9. A monopolistic producer of two goods, 1 and 2, has a joint total cost function TC = 100, + Q0. +10Q, where and : denote the quantity of items of goods 1 and 2, respectively that are produced. If P, and P, denote the corresponding prices then the demand equations are P = 50 -Q, +Q, P = 30 + 20, - Q,
9. A monopolistic producer of two goods, 1 and 2, has a joint total cost function TC = 100, + Q0. +10Q, where and : denote the quantity of items of goods 1 and 2, respectively that are produced. If P, and P, denote the corresponding prices then the demand equations are P = 50 -Q, +Q, P = 30 + 20, - Q,
Chapter14: Monopoly
Section: Chapter Questions
Problem 14.3P
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![9. A monopolistic producer of two goods, 1 and 2, has a
joint total cost function
TC = 100, + 00, +100,
where 9 and denote the quantity of items of goods 1
and 2, respectively that are produced. If P, and P, denote
the corresponding prices then the demand equations are
P = 50 – Q, + Q,
P, = 30 + 2Q, - Q,
Using the Lagrange multiplier approach, find the
maximum profit if the firm is contracted to produce a
total of 15 goods of either type. Estimate the new optimal
profit if the production quota rises by 1 unit.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8720924c-5261-4e1f-a86c-fda8b609a922%2F30619548-eada-4fb5-98a6-4afb45b87b17%2F9j5rl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:9. A monopolistic producer of two goods, 1 and 2, has a
joint total cost function
TC = 100, + 00, +100,
where 9 and denote the quantity of items of goods 1
and 2, respectively that are produced. If P, and P, denote
the corresponding prices then the demand equations are
P = 50 – Q, + Q,
P, = 30 + 2Q, - Q,
Using the Lagrange multiplier approach, find the
maximum profit if the firm is contracted to produce a
total of 15 goods of either type. Estimate the new optimal
profit if the production quota rises by 1 unit.
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