This is actually a "part b" whereas I've finished "part a".
Here is the practice problem:
Suppose you are a patent officer. Assume that the marginal social cost of the patent increases over time and is given by MSC = 17 * t^2 [by "^2" I mean Squared].
The marginal social benefit of innovation decreases over time: MSBI = 278 - t^2. Also assume that the marginal profit function of the company is given by X = 200 - 2t^2. You want to set the length of the patent efficiently. However, you do not have that option. If you grant the patent, it will last for 20 years. But, you can choose the company's annual renewal fee. What renewal fee would you choose if you wanted to promote an efficient allocation of resources?
NOTE: OTAs have been having trouble. This is actually "part" b of a question. I'm going to add "part a" to see if it helps, but keep in mind you DO NOT have to explain this question below:
I am considering giving a patent for a new drug. The public demand is given by: P = 120 - 10Q, where Q is quantity of the drug and P is price. If the marginal cost of production is given by MC = 2Q, what will be the monetary value of the efficiency loss of granting the company monopoly power (meaning a patent)?
Remember that a marginal revenue function can be derived from a linear demand function by doubling the slope of that function.
Another OTA helped me with that.