Cray 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 the Crays 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.
Glen Cray, founder and research director, has recently announced his retirement, the timing of which will, unfortunately, coincide with the expiration of several patents covering key aspects of the Cray computer. Your company, a potential entrant into the market for supercomputers, has asked you to evaluate the short- and longer-run potential of this market. Based on data gathered from your company's engineering department, user surveys, trade associations, and other sources, the following market Demand and cost information has been developed:
P = $54 - $1.5Q
TC = $200 + $6Q + $0.5Q2
where P is the price, Q is units measured by the number of supercomputers, TC is total costs, including a normal rate of return and all figures are in millions of dollars.
A. Assume that these demand and cost data are descriptive of Cray's historical experience.
i.Calculate the profit-maximizing output, price, and economic profit earned by Cray Computer as a monopolist.
ii. What is the point price elasticity of demand at this output level?
Ā
B. After the patents expire and barriers to entry are eliminated, the market structure changes.
i.If the new entrants have the same total cost structure as Cray, and a competitive equilibrium results.
ii. What will the output of one firm be after all adjustment has taken place; and what will the price be in the market?
iii. What will one firm's profits be?
C. Assume as in B that barriers to entry are eliminated and all entrants have the same cost conditions; however, firms are able to differentiate their products in the eyes of their customers.
i. What will the output of one firm be after all adjustments have taken place?
ii. What will the price be? (Assume that entry causes a parallel shift in the demand curve, as in the monopolistic competitive market).
iii. What will the firm's profits be?
D. Assume that the point price elasticity of demand calculated in part A is a good estimate of the relevant arc price elasticity. What are the estimates for the potential overall market size (i.e., total quantity demanded in the market) for super-computers in B and C?
E.If no other near-term entrants are anticipated, should your company enter the market for supercomputers using the estimates of the market size in D? Why or why not? (Hint: Criterion for entry: if in the longer-run equilibrium the total quantity demanded in the market is greater or equal to the sum of the amounts produced by two firms. There is room for another firm.)
Cray 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 the Crays 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.
Glen Cray, founder and research director, has recently announced his retirement, the timing of which will, unfortunately, coincide with the expiration of several patents covering key aspects of the Cray computer. Your company, a potential entrant into the market for supercomputers, has asked you to evaluate the short- and longer-run potential of this market. Based on data gathered from your company's engineering department, user surveys, trade associations, and other sources, the following market Demand and cost information has been developed:
P = $54 - $1.5Q
TC = $200 + $6Q + $0.5Q2
where P is the price, Q is units measured by the number of supercomputers, TC is total costs, including a normal rate of return and all figures are in millions of dollars.
A. Assume that these demand and cost data are descriptive of Cray's historical experience.
i.Calculate the profit-maximizing output, price, and economic profit earned by Cray Computer as a monopolist.
ii. What is the point price elasticity of demand at this output level?
Ā
B. After the patents expire and barriers to entry are eliminated, the market structure changes.
i.If the new entrants have the same total cost structure as Cray, and a competitive equilibrium results.
ii. What will the output of one firm be after all adjustment has taken place; and what will the price be in the market?
iii. What will one firm's profits be?
C. Assume as in B that barriers to entry are eliminated and all entrants have the same cost conditions; however, firms are able to differentiate their products in the eyes of their customers.
i. What will the output of one firm be after all adjustments have taken place?
ii. What will the price be? (Assume that entry causes a parallel shift in the demand curve, as in the monopolistic competitive market).
iii. What will the firm's profits be?
D. Assume that the point price elasticity of demand calculated in part A is a good estimate of the relevant arc price elasticity. What are the estimates for the potential overall market size (i.e., total quantity demanded in the market) for super-computers in B and C?
E.If no other near-term entrants are anticipated, should your company enter the market for supercomputers using the estimates of the market size in D? Why or why not? (Hint: Criterion for entry: if in the longer-run equilibrium the total quantity demanded in the market is greater or equal to the sum of the amounts produced by two firms. There is room for another firm.)
