Consider a competitive industry and a price-taking firm that produces in that industry.The market demand and supply functions are estimated to be: Demand: $Q _ { d } = 10,000 - 10,000 P + 1.0 M$ Supply: $Q _ { s } = 80,000 + 10,000 P - 4,000 P _ { I }$ where Q is quantity,P is the price of the product,M is income,and $P _ { I }$ is the input price.The manager of the perfectly competitive firm uses time-series data to obtain the following forecasted values of M and $P _ { I }$ for 2021: $\hat { M } = \$ 50,000 \text { and } \hat { P } _ { I } = \$ 20$ The manager also estimates the average variable cost function to be $A V C = 3.0 - 0.0027 Q + 0.0000009 Q ^ { 2 }$ Total fixed costs will be $2,000 in 2021.The marginal cost function is:

Question

Quizplus · Accepted Answer

The marginal cost (MC) function is derived by taking the first derivative of the total cost (TC) function with respect to quantity (Q). The total cost function is the sum of total fixed costs and total variable costs, where total variable costs are derived from the average variable cost (AVC) function. Given the AVC function $AVC = 3.0 - 0.0027Q + 0.0000009Q^2$, the total variable cost (TVC) function would be the integral of AVC with respect to Q, not directly given in the options. The marginal cost (MC) is the derivative of the total cost (TC), which includes both fixed and variable components. Since none of the provided options correctly represent the derivative of the given AVC function, the correct answer is "none of the above."

Consider a Competitive Industry and a Price-Taking Firm That Produces Qd=10,000−10,000P+1.0MQ _ { d } = 10,000 - 10,000 P + 1.0 MQd​=10,000−10,000P+1.0M

Consider a Competitive Industry and a Price-Taking Firm That Produces $Q _ { d } = 10,000 - 10,000 P + 1.0 M$