Notes on Price Elasticity of Demand, Dynamic Pricing, and Group Project Logistics

Price Elasticity of Demand: Definition, Interpretation, and Sports Context

This section collects the core ideas from the lecture about price elasticity of demand (PED), its calculation, interpretation, and why it matters in the sports industry—especially for ticket sales. The PED is the ratio of the percent change in quantity demanded to the percent change in price. In formal terms, the elasticity of demand is:

$E_d = \left|\dfrac{\%\Delta Q}{\%\Delta P}\right| = \left|\dfrac{(\Delta Q / Q)}{(\Delta P / P)}\right|.$

Note that the sign is typically ignored in the absolute value when classifying elasticity (so we speak of elastic, inelastic, or unit elastic), even though the underlying relationship between price and quantity demanded is negative for most goods.

Key qualitative points:

Elastic demand: |E_d| > 1. Quantity demanded changes by a larger percentage than the price change. Revenue tends to fall when price rises (for elastic goods) because the quantity drop more than offsets the higher price.
Inelastic demand: |E_d| < 1. Quantity demanded changes by a smaller percentage than the price change. Revenue tends to rise when price rises (for inelastic goods) because the quantity drop is small.
Unit elastic demand: |E_d| = 1. Price changes are offset by opposite changes in quantity such that total revenue remains unchanged.

Sports-specific motivation: ticket sales in spectating sports often exhibit inelastic demand due to high interest and a lack of close substitutes for live games, especially for marquee events like the Super Bowl. The instructor points to the Super Bowl as a case where average ticket prices can be very high (for example, around $5{,}000$ in a given year) alongside high viewership. The same price change can have a much smaller effect on quantity demanded if demand is highly inelastic.

PED in practice: the percent changes used are not about absolute quantities or prices but about their percentage changes. In the example with running shoes and football tickets, the elasticity is computed from observed percent changes, not from the price or quantity levels alone.

PED and total revenue: total revenue (TR) is the area under the price-quantity rectangle, i.e.

$\text{TR} = P \times Q.$

When PED is elastic, a price increase reduces TR; when PED is inelastic, a price increase can raise TR; when PED is unit elastic, changes in price do not affect TR.

Illustrative examples from the transcript:

1) Running shoes:

Last year price: $P1 = 75$ ; this year price: $P2 = 82.50$ . The price increased by $\%\Delta P = \dfrac{82.50 - 75}{75} = 0.10 = 10\%.$
Quantity demanded: from $Q1 = 1{,}400{,}000$ to $Q2 = 1{,}230{,}000$ , a drop of $\%\Delta Q = \dfrac{1{,}230{,}000 - 1{,}400{,}000}{1{,}400{,}000} \approx -12.1\%.$
Elasticity: $E_d \approx \left|\dfrac{-12.1\%}{+10\%}\right| \approx 1.21.$ This is elastic.
Result on TR: last year TR = $75 \times 1{,}400{,}000 = 105{,}000{,}000$ ; this year TR = $82.50 \times 1{,}230{,}000 \approx 101{,}175{,}000$ . TR declined despite the higher price.

2) Football game tickets:

Last year price: $P1 = 120$ ; this year price: $P2 = 132$ . Percent price change:
$\%\Delta P = \dfrac{12}{120} = 10\%.$
Quantity demanded: from $Q1 = 58{,}000$ to $Q2 = 57{,}900$ , a change of $\%\Delta Q = \dfrac{-100}{58{,}000} \approx -0.17\%.$
Elasticity: $E_d \approx \left|\dfrac{-0.17\%}{+10\%}\right| \approx 0.02.$ This is inelastic (very low sensitivity to price changes).
In this inelastic case, a price rise can increase TR (though the example notes a smaller percentage change in quantity), consistent with the idea that elastic vs inelastic shapes how revenue responds to pricing.

Useful intuition: the lecture emphasizes that the decision to raise price to increase revenue depends on PED, not just intuition. For elastic products, price hikes can reduce total revenue; for inelastic products (common in sports tickets for marquee games), price hikes can raise total revenue.

Dynamic pricing is a related concept that exploits PED by using multiple price points to maximize total revenue. In sports contexts, dynamic pricing assigns different prices to different seats and times, aiming to capture more consumer surplus and fill more seats, with the understanding that consumer responsiveness to price can vary by seat location, game importance, opponent, and other factors.

