Suppose the demand curve for a firm is Q = 50 - 0.125P, where Q measures units of output and P is the price per unit. The value of marginal revenue at 5 units of output is $____.

Question

Quizplus · Accepted Answer

To find the marginal revenue (MR) when Q = 5, we first need to express the demand curve in terms of P, then differentiate it to get the MR curve, and finally substitute Q = 5 into the MR equation. The demand curve is Q = 50 - 0.125P, which can be rearranged to P = 400 - 8Q. Differentiating this with respect to Q gives MR = d(400 - 8Q)/dQ = -8. Substituting Q = 5 into the MR equation gives MR = -8(5) = -40. However, to find the value of marginal revenue at 5 units of output in terms of price, we substitute Q = 5 into the original P equation: P = 400 - 8(5) = 400 - 40 = 360. Thus, the price per unit at 5 units of output is $360, but the question asks for the value of marginal revenue at 5 units of output, which was calculated as -40, indicating a decrease in revenue for each additional unit sold beyond this point. The misunderstanding here stems from the interpretation of the question's request for a "value" in terms of price or marginal revenue change. Given the options and the typical context of such questions, it seems there was a mistake in the explanation process. The correct approach should involve directly calculating the marginal revenue from the demand function, but the provided options and the calculation mismatch suggest an error in interpreting the question's demand. The correct answer, based on the calculation provided, does not match the options, indicating a mistake in the explanation.

Suppose the Demand Curve for a Firm Is Q =