KOALA PLC manufactures a special type of computer chips and has 2 production plants located in Sydney and Melbourne. Both plants produce an identical product. The total cost functions for the 2 plants are given by: TC₁ = 10q₁ +5q2 for the Sydney plant TC₂ = 10q2 + 2q2 for the Melbourne plant Where 91,92 are the outputs of the Sydney and Melbourne plants respectively. Suppose the company is a monopolist and sells the computer chip at a price p given by the inverse demand function p = 124-Q where Q = 9₁ +92 i) ii) iii) Write down the expression for the company's profit (n) as a function of 91,92 Determine the profit maximising levels of q₁,92 and making sure to check that the second order conditions for a maximum are satisfied. What will be the price at the profit maximising levels of production?
KOALA PLC manufactures a special type of computer chips and has 2 production plants located in Sydney and Melbourne. Both plants produce an identical product. The total cost functions for the 2 plants are given by: TC₁ = 10q₁ +5q2 for the Sydney plant TC₂ = 10q2 + 2q2 for the Melbourne plant Where 91,92 are the outputs of the Sydney and Melbourne plants respectively. Suppose the company is a monopolist and sells the computer chip at a price p given by the inverse demand function p = 124-Q where Q = 9₁ +92 i) ii) iii) Write down the expression for the company's profit (n) as a function of 91,92 Determine the profit maximising levels of q₁,92 and making sure to check that the second order conditions for a maximum are satisfied. What will be the price at the profit maximising levels of production?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![KOALA PLC manufactures a special type of computer chips and has 2 production plants
located in Sydney and Melbourne. Both plants produce an identical product. The total cost
functions for the 2 plants are given by:
TC, = 10q, + 5q? for the Sydney plant
TC2 = 10q2 + 2qž for the Melbourne plant
Where q1,92 are the outputs of the Sydney and Melbourne plants respectively.
Suppose the company is a monopolist and sells the computer chip at a price p given by the
inverse demand function p = 124 – Q where Q = q1 + 92
i)
ii)
Write down the expression for the company's profit (n) as a function of q1,92
Determine the profit maximising levels of q1, 92 and making sure to check that
the second order conditions for a maximum are satisfied.
iii)
What will be the price at the profit maximising levels of production?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F850188c5-4760-4e8f-8164-dc5474ceb858%2F34d77c9d-7910-4234-aa94-c82b89cf3a95%2Fqthqrzk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:KOALA PLC manufactures a special type of computer chips and has 2 production plants
located in Sydney and Melbourne. Both plants produce an identical product. The total cost
functions for the 2 plants are given by:
TC, = 10q, + 5q? for the Sydney plant
TC2 = 10q2 + 2qž for the Melbourne plant
Where q1,92 are the outputs of the Sydney and Melbourne plants respectively.
Suppose the company is a monopolist and sells the computer chip at a price p given by the
inverse demand function p = 124 – Q where Q = q1 + 92
i)
ii)
Write down the expression for the company's profit (n) as a function of q1,92
Determine the profit maximising levels of q1, 92 and making sure to check that
the second order conditions for a maximum are satisfied.
iii)
What will be the price at the profit maximising levels of production?
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