Problem Set #, You are allowed to work in groups, but each student must write up his or her work independently;please note on your answer sheet with whom you worked. Be sure to provide the reasoning behindyour answer in order to receive full credit. Deciding on Capacity You are a division manager for Wayne Biotech, and are tasked with deciding on the capacity of yournew factory for a new ecologically friendly weed killer. A similar new product has been developed byIsley Industries. The demand for the new weed killer is given = 48 ? 2, where is the price, = ! + ! , and ! and ! are the quantity produced by Wayne and Isley, respectively. Wayne’scost of production per unit is 4; Isley’s cost of production per unit is 2.a) Wayne and Isley will simultaneously decide on the capacity of their production facility, i.e.,each will simultaneously decide on quantity. What quantity will you produce? What quantitydo you expect Isley to produce? What are your expected profits? (20 points)b) You have the ability to accelerate the building of your production facility, but doing so willincrease the total cost of the facility by 7. If you do so, Isley will observe your capacitybefore choosing the capacity of their plant. What quantity will you choose if you acceleratethe building of your plant? Is accelerating the building of your production facilityworthwhile? Why or why not? (20 points) Differentiation as Defense Hastur Hospitality offers a quaint bed-and-breakfast (B&B) experience in the coastal city ofInnsmouth in northeast Massachusetts. Demand comes both from travelers visiting the town ofInnsmouth as well as travelers visiting the nearby town of Dunwich. Demand for staying inInnsmouth is given by ! = 24 ? ! , where ! is the price that Hastur charges for staying at itsB&B in Innsmouth. There is additional demand from Dunwich, and is given by ! = 20 ? ! , solong as no B&B is present in Dunwich, which is currently the case. Hastur’s marginal cost of serviceis 8.a) Your goal as the manager in charge of pricing is to maximize profit. What price will you setat your Innsmouth location? What is your expected profit? (15 points)A desirable piece of real estate in Dunwich has recently gone on sale; Hastur now has the chance tobuild a B&B in Dunwich as well, at a fixed cost of 40. Vacationers in Dunwich generate a demandfor a B&B in Dunwich of ! = 24 ? ! , where ! is the price charged at the Dunwich location; of course, building a B&B in Dunwich will completely eliminate demand from Dunwich for theInnsmouth facility. (The marginal cost of production for Hastur will be 8 at this site as well.)b) What pricing strategy will you use if you decide to expand, i.e., build a Dunwich facility? Is itprofitable to build such a facility? Why or why not? (20 points)You now learn that your competitor, Nyarlathotep Accomodations (“Live like a pharaoh!”) is alsocontemplating buying the property in Dunwich; if you pass on the opportunity, Nyarlathotep willthen have a chance to enter (at the same fixed cost of 40) the Dunwich market. Nyarlathotep’s costof entry is the same as yours, 40, and his marginal cost of production is also 8. If Nyarlathotepenters, you will first set your price, and then he will set his. Note that the B&B in Dunwich will nottake customers from the B&B in Innsmouth, nor will the B&B in Innsmouth take customers fromthe B&B in Dunwich.c) If Nyarlathotep enters, what will your pricing strategy be? What do you expect his pricingstrategy to be? Will you now choose to enter the Dunwich market yourself? Why or whynot? (25 points)
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