Thank you for visiting Suppose that a firm faces the demand equation tex Q 100 0 5P tex where tex P tex is the price and tex Q tex. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
The output level that will maximize the firm's total revenue is 50.
From the given answer choices, the correct option is (d) 50.
To find the output level that will maximize the firm's total revenue, we need to determine the quantity at which the firm's marginal revenue equals zero.
First, let's find the firm's total revenue function. Total revenue (TR) is calculated by multiplying the price (P) by the quantity (Q) sold.
Given the demand function Q = 100 - 0.5P, we can rewrite it as P = 200 - 2Q.
Now, substitute this expression for P into the TR equation: TR = P * Q = (200 - 2Q) * Q = 200Q - 2Q^2.
To find the output level that maximizes total revenue, we differentiate the total revenue function with respect to Q and set it equal to zero.
d(TR)/dQ = 200 - 4Q = 0.
Solving this equation, we get Q = 50.
Therefore, the output level that will maximize the firm's total revenue is 50.
Hence, the correct answer is (d) 50.
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