What is the firm's optimal output level if its total cost function is TC = 30 + 2Q + 0.5Q² and the demand function is P = 110 - 0.25Q?

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Study for the University of Central Florida ECO2023 Principles of Microeconomics Final. Prepare with multiple choice questions, flashcards with helpful hints and explanations. Ace your exam!

To determine the firm's optimal output level, it's essential to identify the point where marginal cost (MC) equals marginal revenue (MR). Start with the total cost (TC) function given as TC = 30 + 2Q + 0.5Q². The marginal cost can be derived by differentiating the total cost function with respect to quantity (Q):

TC = 30 + 2Q + 0.5Q²
MC = d(TC)/dQ = 2 + Q

Next, consider the demand function P = 110 - 0.25Q. The total revenue (TR) can be calculated as follows:

TR = P * Q = (110 - 0.25Q) * Q = 110Q - 0.25Q²

Now, find the marginal revenue by differentiating the total revenue with respect to quantity (Q):

MR = d(TR)/dQ = 110 - 0.5Q

Set the marginal cost equal to marginal revenue to find the optimal output level:

2 + Q = 110 - 0.5Q

To solve for Q, rearrange the equation:

1.5Q = 108 Q = 72

Thus,