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Quantity Discount Back Bay Book sells paperbacks for a standard price of $12 each. Customers who buy five or more books can get a price of $8 per book. All customers with an elastic demand have the...

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Quantity Discount

Back Bay Book sells paperbacks for a standard price of $12 each. Customers who buy five or more books can get a price of $8 per book.

All customers with an elastic demand have the following individual demand curve.

Qd= 6-0.25P

  1. How many books would this customer buy at the regular price of $12 each?

  2. What is the net change in consumer surplus if the customer buys five books to get the discount price of $8 each?

  3. Would this customer take advantage of a quantity discount?

  4. Bay Back Books wants to use quantity discount to reveal the difference between customers with the elastic demand and customers with the inelastic demand. What additional information would be needed in order to determine whether the quantity discount scheme is incentive compatible?


Versioning

The Green Gables Amphitheater has these three equal-sized seating areas for concerts.

  • Close: Seats right in front of the stage

  • Mid-range: average seats

  • Far: Seats in the very back

For an upcoming concert, there are three types of potential concert-goers: Fanatics, enthusiasts, and Casual Fans.

Each of these three groups has the following set of willingness to pay values for the various types of tickets:

  • Fanatics are willing to pay:

    • $300 for a good seat

    • $150 for a mid-range set

    • $100 for a far set

  • Enthusiast are willing to pay:

    • $150 for a good seat

    • $100 for a mid-range seat

    • $75 for a far seat

  • Casual fans are willing to pay:

    • $85 for a good seat

    • $75 for a mid-range seat

    • $65 for a far seat

The green gables amphitheater estimates that ⅓ of the potential audience falls into each category, but there is no way to identify which category a person belongs to which they purchase their tickets. The amphitheater has set up the following price structure.

  • Price for a good seat is $200

  • Price for a mid-range seat $95

  • Price for a far seat is $60

The amphitheater wants to fill the venue completely, with fanatics in the good seats, enthusiasts in the mid-range seats, and casual fans in the far seats. You have been consulted to determine whether this price structure will meet their goals

Answer these questions:

  1. What type of ticket will each group want to purchase?

  2. Is there any type of ticket that no one would want to purchase?

  3. Is the pricing scheme incentive compatible?

  4. If it is not incentive-compatible, explain in a couple of sentences why this is the case?


Answered Same DayMar 12, 2022

Solution

Manashi answered on Mar 13 2022
31 Votes
Quantity Discount
Demand Curve Equation: Qd = 6 – 0.25p
1. How many books would consumer buy at a regular price of $12?
Solution: Given the demand equation Qd = 6 – 0.25p
Here P = $12
Hence Quantity demanded (Qd) will be
= 6 – 0.25 x $12
= 6 – 3
= 3 books
2. What is the net change in consumer surplus if the customer buys five books to get the discount price of $8 each?
Solution: If the consumer buys 5 books, he will be able to avail the offer of a discount in the form $4 per book (since each book he will be able to buy for $8)
So, the consumer will spend = $8 x 5 books = $40
At regular price of $12, the total price of 5 books will be
$12 x 5 books = $60
The consumer surplus = Maximum price willing to pay – Market Price
= $60 - $40 = $20
3. Would this customer take advantage of a quantity discount?
Solution: There is a change in consumer surplus by $20. Also, the consumer has an inelastic demand. Hence the consumer will take advantage of the discount.
4. Bay Back Books wants to use quantity...
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