Conclusions

Key Findings¶

1. Observed Prices Are Profit-Maximizing¶

Stadium beer at $12.50 is approximately profit-maximizing ($13.87 optimal) when accounting for:

• Taxes ($1.30/beer)

• Production costs ($2.00/beer)

• Internalized costs (varies by volume, C = 62.3(Q/1000)^2)

2. Stadiums Already Internalize Some Externalities¶

Crowd management, brand damage, and experience degradation are already priced in:

• Convex cost function: $C_{intern}(Q) = 62.3 \cdot (Q/1000)^2$

• At low prices ($5-7): Internalized costs become prohibitively high

• This explains why stadiums don’t sell cheap beer despite apparent profit potential

3. Significant External Costs Remain¶

Society bears $4.00/beer in external costs:

• Crime & violence: $2.50

• Public health: $1.50

Current taxes ($1.30) cover only 33% of these costs.

Pigouvian tax gap: $2.70/beer

4. Price Ceiling ($7) Has Mixed Effects¶

Pros:

• Consumer surplus: significant gains (+$3.9%)

• More affordable access

Cons:

• Stadium profit: $-34.5M/season

• Externality costs: increase (+$130.7%) due to higher consumption

• May face legal/constitutional challenges

Net: Complex welfare trade-offs with distributional concerns.

5. Pigouvian Tax is More Efficient¶

Adding $2.70/beer tax:

• ✓ Internalizes external costs

• ✓ Raises $8.7M/year for affected communities

• ✓ Reduces consumption to optimal level

• ✓ No deadweight loss (price = social MC)

• ✓ Economically efficient

Recommended policy: Pigouvian tax over price controls.

Policy Recommendations¶

Recommended: Pigouvian Tax¶

Implement $2.70/beer additional tax on stadium alcohol

• Consumer price: $13.87 → ${{ pigouvian_consumer_price }}

• Consumption: reduces to optimal level

• Revenue: $8.7M/year

• Allocate to Bronx community, public health, police

Alternative: Moderate Hybrid¶

If political constraints:

• Moderate tax (+$1.50/beer)

• Earlier sale cutoff (6th inning instead of 7th)

• Purchase limits (2 beers per transaction)

Not Recommended: Price Ceiling¶

• Large stadium revenue loss

• Increases externalities

• Potential legal challenges

• Less efficient than taxation

Broader Implications¶

For Other Stadiums¶

This framework applies to all sports venues:

• NFL, NBA, NHL stadiums face similar trade-offs

• Internalized vs external costs distinction is general

• Optimal taxation varies by local externality levels

For Alcohol Policy¶

General principle: Distinguish internalized from external costs.

Monopolists (stadiums, bars, restaurants) internalize negative effects on their own customers.

Policy should target true external costs (non-customers, public goods).

For Price Control Theory¶

Important insight: Observed prices may reflect internalized externalities, not just production costs.

Standard models that ignore firm’s internalization of customer experience effects will mis-predict optimal prices.

Limitations¶

1. Static model: Doesn’t capture long-run effects (season tickets, loyalty)

2. Single representative consumer: Ignores heterogeneity

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

4. Partial equilibrium: No competition from other entertainment

5. Perfect enforcement: Assumes price controls fully enforced

Future Research¶

• Rowdiness Feedback Loop: Explicitly model the negative utility of non-drinkers from high aggregate beer consumption.

• Convex Externalities: Investigate how social externalities (crime, health) might increase non-linearly with consumption.

• Heterogeneous consumers: Deeper dive into casual vs regular fans, potentially expanding consumer types.

• Dynamic model: Repeated games, learning, habit formation.

• Substitution patterns: Pre-game bars, tailgating.

• Spatial analysis: Crime externalities by distance from stadium.

• Empirical validation: Natural experiments with policy changes.

Final Thought¶

The key innovation is recognizing that monopolists internalize negative effects on their own customers.

This is why simple supply-demand models fail to predict stadium pricing - they miss the convex experience degradation costs that stadiums face.

For policy: Focus on true external costs (crime, public health) that remain uninternalized. Current taxes cover only 33% of these costs.

Optimal policy: $2.70/beer Pigouvian tax, raising $8.7M/year for NYC.