A practical takeaway: the elasticity of demand helps sports managers decide whether to raise prices, lower them, or implement dynamic pricing across different games and seating categories to optimize total revenue.

Foundational backdrop: the discussion reviews the basic supply-demand framework, including how price interacts with quantity supplied and demanded to determine market clearing price, and how surpluses and shortages arise when markets are not at equilibrium. A few classic determinants are introduced for both demand and supply, which feed into the elasticity analysis.

Supply and Demand refresher (core concepts):

The supply curve shows the relationship between the price of a good and the quantity producers are willing to supply. It typically slopes upward because higher prices reward producers with more profit per item, incentivizing larger production. The demand curve shows the relationship between price and the quantity buyers want to purchase, usually sloping downward since lower prices lead to higher quantity demanded.
The intersection of supply and demand gives the market-clearing price (equilibrium). If price is above equilibrium, a surplus exists; if below, a shortage exists. These statements refer to price phenomena rather than absolute quantities.
Several determinants influence demand: substitutes and complements, expectations about future prices or income, marketing and consumer tastes, income levels (normal vs inferior goods), demographics (age, gender, education), travel time/accessibility, team performance and attendance, and the degree of uncertainty about outcomes. In sports, these determinants shape how many fans are willing to attend a game at a given price.
Determinants of supply include input prices, technology, taxes and subsidies, and the number of suppliers in the market. In sports, these factors affect the cost and willingness of venues or teams to supply seats.
The lecture notes that in many sports markets, a monopoly-like situation or dominant supplier can give the seller more price-setting power, which brings PED into sharper focus for revenue planning.

Elastic vs. inelastic demand in practice:

The slope of the demand curve matters for elasticity: a flatter (more horizontal) demand curve implies higher elasticity; a steeper (closer to vertical) curve implies lower elasticity.
Elastic demand (>1) means large reactiveness of quantity to price changes; in such cases, price increases tend to reduce total revenue. Inelastic demand (<1) means smaller quantity changes, so price increases can increase total revenue. Unit elastic demand (=1) implies total revenue is unchanged when price changes.

Revenue considerations and dynamic pricing in sports:

The sports market often exhibits inelastic demand for certain events (e.g., highly anticipated games or rival matchups) where fans are relatively insensitive to price increases in the short run.
Dynamic ticket pricing uses multiple price points to maximize revenue by capturing different levels of willingness to pay among fans. It can apply beyond sports to airlines and hotels.
When demand is inelastic, raising prices can be a viable strategy to lift total revenue, while with elastic demand, higher prices may reduce revenue. In unit elastic cases, revenue remains unchanged with price moves.
In practice, dynamic pricing also considers factors such as opponent quality, rivalry games, resale values on secondary markets, promotions, team performance, weather, and scheduling (weekday vs weekend), among others.
If tickets remain unsold, venues may still generate incremental revenue through concessions, parking, merchandise, and other on-site spending, which can justify selling remaining seats at lower prices later.

Examples of dynamic factors affecting price changes in sports tickets (factors listed in the lecture):

Opponents and rivalry status; competitiveness of the matchup.
Resale value on the secondary market, including expectations of high demand for premium events.
Game promotions and in-game incentives (e.g., bobblehead nights, memorabilia giveaways).
Win/loss streaks and overall team performance; the number of remaining games in the schedule.
Weather conditions for outdoor venues, which can depress or boost attendance.
Day of the week (weekend vs weekday) and time of day; weekend games usually have higher demand.
Other entertainment activities around the same time (e.g., major events like the Super Bowl weekend) that could affect demand.

Group project logistics and resources (course management and planning details)

The instructor uses Brightspace for the group project and communicates several procedural points important for organizing work and submitting deliverables. The course folder for assignment number two contains five sections that must be addressed for the sportswear industry and the chosen brand. Group presentations are scheduled for Monday, Wednesday, and Friday, October 6–8, with each group allotted about 12–15 minutes. PowerPoint slides must be submitted to Brightspace by midnight on October 5; peer evaluations are due by Wednesday, October 8 via a separate submission link. A single group member should upload the final group submission (macro file) so the platform recognizes it as a group submission; Mac users should not submit Google Docs or Pages files, as those formats are not allowed on Brightspace.

