Question: Gray Computer Inc located in Colorado Springs Colorado is a

Gray Computer, Inc., located in Colorado Springs, Colorado, is a privately held producer of high-speed electronic computers with immense storage capacity and computing capability. Although Gray’s market is restricted to industrial users and a few large government agencies (e.g., Department of Health, NASA, National Weather Service, etc.), the company has profitably exploited its market niche. Suppose a potential entrant into the market for supercomputers has asked you to evaluate the short- and long-run potential of this market. The following market demand and cost information has been developed:
P = $54 - $1.5Q,
MR = TR/Q = $54 - $3Q,
TC = $200 + $6Q + $0.5Q2,
MC = TC/Q = $6 + $1Q,
Where P is price, Q is units measured by the number of supercomputers, MR is marginal revenue, TC is total costs including a normal rate of return, MC is marginal cost, and all figures are in millions of dollars.
A. Assume that these demand and cost data are descriptive of Gray’s historical experience. Calculate output, price, and economic profits earned by Gray Computer as a monopolist. What is the point price elasticity of demand at this output level?
B. Calculate the range within which a long-run equilibrium price/output combination would be found for individual firms if entry eliminated Gray’s economic profits. (Note: Assume that the cost function is unchanged and that the high-price/low-output solution results from a parallel shift in the demand curve while the low-price/high-output solution results from a competitive equilibrium.)
C. Assume that the point price elasticity of demand calculated in Part A is a good estimate of the relevant arc price elasticity. What is the potential overall market size for supercomputers?
D. If no other near-term entrants are anticipated, should your company enter the market for supercomputers? Why or why not?

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