Question

Ten potential attendees of a sporting event have valuations that can be arrayed from the most to the least in $1 increments starting from $10. Thus, highest valuer is willing to pay $10 for a ticket, the next highest, $9, and so on down to $1. Suppose that the stadium only seats 5. (a) What is the market-clearing price? (Assume that the price must be in whole dollar amounts.) (b) Suppose the price is set at $3. How many consumers will desire to attend the event? How will the 5 available tickets likely be allocated? (c) Suppose a consumer with a willingness to pay less than $5 acquires a ticket for the $3 selling price. Describe the side transaction between this consumer and one who values the ticket at more than $5 but did not get one.

Answer 1

a) The stadium has only 5 seats . So market clearing price will be $5 . The last 5 valuers with $5 to $10 as reservation price will buy the tickets . People with reservation price below $5 will not be able to afford .

b) At $3 , 8 people will desire to attend the event ( reservation price from $3 to $10 ) . The 5 available tickets will probably be allocated on first come first serve basis among 8 people .

c) Suppose the consumer has willingness to pay = $4 ( < $5 )

Selling price = $3

Consumer surplus = 4 - 3 = $1

Now let another consumer value the ticket at $6 ( more than $5 )

This consumer did not get the ticket .

If the previous consumer sells the ticket at $5 , then this second consumer will buy the ticket and have a consumer surplus of $1 ( 6 - 5)

The first consumer gets the ticket at $3 , sells at $5 , makes a profit of $2 . The second consumer buys at $5 , gets a consumer surplus of $1 .