week 3.2 Flashcards
What decisions must a team make in joint optimization?
Teams decide on both the level of player/coaching talent and the optimal ticket price.
What does the ticket demand function depend on?
The ticket demand function depends on both talent (t) and price (p).
What is the formula for ticket demand?
q = at^(1/2) - bp.
What is the cost function for talent?
TC(t) = kt^2.
Why does talent cost increase at an increasing rate?
Because hiring more talent requires increasing investment.
What is the formula for total revenue in ticket pricing?
TR = q * p = at^(1/2) p - bp^2.
How do we optimize ticket pricing using the profit function?
Differentiate profit function with respect to price and set the derivative to zero.
What is the formula for the optimal ticket price (p*)?
p* = (1/2) (a/b) t^(1/2).
How does talent level (t) influence optimal ticket price?
Higher talent increases demand, allowing teams to charge a higher price.
What is the revenue function after substituting p*?
TR(t) = (1/4) (a^2 / b) t.
What is the profit function including talent costs?
π(t) = (1/4) (a^2 / b) t - kt^2.
What is the formula for the optimal talent level (t*)?
t* = (1/8) (a^2 / bk).
How does price sensitivity (b) impact optimal talent level?
Higher price sensitivity (b) reduces talent investment.
Why does a profit-maximizing team invest in talent until MR = MC?
Because profit maximization occurs where marginal revenue equals marginal cost.
What is the revenue function for a win-maximizing team?
TR(t) = βt.
How does a win-maximizing team determine the optimal talent level?
By setting profit to zero: π = TR - TC = βt - kt^2 = 0.
What equation is used to set profit to zero?
βt - kt^2 = 0.
What are the two possible solutions for t*?
t* = β/k or t* = 0.
Which solution is valid for the optimal talent level?
Since t* = 0 is unrealistic, the valid solution is t* = β/k.
How does win-maximization differ from profit-maximization in talent investment?
Win-maximizing teams invest more in talent than profit-maximizing teams.
What does a win-maximizing team prioritize in ticket pricing?
It prioritizes maximizing ticket demand (i.e., increasing wins → increasing attendance).
How does a win-maximizing team adjust ticket prices to maximize attendance?
By adjusting ticket prices dynamically based on talent level and demand.
Why might a win-maximizing team set lower ticket prices?
To sustain higher fan engagement and revenue stability.
How does market demand (a) affect optimal talent level?
Higher a increases optimal talent investment.
