You are the manager of a firm that sells CD players and DVD players. You work in Buffalo,
New York and this is the middle of winter. So the people that live within walking distance are
the only customers you might get, and there are no other stores nearby. (FedEx and UPS can't get
through the snow either, so don't think about these customers shopping online). You know that
there are three different types of consumers who value your two products differently, but you are
unable to identify these consumers individually at the time of the sale. Assume that the firm’s
costs are zero (for simplicity). Also, assume that there is one consumer of each type. However,
the three types of consumers have the following valuations (reservation prices) for the two
products:
Consumer Type DVD Player CD Player
A $200 $500
B $700 $200
C $520 $0
a) If the firm sells the products separately, what price should it charge? How much profit will it
earn?
b) If the firm sells the two products as a bundle, what price should it charge? How much profit
will it earn? Does bundling make sense here?
c) Finally, suppose that the firm offers its consumers a choice. They can either buy the DVD
player by itself for a certain price or they can buy the bundle at a different price. What price
should the firm set for the DVD player by itself? For the bundle? What profit will the firm earn
using this strategy?
a) To determine the price that the firm should charge for each product when sold separately, we need to consider the consumer with the lowest reservation price for each product.
For the DVD player, consumer C has the lowest reservation price of $520. Therefore, the firm should charge a price higher than $520 to maximize its profit. Let's assume that the firm charges $550 for the DVD player.
For the CD player, consumer B has the lowest reservation price of $200. Therefore, the firm should charge a price higher than $200 to maximize its profit. Let's assume that the firm charges $250 for the CD player.
Profit for selling DVD player = Price charged - Cost of the DVD player = $550 - $0 = $550
Profit for selling CD player = Price charged - Cost of the CD player = $250 - $0 = $250
b) To determine the price that the firm should charge for the bundle of both products, we need to consider the consumer with the highest reservation price for each product.
For the DVD player, consumer B has the highest reservation price of $700. For the CD player, consumer A has the highest reservation price of $500. Therefore, selling the bundle to these consumers would maximize the firm's profit.
The firm can charge the maximum amount that consumer B is willing to pay for the DVD player ($700) and add the price of the CD player, which is $500.
Price for the bundle = Maximum reservation price for DVD player + Price for CD player = $700 + $500 = $1,200
Profit for selling the bundle = Price charged for the bundle - Cost of the products (both DVD and CD players) = $1,200 - $0 = $1,200
Bundling makes sense here as it allows the firm to capture the maximum value from both consumer types and maximize its profit.
c) If the firm offers consumers a choice between buying the DVD player by itself or the bundle, it needs to set prices to incentivize consumers to choose the bundle.
Price for the DVD player by itself: Since consumer C is willing to pay the least for the DVD player ($520), the firm should set the price slightly above this reservation price to encourage consumers to choose the bundle. Let's assume the firm charges $550 for the DVD player by itself.
Price for the bundle: To make the bundle attractive, the firm should offer a lower price than the sum of the individual prices of the DVD and CD players. Let's assume the firm charges $1,100 for the bundle.
Profit for selling the DVD player by itself = Price charged for the DVD player - Cost of the DVD player = $550 - $0 = $550
Profit for selling the bundle = Price charged for the bundle - Cost of the products (both DVD and CD players) = $1,100 - $0 = $1,100
Using this strategy, the firm will earn a profit of $550 for selling the DVD player by itself and $1,100 for selling the bundle.
a) To determine the price the firm should charge for each product when sold separately, we need to consider the reservation prices of the different consumer types.
For the DVD player:
- Consumer A has a valuation of $200
- Consumer B has a valuation of $700
- Consumer C has a valuation of $520
The firm should charge the highest price that each consumer is willing to pay. So, the price for the DVD player should be set at $700 to capture the highest valuation.
For the CD player:
- Consumer A has a valuation of $500
- Consumer B has a valuation of $200
- Consumer C has a valuation of $0
Similar to the DVD player, the firm should charge the highest price each consumer is willing to pay. Hence, the price for the CD player should be set at $500.
The profit earned by the firm when selling the products separately is calculated by subtracting the cost (assumed to be zero) from the revenue. In this case, the profit would be $700 - $0 for the DVD player and $500 - $0 for the CD player. Therefore, the firm would earn a profit of $700 for selling the DVD player and $500 for selling the CD player.
b) When selling the products as a bundle, the firm should set the price based on the highest combined valuation of a consumer.
The highest combined valuation is from Consumer B, who values the DVD player at $700 and the CD player at $200. Therefore, the price for the bundle should be set at $900 (the summed valuations).
To calculate the profit earned from selling the bundle, we subtract the cost (zero) from the revenue obtained. The profit in this case would be $900 - $0, which is $900.
Bundling in this scenario makes sense because it allows the firm to capture a higher total value (valuation) from Consumer B by bundling the products together. Selling them separately would not have yielded as much profit.
c) When offering a choice between buying the DVD player by itself or the bundle, the firm should consider the valuations of the customers and set prices accordingly.
For the DVD player sold by itself, the firm should charge the highest price that a consumer is willing to pay. In this case, that would be $700 (Consumer B's valuation).
For the bundle, the firm should set the price at the highest combined valuation, which is $900 (from Consumer B).
The profit earned from this strategy would be calculated by subtracting the cost (zero) from the revenue obtained. The profit for selling the DVD player separately would be $700 - $0, and the profit from selling the bundle would be $900 - $0. Therefore, the firm would earn a profit of $700 by selling the DVD player alone and $900 by selling the bundle.
This strategy allows the firm to capture the maximum value from Consumer B, who values both products highly. It also provides an option for consumers who do not need both products to purchase just the DVD player at a lower price.