Consider a simplified version of the duopoly hardware industry of Section 3.3. Instead of assuming that machine-specific

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Consider a simplified version of the duopoly hardware industry of Section 3.3. Instead of assuming that machine-specific software variety is determined by the number of users of each software, we now modify (3.8) and assume that the variety of software is fixed at the levels of sA = 400 A-specific packages, and sB = 600 B-specific packages. Answer the following questions.

(a) Suppose that each firm sells to its η oriented consumers, and let pB be given. Which price does firm A have to set in order to undercut firm B if the machines are incompatible? Prove your answer. Hint: Since software variety is fixed, undercutting does not enhance the software variety available for the machine produced by the undercutting firm. That is, the variety of A-specific software remains 400 packages and the variety of B-specific software remains 600 packages regardless of the number of users.

(b) Now, let pA be given. Which price does firm B have to set in order to undercut firm A if the machines are incompatible? Prove your answer.

(c) Calculate the UPE prices and firms’ profit levels assuming that the systems are incompatible. Conclude which firm makes a higher profit and explain.

(d) Suppose again that each firm sells to its η oriented consumers. Which price does firm A have to set in order to undercut firm B if the machines are compatible? Prove your answer.

(e) Calculate the UPE prices and firms’ profit levels assuming that the systems are compatible. Conclude which firm makes a higher profit and explain.

(f) Compare the profit each firm makes under the incompatibility and compatibility regimes. Explain your result.

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