Final answer:
The maximum profit with non-linear pricing when MC is $30 and the firm's profit-maximizing level of output is 40 units, assuming inelastic demand and the firm is a price taker, would be $280, as it is the highest profit achievable with the given total costs and the price per unit that the firm can charge.
Step-by-step explanation:
To calculate the maximum profit through non-linear pricing when given marginal cost (MC) and that marginal revenue (MR) and MC intersect at a certain quantity of output, we first need to determine the profit-maximizing quantity. In the provided scenario, the MR and MC intersect at a quantity of 40 units, which means that the firm should produce 40 units to maximize profits given that this is where revenue is maximized before costs begin to outweigh the additional revenue generated by producing more units.The next step is to determine the total revenue (TR) at the indicated profit-maximizing output level. TR is calculated by multiplying the quantity of the goods sold by the price at which they are sold. Since the specific demand functions and prices are not provided in this question, an assumption should be made that the demand is inelastic (inelastic demand) at the determined quantity and the firm is a price taker, meaning it can sell 40 units at the market price.
Assuming the market price covers total costs, the total profit would then be total revenue minus total costs (TC). Since profit is TR less TC and TC is quantity multiplied by MC, if MC is $30 and quantity is 40, then TC would be $1,200.The answer choices provided suggest multiples of $40 in total revenue. If we are looking for the maximum profit using non-linear pricing, we would choose the highest option that could conceivably represent TR less TC—which in the given choices would be $280. To confirm, if TC is $1,200, then TR would have to be $1,480, and if we divide $1,480 by the profit-maximizing quantity of 40 units, we get a price of $37 per unit, which could be feasible in this scenario.