You are the sole producer of a novel polymer that has the potential to transform a number of other industries: synthetic clothing, medical devices, and sports equipment, for example. You have a patent on the chemical structure for this polymer for 9 more years. From the entirety of industries that will use your product, you face a demand curve given by = 425 - 10Q. (Units are in thousands of tons produced per year.) Your marginal cost curve is given by = 5 + 15.

A. Identify the quantity at which you'll want to produce, , to maximize profit. (Round down to the nearest thousand tons of production and maintain this rounding for all subsequent questions.)

B. Identify the price that you could set to maximize profit

C. Through various discussions you've been able to construct this demand curve by learning other firms' [maximum] willingness to pay for your product. Someone on your team suggested charging different prices to different firms.

i. If it is possible to achieve this, how much would you benefit? ii. If it is possible to achieve this, would there be an overall social benefit (increase in welfare)? Why or why not? iii. Do you think you'd be able to charge different prices to different firms? Why or why not?

D. Your patent expires and several other firms enter the market for production of the polymer you created. You estimate that the demand curve you will now face from residual demand is = 320 - 10Q.

i. Now that you are operating in an oligopolistic market, do you plan to set the quantity you produce or price of your polymer? Why? ii. What is the new you'd produce? iii. What will be the new in the market? iv. Your long-run average cost curve is given by = 5 + 108/Q + 15Q. What was your profit this year, right after more firms entered the market? What was your profit last year, before your patent expired?