You have 10 individuals with values {$1, $2, $3, $4, $5, $6, $7, $8, $9, $10}, and suppose you find a way to charge one price to the consumers whose values are {$1, $2, $3, $4, $5}, and a different price to those consumers whose values are {$6, $7, $8, $9, $10}. MC of production is $2.50.
a. What price should you charge to the second group?
b. What are your expected profits from selling to the second group?
c. What price should you charge to the first group?
d. If it costs $5 to implement this price-discrimination scheme (to identify the two groups and prevent arbitrage between them), should you do it?