Conclusions

Key Findings¶

1. Price Ceilings Increase Consumption¶

A $7 beer ceiling at Yankee Stadium increases total beer consumption by approximately 77%, despite reducing attendance by 6%. This occurs because:

• The stadium raises ticket prices ~10% to offset lost beer margin

• Per-fan beer consumption more than doubles (from 1.0 to 2.1 beers)

• The intensive margin effect dominates the attendance decline

2. Selection Effects Alter Crowd Composition¶

The heterogeneous consumer model reveals differential attendance responses:

This shifts crowd composition from 40% to 41.4% drinkers (+1.4 percentage points).

3. Decomposition: Intensive vs Extensive Margin¶

Using Shapley decomposition:

• Intensive margin: +116% (each fan drinks more)

• Extensive margin: -16% (attendance falls)

The intensive margin accounts for more than 100% of the consumption increase because the extensive margin partially offsets it—attendance falls, which would reduce consumption if per-fan consumption stayed constant.

4. Results Are Robust¶

Monte Carlo analysis over 1,000 parameter combinations:

• Tickets rise in >95% of scenarios

• Consumption increases in >95% of scenarios

• Stadium profit falls in >99% of scenarios

The qualitative conclusions hold across wide parameter ranges for cross-price elasticity (0.0-0.3) and drinker share (30%-50%).

5. Model Validates Against Observed Prices¶

The heterogeneous model predicts an optimal beer price of $12.51, compared to$12.50 observed. This 0.08% calibration error (vs 20-30% for homogeneous models) suggests:

• Stadiums approximately profit-maximize

• The two-type consumer structure captures key demand features

• Observed prices reflect equilibrium behavior

Limitations¶

1. Simulation study: Parameters are calibrated, not estimated from transaction data

2. Static model: Doesn’t capture dynamic adjustments (season tickets, reputation effects)

3. No substitution: Doesn’t model pre-game drinking or smuggling responses

4. Partial equilibrium: No competition from other entertainment venues

5. Perfect enforcement: Assumes price controls are fully enforced

Testable Predictions¶

The model generates predictions that could be tested with stadium transaction data:

1. Under price ceilings, drinker share of attendance should increase

2. Per-fan consumption should rise more than proportionally to the price decrease

3. Ticket prices should partially offset beer margin compression

These predictions distinguish the heterogeneous model from representative agent approaches.

Broader Implications¶

For Stadium Pricing¶

The heterogeneous consumer framework reveals that:

• Price policies change who attends, not just how many

• Selection effects can amplify or dampen policy impacts

• Simple demand elasticity estimates miss composition effects

For Complementary Goods¶

When a monopolist controls two complements:

• Constraining one price shifts optimization to the other

• Consumer heterogeneity creates differential responses

• General equilibrium effects can dominate partial equilibrium intuitions

For Policy Analysis¶

Representative agent models may underestimate policy effects when:

• Consumers have heterogeneous preferences for the regulated good

• Price changes induce selection on consumer composition

• Multiple margins of adjustment exist

Future Research¶

• Empirical validation: Natural experiments from stadium policy changes

• Dynamic model: Repeated games, season ticket holder behavior

• Substitution patterns: Pre-game drinking, tailgating responses

• Spatial analysis: Crime externalities by distance from stadium

• Welfare analysis: Distributional effects across consumer types