Question 2 Fool-Proof Mandoline (35 Points)

Varun grew up cooking in the kitchen with his parents and witnessed first-hand multiple kitchen accidents. Far too many of them involved the most dangerous kitchen tool the mandoline. After graduating from business school, Varun partnered up with a Jen, mechanical engineering student from Berkeley to put together a prototype for a fool-proof mandoline. Making one small change to the traditional mandoline design, Varun and Jen were able to create a slicing tool that was incapable of slicing human skin making it virtually fool-proof!

Varun understands the benefits of market power, so after finishing the prototype, they immediately applied for a patent on the kitchen tool, and it was granted.

During the validity period, Varuns firm will be the only player in the new market for safe mandolines. Varun asked a few of his business school friends with marketing experience to join his firm. After studying the market and running a few experiments, they determined that when prices are set to $35, total demand for safe mandolines is 7,000 per year, and when prices are set to $40, total demand falls to 6,400 per year.

Marginal costs are $20 for all production levels. There are no fixed costs.

Varuns & Jens groundbreaking design only requires a small change to the usual mandoline manufacturing process. As soon as the patent expires, the market will be flooded by previous un-safe mandoline producers who can now copy Varuns design.

A. (5 points) Whats the market structure during the validity period of the patent and after its expiration? Please explain.

B. (10 points) Assume that the demand is linear. Calculate the inverse demand function and the marginal revenue curve.

C. (10 points) Calculate the optimal prices and the annual profits for the firm during the validity of the patent. Whats the annual profit of Varuns firm after the expiration of the patent, considering that copycats would enter the market instantaneously?

D. (10 points) The total cost in developing the new fool-proof mandoline is $800,000. After the investment was paid, there was still 50% probability of failure in the development process, in which case no profitable product would be created. Whats the minimal period of validity of the patent so that Varun would have rationally invested in the product in the first place? Assume that Varun is risk neutral and ignore interest rates between different periods, so that payoffs in different dates can be summed.