Monopolistic Competition. Gray Computer, Inc., located in Colorado Springs, Colo
ID: 1210552 • Letter: M
Question
Monopolistic Competition. 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?
I understand this:
Set MR = MC to determine the profit-maximizing activity level.
MR = MC
$54 - $3Q = $6 + $1Q
4Q = 48
Q = 12
and
P = $54 - $1.5Q
= $54 - $1.5(12)
= $36 million
= -$2(122) + $48(12) - $200
= $88 million
I DO NOT understand how to derive the following:
From the demand curve note that:
Q = 36 - 0.67P
(The equation was not given. Only the information above was given in the problem.)
Explanation / Answer
if your demand equation is correctly derived as
Q=36 -0.67P
Elasticity = first derivative of this equattion. whic is
0.67