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MonopolisticCompetition. Gray Computer, Inc., located inColorado Springs, Colorado, is a privately held producer ofhigh-speed electronic computers with immense storage capacity andcomputing capability. Although Gray’s market is restricted toindustrial users and a few large government agencies (e.g.,Department of Health, NASA, National Weather Service, etc.), thecompany has profitably exploited its market niche. Suppose apotential entrant into the market for supercomputers has asked youto evaluate the short- and long-run potential of this market. Thefollowing market demand and cost information has beendeveloped:

                                          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 unitsmeasured by the number of supercomputers, MR is marginal revenue,TC is total costs including a normal rate of return, MC is marginalcost, and all figures are in millions of dollars.

A.     Assumethat these demand and cost data are descriptive of Gray’shistorical experience. Calculate output, price, and economicprofits earned by Gray Computer as a monopolist. What is the pointprice elasticity of demand at this output level?

I understandthis:

Set MR = MC to determine theprofit-maximizing activity level.

                                        MR     =   MC

                               $54 - $3Q     =   $6 + $1Q

4Q     =   48

                                            Q     =   12


                                              P   =   $54 - $1.5Q

                                                    =   $54 - $1.5(12)

                                                    =   $36 million

π   =   -$2(122) + $48(12) -$200

   =   $88 million

I DO NOT understand how to derive thefollowing:

From the demand curve note that:

   Q   =   36 - 0.67P

(The equation was not given. Only the information above wasgiven in the problem.)


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