Download Practice Question Set 1 Demand and Revenue Econ 416/516 Sports

Practice Question Set 1
Demand and Revenue
Econ 416/516 Sports Economics
Each of the following 4 questions gives an equation that represents the demand for tickets for a sports
team’s games. P represents the ticket price in dollars and Q represents the quantity of tickets
demanded per game in thousands. For simplicity, assume that facility capacity is not an issue (i.e. ignore
it). Round all dollars to the nearest 100th and round all quantity numbers to the nearest hundredth.
1)
a.
b.
c.
d.
Express Q as a function of P.
If Q = 40 (40,000) fans attend a game, what was the ticket price?
If the team charges a price of $100, how many tickets will be demanded?
Find the total revenue function and the marginal revenue function. Express both as a
function of Q.
e. What ticket price maximizes total revenue? What Q?
f. What is the elasticity of demand between $100 and $90?
g. What is the elasticity of demand at $70?
2)
a.
b.
c.
d.
Express Q as a function of P.
If 500 fans (Q = 0.5) attend a game, what was the ticket price?
If the team charges a price of $4, how many tickets will be demanded?
Find the total revenue function and the marginal revenue function. Express both as a
function of Q.
e. What ticket price maximizes total revenue? What Q?
f. What is the elasticity of demand between $6 and $4?
g. What is the elasticity of demand when 1,000 fans attend a game (Q = 1)?
3)
a.
b.
c.
d.
e.
f.
g.
4)
a.
b.
c.
Find the inverse demand function.
If Q = 20 fans attend a game, what was the ticket price?
If the team charges a price of $20, how many tickets will be demanded?
Find the total revenue function and the marginal revenue function. Express both as a
function of Q.
What ticket price maximizes total revenue? What Q?
What is the elasticity of demand between P = 12 and P = 15?
What is the elasticity of demand at P = $12?
,
Find x (the slope of the inverse demand function).
If 8,000 fans attend a game, what was the ticket price?
If the team charges a price of $10, how many tickets will be demanded?
d. Find the total revenue function and the marginal revenue function. Express both as a
function of Q.
e. What ticket price maximizes total revenue? What Q?
f. What is the elasticity of demand between $3 and $4?
g. What is the elasticity of demand at P = $2?
Answers to selected questions:
2.
a.
b.
c.
d.
e.
f.
g.
Q = 2 – 0.2Q
P = $7.50
Q = 1.2 (1,200)
TR = 10Q – 5Q2; MR = 10 – 10Q
P = 5; Q = 1 (1,000)
d = -1
d = -1