the 7th inning. Key finding: extra innings significantly reduce stadium-area crime, especially assaults, by giving fans more time to sober up before departure.

Montolio & Planells-Struse (2019) studied FC Barcelona home games and found elevated thefts within a 700-meter radius of the stadium on game days. Away matches showed no effect, confirming the stadium as the crime generator.

Glassman et al. (2018) documented a natural experiment at a college football stadium: 330 crime incidents/year without alcohol sales (2009-2011) vs 475 with alcohol (2012-2013)—a 44% increase.

Stadium alcohol cutoff policies (e.g., stopping sales after 7th inning) reduce post-game crime by allowing fans to sober up before leaving.

Public Health Costs¶

Manning et al. (1991) estimated external costs of alcohol at $0.48-$1.19 per drink (1986 dollars), including:

• Traffic accidents

• Emergency room visits

• Long-term health impacts

• Fetal alcohol syndrome

Inflation-adjusted to 2025: ~$1.50-$3.00 per drink.

Rehm et al. (2009) provide global estimates of alcohol-related disease burden and economic costs.

Total External Costs¶

Combining crime and health externalities:

• Crime: $2.50 per beer

• Health: $1.50 per beer

• Total: $4.00 per beer

These are costs borne by society, not the stadium.

Stadium-Specific Adjustments¶

Our $4.00/beer estimate may be conservative or generous depending on stadium-specific factors:

Factors suggesting HIGHER externalities:

• Concentrated timing: 40,000+ fans leaving at once creates peak-load problems for police, transit

• Geographic concentration: Bronx neighborhood bears costs of 81 home games

• Driving risk: Some fans drive home (vs. bar patrons who may cab/walk)

• Group dynamics: Stadium crowds may amplify aggressive behavior

Factors suggesting LOWER externalities:

• Controlled environment: Security, sales cutoffs, ID checks reduce worst outcomes

• Public transit access: Most fans use subway (4 train), reducing DUI

• 7th inning cutoff: Allows sobering before departure

• Premium pricing: $12.50/beer naturally limits consumption

Uncertainty range:

• Conservative: $2.50/beer (stadium safety measures effective)

• Baseline: $4.00/beer (used in model)

• High: $6.00/beer (neighborhood bears concentrated costs)

This uncertainty is incorporated in our Monte Carlo analysis, which samples crime costs from $1.50-$3.50 and health costs from $1.00-$2.00.

Theoretical Foundation: Price Controls and Complementary Goods¶

Leisten (2025): Rigorous Analysis of Beer Price Ceilings¶

Leisten (2025) provides the theoretical foundation for analyzing beer price controls at stadiums through a rigorous monopoly model with complementary goods.

His Model Setup:

• Ticket demand: $q_x(p_x)$

• Beer demand: $q_y = q_x(p_x) \cdot q_y(p_y)$ (multiplicative form)

• Key assumption: Beer prices do NOT directly affect ticket demand (one-way complementarity: tickets → beer)

• Zero marginal costs (simplification)

• Log-concave demand functions

First-Order Conditions (Unconstrained):

For beer (standard monopoly markup):

For tickets (markup with complementarity discount):

The second term represents a “complementarity discount” - stadium lowers ticket prices because each attendee brings complementary beer revenue.

With Beer Price Ceiling $Z$:

When ceiling binds, the FOC for tickets becomes:

The complementarity discount shrinks as $Z$ falls, so $p_x$ must rise to restore the FOC.

Key Result:

Taking total derivatives with respect to ceiling $Z$:

The sign depends on whether $2q_x'(p_x)^2 > q_x(p_x)q_x''(p_x)$.

Under log-concavity (his key assumption), this inequality holds, proving:

Meaning: Lower beer ceilings cause ticket prices to rise.

Our Extension:

We extend Leisten’s framework by:

1. Two-way complementarity: Beer prices affect ticket demand in our model ($A(P_T, P_B)$)

2. Realistic costs: Marginal costs, taxes, internalized externalities

3. Quantitative calibration: Predicts magnitude (not just sign) of effects

4. Welfare analysis: Decompose impacts across consumers, producers, society

Both approaches reach the same qualitative conclusion but through different mechanisms:

• Leisten: Complementarity discount shrinks → tickets rise to restore markup

• Our model: Beer margin collapses → stadium shifts to tickets → attendance falls (limiting beer sales at bad margin)

Why Stadiums Charge $12.50¶

Internalized Costs (Already in Stadium’s Optimization)¶

Stadiums face costs from excessive alcohol consumption that affect their own profits:

1. Crowd Management: Security, cleanup, liability insurance

2. Experience Degradation: Drunk fans hurt experience for other customers → reduces repeat attendance

3. Brand/Reputation: “Cheap beer stadium” image → lowers long-run revenue

4. Capacity Constraints: Service bottlenecks, operational costs

These are negative externalities on other customers that the monopolist stadium internalizes.

Our model shows these internalized costs are convex (accelerating):

At $5 beer: Would sell 117k beers → internalized cost = $13.8M At $12.50: Sells 40k beers → internalized cost = $1.6k

Stadium chooses $12.50 to maximize profit accounting for these costs.

Distinction: Internalized vs External¶

Only the external costs ($4.00/beer) justify policy intervention beyond what the stadium already does.

Policy Context¶

Current Alcohol Policies at Stadiums¶

Lenk et al. (2010) surveyed 100+ professional stadiums and found:

• Most stop alcohol sales after 7th inning

• Varying ID checking enforcement

• Few quantity limits per transaction

• No stadium-specific price controls

Proposed Policies¶

Various jurisdictions have considered:

• Price floors (minimum prices)

• Price ceilings (maximum prices)

• Purchase limits (beers per transaction)

• Earlier sale cutoffs

• Complete alcohol bans

Our analysis evaluates these policies using welfare economics framework.