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.