A Baseball Teams Attendance Depends on the Number of Games

question 57

Essay

A baseball teams attendance depends on the number of games it wins per season and on the price of its tickets.The demand function it faces is Q = N(20 - p), where Q is the number of tickets (in hundred thousands)sold per year, p is the price per ticket, and N is the fraction of its games that the team wins.The team can increase the number of games it wins by hiring better players.If the team spends C million dollars on players, it will win .7 - 1/C of its games.Over the relevant range, the marginal cost of selling an extra ticket is zero.
a.Write an expression for the firms profits as a function of ticket price and expenditure on players.
b.Find the ticket price that maximizes revenue.
c.Find the profit-maximizing expenditure on players and the profit-maximizing fraction of games to win.

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Definitions:

Dendritic Spines

Small protrusions on dendrites of neurons that receive signals from other neurons and are key to synaptic strength and learning.

Axon Terminals

The very end of a branch of a nerve's axon, a long slender nerve fiber that conducts electrical signals to a nerve synapse.

Neural Plasticity

Refers to the brain's ability to change and adapt as a result of experience.

Synaptic Function

The process by which neurons communicate with each other across synapses, involving the release and detection of neurotransmitters.