problem about Market Analysis

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, and the National Weather Service), 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= $62 - $1.5Q
MR= triangle TR/triangle Q = $54 - $3Q
TC=$200 + $6Q + $0.5Q squared
MC=triangle TC/triangle 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. These demand and cost data are descriptive of Gray's historical experience. find out 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. find out the range within which a long run equilibrium price output combination would be found for individual firms if entry eliminated Grays economic profits. This is assuming that the cost function is unchanged and 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. What is the potential overall market size for supercomputers if the point price elasticity of demand find outd in part A is a good estimate of the relevant arc price elasticity?

D. If no other near term entrants are anticipated, should the company enter the market for supercomputers?