A short-run marginal cost function is estimated as $S M C = 96 - 4 Q + 0.15 Q ^ { 2 }$ .Which of the following cost functions is associated with this estimated SMC equation? A)TVC = 96Q - 2Q² + 0.05Q³ B)SMC = 96 - 4Q + 0.1Q² C)TVC = 96Q + 4Q² + 0.15Q³ D)AVC = 96 - 2Q + 0.05Q² E)a and d

Question

Quizplus · Accepted Answer

The correct total variable cost (TVC) and average variable cost (AVC) functions can be derived by integrating and dividing the given short-run marginal cost (SMC) function, respectively. Integrating $SMC = 96 - 4Q + 0.15Q^2$ gives $TVC = 96Q - 2Q^2 + 0.05Q^3 + C$, where $C$ is the constant of integration, typically representing fixed costs which are omitted here since we're focusing on variable costs. Dividing the SMC by $Q$ gives $AVC = 96 - 4 + 0.15Q$, which simplifies to the form in option D. Therefore, both A and D are correct interpretations of the given SMC function, making E the correct choice.

A Short-Run Marginal Cost Function Is Estimated As SMC=96−4Q+0.15Q2S M C = 96 - 4 Q + 0.15 Q ^ { 2 }SMC=96−4Q+0.15Q2

A Short-Run Marginal Cost Function Is Estimated As $S M C = 96 - 4 Q + 0.15 Q ^ { 2 }$