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To solve this problem, we need to follow several steps: ### 1. Cost Function of the Firm: The total cost for each firm is given by: \[ C(q) = q^3 + 2q^2 + 4q + 6 \] To find the supply function, we need to first determine the marginal cost (MC), which is the derivative of the total cost with respect to quantity \( q \): \[ MC = \frac{dC(q)}{dq} = 3q^2 + 4q + 4 \] ### 2. Supply Function of the Firm: In a competitive market, the supply function is determined where the firm’s marginal cost equals the price \( p \). This is because firms will supply goods as long as the price covers their marginal cost. Thus, the supply function of each firm is given by: \[ p = MC = 3q^2 _______ ______ _______ _______ ____ ______ _____.
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