Final answer:
The question involves comparing marginal cost and marginal revenue to determine profit-maximizing strategies. Statement II is true as MR > MC at Q = 20 and the firm should expand output. Statement III is also true because MR < MC at Q = 50 and the firm should reduce output to increase profits.
Step-by-step explanation:
The question asks us to determine the truth of statements regarding a firm's profit-maximizing output, based on comparisons between marginal cost (MC) and marginal revenue (MR).
Statement I is not directly related to given functions and cannot be confirmed. Using the given marginal cost function MC = 80 + 2Q and marginal revenue function MR = 200 - Q, we can set MC = MR to find the profit-maximizing quantity:
- 80 + 2Q = 200 - Q
- 3Q = 120
- Q = 40
At Q = 40, MR and MC are equal, which is the condition for profit maximization. Hence, the profit-maximizing price cannot be determined from this information alone and statement I is inconclusive.
For statement II, if Q = 20:
- MR = 200 - 20 = 180
- MC = 80 + 2(20) = 120
Since MR > MC, the firm should indeed expand output to increase profits, making statement II true.
For statement III, if Q = 50:
- MR = 200 - 50 = 150
- MC = 80 + 2(50) = 180
Here MR < MC, suggesting that the firm should reduce output to increase profits, which makes statement III true. As additional information, any output level between 70 and 80 units is associated with maximum profit as long as MR > MC, with MR = MC as the signal to cease expansion. However, once MR < MC, profits begin to fall. The firm aims for the output where MR = MC to maximize profits.