Question

Suppose Robert is a typical Arizona Wildcats fan, and his demand curve for UArizona football games is given by Pp = 120 - 10G, where G is the number of home games that Robert attends. Suppose the marginal cost of supplying tickets is $0. a) If UArizona must charge the same price for each home game, what price should they charge so that Robert will attend all 8 home games (1st blank]? How much revenue do they earn from Robert (2nd blank]? What is Robert's consumer surplus [3rd blank]? (Hint: It might be helpful to draw a graph. Recall that the area of a triangle is equal to % x base x height.] b) Suppose Robert is a season ticket holder, and all season ticket holders must pay a one-time personal seat license fee, in addition to the price for each ticket. What should UArizona charge Robert for his personal seat license [4th blank)? [Hint: This is an example of two-part pricing.) c) How much revenue would UArizona earn if instead they used perfect price discrimination on Robert [5th blank]? [Hint: UArizona would charge Robert a different price for each game.)

Answer 1

a) The demand curve for Robert is given as,

Pd = 120 - 10G

Here Pd = price per game

G = total number of games attented by Robert.

To calculate the price at which robert will attend exactly 8 home games, we just need to put G=8 in Roberts demand function. Let's calculate the price at which robert will attend exactly 8 games.

Pd = 120 - 10×8

Pd = 120 - 80

Pd = $40.

So the price per game will be 40 at which robert will attend exactly 8 home games.

The total revenue that they will earn from robert will simply be = Pd×G

Where Pd = price per game charged

And G = number of games attended by Robert.

Total revenue = 40×8 = $320

The total consumer surplus of Robert will be calculated as,

Consumer surplus = 1/2×(MWP - Pd)×G

Here MWP = maximum willingness to pay which is calculated by putting G=0 in Robert's demand function. Which will tell us what is the maximum aamount of price that Robert is willing to pay for a game.

Putting G=0, in Robert's demand function we get,

Pd = 120 - 0

Pd = $120= MWP

So the maximum willingness to pay for a game for Robert is $120.

Now putting this value to calculate the consumer surplus of Robert, we get.

Consumer surplus = 1/2×(120-40)×8

Consumer surplus = 1/2×(80)×8

Consumer surplus = 80×4 = 320.

So the consumer surplus that Robert is enjoying is equal to $320.

b) In case of two-part pricing, consumers are made to pay one time fees apart from per unit price that they pay.

In this case Robert needs to pay time license fee to be able to buy match tickets. The license fees will be set as to make Robert indifferent between buying a match ticket or not.

Robert will be indifferent between buying a match ticket or not, when his consumer surplus will be become zero. In other words as long as he is enjoying some positive consumer surplus he will be happy to buy match ticket and watch match.

We already calculated the consumer surplus for Robert, so to make his consumer surplus zero the one time license fees that will be set for Robert will be $320.

Now you can see the consumer surplus of Robert is 0, now he will be indifferent between buying a match ticket or not.

C) Under perfect price discrimination the price is charged from consumers is not uniform.

The price is charged as much as consumer is willing to pay, such that he enjoys no consumer surplus. As you can already see the total revenue in this case will be $320 from the first part plust the $320 of consumer surplus that will be taken away from robert under perfect price discrimination.

Total revenue in this case will be = $320 + $320= $640.

Let's see how it's done.

Given the demand function of Robert,

Pd = 120 - 10G

We need to integrate the price function over the given limit of G that from 0 to 8​​​​​

Total revenue = $\int$ ​​​​​​(120 - 10G) dG

The lower limit of G is 0 and upper limit of G will be 8, since he is purchasing 8 match tickets as given to us in part a.

Total revenue = [120G - 10G^2/2]

Putting upper limit of G=8 and lower limit G=0we get,

Total revenue = [120×8 - 10(8)^2/2] - [120×0 -10(0)^2/2]

Total revenue = [960 - 5×64]

Total revenue = 960 - 320 = $640.

So the total revenue in this case will be equal to $640.

Note: If you still have any doubts regarding step or concept please ask me through comment section.

Thank you.