Question

Pear Inc. is introducing a new smart phone, xPhone. The cost of xPhone is $200 per phone. There are six millions of potential customers who are interested in buying xPhone. The two million Pear fans each have a value of $600 for the new phone. Their value for the new phone drops by $200 per 6 months they wait. The two million regular Pear customers each have a value of $500 for the new phone, and their values drops by $100 per six months they wait. The rest two million customers each have a value of $400 for the new phone, and their value drops by $50 per six months they wait. The xPhone will be on the market for 18 months. Please answer the following two questions for Pear Inc. First, suppose that Pear Inc. cannot change the price for xPhone over time, and it decides to adopt the value-based pricing strategy.

Q1. What is the optimal price (in dollars) per phone that maximizes Pear Inc.’s profit from xPhone? If two prices result in the same amount of profit, please answer with the lower price. 

Q2. What is the corresponding total profit (in billion dollars) under the optimal price?   

Now, suppose that Pear Inc. can adjust its price once every six months (and the price adjustments will not negatively impact its reputation). Pear Inc. wants to apply the skimming pricing strategy, by first setting an initial price and then making adjustments at the beginning of the seventh month and at the beginning of the thirteenth month, to maximize its total profit over the 18 months. How should Pear Inc. price its new xPhone in this case?

In particular: 

Q3. What should the initial price (in dollars) be?  

Q4. What should the price (in dollars) at the beginning of the seventh month be? 

Q5. What should the price (in dollars) at the beginning of the thirteenth month be?  

Q6. What is the optimal profit (in billion dollars) that Pear Inc. can make through the skimming pricing strategy?  

Answer 1

Ans. 1 :- Optimal Price per phone :-

Price of the xPhone	Cost	Profit per Unit	Units	Total Profit
			(Millions)	(Million Dollars)
$600	$200	$400	2	$800
$500	$200	$300	4	$1,200
$400	$200	$200	6	$1,200

• As evidenced in the above calculation, Pear Inc. can have highest profits at a price of $500 as well as $400. Thus, Lower of this two prices i.e. $400 shall be the price for the xPhone.

Ans. 2 :- Total optimal profit :-

• As calculated in above table, Pear could earn total profit of $1.2 Billion ($1,200 Million) at the price of $400 per phone.

Ans. 3 :- Initial Price :-

• Considering that Pear Inc. can adjust the price every 6 months, and adopts Skimming Strategy for the pricing of the phone;
• Under Skimming Pricing Strategy, Pear inc. shall set a relatively high price initially and lower it down gradually.
• Hence, for initial 6 months, Price per xPhone would be $600.

Ans. 4 :- At the beginning of 7th Month :-

• Gradually, Pear Inc. would lower its price to increase the reach of the product to more customer.
• Moreover, in the given case, 2 Million customers who have value of $500 per phone, would drop the value by $100 for each 6 months they wait.
• At beginning of the Seventh Month, the price of xPhone per unit would be $400 [$500 - $100].

Working note :-

• When Pear Inc. can adjust price every Six months :-

Price of the xPhone	Cost	Profit per Unit	Units	Total Profit
			(Millions)	(Million Dollars)	Explanation
$600	$200	$400	2	$800	[ $400 * 2m units]
$400	$200	$200	4	$1,200	[($400 * 2m units) + ($200 * 2m units)]
$300	$200	$100	6	$1,400	[($400 * 2m units) + ($200 * 2m units) + ($100 * 2m units)]

Answer 2

ANSWER

Month	Price per unit	Cost Per unit	Units sold	Revenue	Total Cost	Total Profit
0	600	200	2000000	1200,000,000	400,000,000	800,000,000
6	500	200	4000000	2000,000,000	800,000,000	1200,000,000
12	400	200	6000000	2400,000,000	1200,000,000	1200,000,000
18	350	200	6000000	2100,000,000	1200,000,000	900,000,000

The table above shows the data. The profit is revenue-cost.The total cost is units sold*cost per unit.

As can be seen, both $500 and $400 give same profit. Since $400 is lower price, that is the answer.

The corresponding profit in billions of dollars is 1.2 billion dollars.

If prices can be reduced, the new table is shown below

Month	Price per unit	Cost per unit	Units sold	Total revenue	Total cost	Profit
0	600	200	2,000,000	1200,000,000	400,000,000	800,000,000
7	500	200	2,000,000	1000,000,000	400,000,000	600,000,000
13	400	200	2,000,000	800,000,000	400,000,000	400,000,000
Total				3000,000,000	1200,000,000	1800,000,000

As can be seen, the initial price should be $600.

The price at 7th month should be $500.

13th month price should be $400.

The total profit, as shown in the table, will be $1.8b in skimming strategy.

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