Group assignments and branding (as listed in the transcript):

Group 1: Andres, Sean, and Alyssa.
Group 2: Nike.
Group 3: Adidas.
Group 4: The New Balance.
Group 5: The Armor (as written in the transcript).
Group 6: Wilson.
Group 7: Puma.
Group 8: Little Lemon.

A dedicated “Groups” tool is available in Brightspace to help students identify group members, communicate, and share contact information. The instructor emphasizes using the Brightspace groups feature to coordinate, given that the fall break is upcoming. A separate assignment folder provides resources, including an “additional resource” folder containing valuable industry reports for Adidas, 86, Blue Moon, and Newbella (as named in the transcript). These industry reports are accessible through the Farmingdale Library, which includes high-value dossiers that can be downloaded for free with the student’s library access. The course guide recommends using the school library’s research portal for sports management, which includes industry reports and academic journal articles. The portal also mentions the “TISTA” dossier site; access to these reports is available through the school library rather than a direct Google search. The Sports Business Journal is also available via full access for Farmingdale State College students through the library. These resources are intended to support the group project with credible sources.

Exam and course schedule reminders:

The first exam is scheduled for October 13, with tentative timeline for the course. A fall break is coming next week, so students should prepare accordingly.
Students should actively locate group members, introduce themselves, and begin coordinating group work. The instructor suggests using the Brightspace Groups tool to share contact information and begin collaboration, especially during the break.

Practical notes for students:

If you have questions, raise your hand in class or use the Brightspace tools to contact group members.
The emphasis is on getting groups formed and starting collaboration early, particularly before the fall break, so you can proceed with the project efficiently.
The instructor anticipates a discussion-heavy session but wants students to focus on forming groups and exchanging basic information to facilitate teamwork.

Overview of key takeaways for study and application

Price elasticity of demand is a central concept for analyzing how price changes affect quantity demanded and total revenue, especially in ticket sales for sports events.
In sports, demand for marquee events tends to be relatively inelastic, which can justify price increases and dynamic pricing strategies to maximize revenue.
Dynamic pricing uses multiple price points to capture varying willingness to pay and optimize revenue, while considering factors like opponent strength, promotions, weather, schedule, and secondary market activity.
A solid understanding of supply and demand basics, as well as elasticity, informs pricing decisions, revenue management, and strategic planning in sports organizations.
For group projects, the Brightspace platform provides grouping features, submission guidelines, and access to a curated set of industry reports and journals to support research. Planned deadlines, group assignments, and submission protocols should be followed carefully to ensure a successful presentation and paper submission.

Determinants of Demand (summary highlights)

Substitutes and complements affect market demand for a sport-related good or event.
Expectations about future prices or future income can shift demand.
Marketing campaigns and consumer tastes can shift demand in favor of a brand or event.
Income effects: normal goods rise with income; inferior goods rise when income falls.
Demographics (age, education, gender), travel time to activities, and urban vs. rural location influence demand patterns, especially for live sports.
Team performance, attendance rates, and the uncertainty of outcome influence fans’ willingness to pay for tickets and attend.

Determinants of Supply (summary highlights)

Input prices and production costs affect the quantity supplied at any given price.
Technology adoption can reduce costs and increase supply.
Taxes and subsidies can alter production costs and thus supply.
The number of suppliers (competition) in the market can change the total quantity supplied.

Important caveats and practical reminders from the lecture

The elasticity concept is used to analyze price changes, but real-world pricing decisions also consider strategic considerations like exclusivity, fan loyalty, and promotional tactics.
In cases of monopoly or strong seller power, priced-based revenue optimization becomes a central managerial task, with PED guiding whether price increases will raise or lower total revenue.
The lecture emphasizes that many sports-related products (e.g., football game tickets) exhibit inelastic demand, which supports the potential for price increases to boost revenue under certain conditions.
The Brightspace platform and the library resources are intended to support the group project with credible industry reports and journal articles, enabling well-sourced analyses of brands such as Adidas, Nike, Puma, Wilson, and others mentioned in the group assignments.

Note: Throughout, LaTeX formatting is used for equations and percent-change expressions to maintain precision across the notes.