1. 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?