Homogeneous product with inverse demand function
1) Two firms compete in a market to sell a homogeneous product with inverse demand function P=600-3Q. Each firm produces at a constant marginal cost of $300 and has no fixed costs. Use this information to compare the output levels and profits in settings characterized by Bertrand, Cournot, Stackleberg, and collusive behavior (i.e when both firm get together and operate as a unit).
2) You are the manager of BlackSpot Computers, which competes directly with Condensed Computers to sell high-powered computers to businesses. From the two businesses’ perspectives, the two products are indistinguishable. The large investment required to build production facilities prohibits other firms from entering this market, and existing firms operate under the assumption that the rival will hold output constant. The inverse market demand for computers is P=5,900-Q and both firms produce at a marginal cost of $800 per computer. Currently, BlackSpot earns revenues of $4.25 million and profits (net of investment, R&D, and other fixed costs) of $890,000. The engineering department at BlackSpot has been steadily working on developing an assembly method that would dramatically reduce the marginal cost of producing these high-powered computers and has found a process that allows it to manufacture each computer at a marginal cost of $500. How will this technological advance impact your production and pricing plans? How will it impact BlackSpot’s bottom line?
3) Suppose that an industry consists of two ﬁrms that produces a homogeneous product. Suppose that each ﬁrm decides how much to produce and assumes that its rival will not alter its level of production in response (Cournot Model). The industry demand equation is: P 145 5(Q1Q2) where Q1and Q2 represents the output of Firm 1 and Firm 2, respectively. The total cost equations of the two ﬁrms are: TC13Q1 and TC25Q2 A. Calculate each ﬁrm’s Best Response function. B. Calculate the equilibrium price, proﬁt maximizing output levels, and proﬁts for each ﬁrm. Assume that each duopolist maximizes its proﬁt and that each ﬁrm’s output decision is invariant with respect to the output decision of each rival. C. Suppose that Firm 2 believes that Firm 1 will take the output of Firm 2 as constant. By contrast, Firm 2 will attempt to exploit the behavior of Firm 1 by incorporating Firm 1’s reaction of the follower into its own production decisions (Stackelberg Model). Calculate the equilibrium price, output levels, and proﬁts of each ﬁrm.