Solved: A firm produces a single commodity and gets p for each unit, Mathematics

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A firm produces a single commodity and gets p for each unit

Question: (a) A firm produces a single commodity and gets p for each unit sold. The cost of producing x units is ax + bx² and the tax per unit is t. Assume that the parameters are positive with p> a + t. The firm wants to maximize its profit. Find the optimal production x∗ and the optimal profit π∗.

(b) Prove that ∂π∗/∂p = x∗, and give an economic interpretation.

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Mathematics: A firm produces a single commodity and gets p for each unit

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