Question

SoS (Sounds of Silence, Inc) prepares to launch a revolutionary system of bluetooth-enabled noise-cancellation headphones. It is estimated that about 800,000 consumers would be willing to pay $500 for the headphones; an additional 1,000,000 consumers would be willing to pay $250 for the headphones. Though SoS knows this marketing information, it cannot identify a consumer as belonging to one group of the other.

SoS is considering the launch of a stripped-down version of the headphones (the stripped- down version uses wires instead of bluetooth). The 800,000 high-valuation consumers would only be willing to pay $325 for the stripped-down version. The remaining 1,000,000 consumers do not particularly care about bluetooth vs. wire connections; they are willing to pay the same $250 for either version. Both the bluetooth version and the stripped-down version cost the same to produce: $100 per unit.

(3) Suppose that SoS only sells bluetooth-enabled headphones. What is the optimal price? And, what is the profit under the optimal pricing policy?

(4) Suppose that SoS sells both versions and wants to charge different prices for different ver- sions. What is the highest price of the bluetooth version for the high-valuation buyers? (Hint: Since low-valuation buyers will not have an incentive to buy the more expensive version, the highest price of the stripped-down version for the low-valuation buyers is equal to their willing- ness to pay, i.e., pL = $250)

(5) What is the total profit under the pricing strategy of question (4)?

Answer 1

3) The company can price the headphones at $250. In that case 1,800,000 consumers will be buying the headphones.

The other option will be to price the headphones at $500. In this case only the high paying 800,000 customers will be willing to buy.

If the headphones are priced at $250,

Total profit = 1,800,000 * (250 - 100) = 270,000,000

If headphones are prices at $500,

Total Profit = 800,000 * (500 - 100) = 320,000,000

Since the profit is higher on pricing the goods higher, so the optimal price will be $500.

The profit under the optimal pricing will be $320 million.

4) Since the high valuation customers are willing to pay $500 for the bluetooth headphones, that price should be set for the bluetooth versions. The problem will arise if the high valuation customers shift to the stripped down version as well. However, since they care for the bluetooth versions and stripped down versions seperately, it is highly likely that they will prefer the bluetooth headphones.

So the highest price that can be set for the bluetooth headphones for the high value buyer will be $500.

5) If the price is set at $500 for high value customers and $250 for low value customers, total profit can be given as

Profit = 1,000,000 * (250 - 100) + 800,000 * (500 - 100)

Profit = 150,000,000 + 320,000,000 = $470 million

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