Using time-series data,the demand function for a profit-maximizing monopolist has been estimated as $Q _ { d } = 142,000 - 500 P + 6 M - 400 P _ { R }$ where $Q _ { d }$ is the amount sold,P is price,M is income,and $P _ { R }$ is the price of a related good.The estimated values for M and $P _ { R }$ in 2021are $25,000 and $200,respectively.The short-run marginal cost curve for this firm has been estimated as: $M C = 200 - 0.024 Q + 0.000006 Q ^ { 2 }$ Total fixed cost is forecast to be $500,000 in 2021.What is the average variable cost function?

Question

Quizplus · Accepted Answer

Average variable cost is total variable cost divided by output. Total variable cost is equal to marginal cost times output. So, average variable cost is equal to marginal cost. The marginal cost curve is given by:$$MC = 200 - 0.024Q + 0.000006Q^2$$So, the average variable cost curve is:$$AVC = 200 - 0.024Q + 0.000006Q^2$$

Using Time-Series Data,the Demand Function for a Profit-Maximizing Monopolist Has Qd=142,000−500P+6M−400PRQ _ { d } = 142,000 - 500 P + 6 M - 400 P _ { R }Qd​=142,000−500P+6M−400PR​

Using Time-Series Data,the Demand Function for a Profit-Maximizing Monopolist Has $Q _ { d } = 142,000 - 500 P + 6 M - 400 P _ { R }$