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,

Microeconomic Theory
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Chapter14: Monopoly
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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.
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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