Evaluating Conditions for a Unique Optimum
An economist makes the following claim: 'To guarantee that there is exactly one optimal level of an activity where its marginal benefit equals its marginal cost, it is sufficient that the marginal benefit of the activity decreases as the level of the activity increases.' Critically evaluate this statement. In your answer, explain why the economist's condition is not sufficient on its own. Then, describe the full set of conditions on the slopes of both the marginal benefit and marginal cost functions that does guarantee a unique solution, assuming a solution exists.
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An agent is choosing an optimal level of an activity by setting its marginal benefit equal to its marginal cost. The marginal benefit is a strictly decreasing function of the activity level. However, contrary to the usual assumption, the marginal cost is also a strictly decreasing function. Which statement best analyzes the consequence of this situation for finding a unique optimal level of the activity?
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Analyzing Conditions for a Unique Optimum
Evaluating Conditions for a Unique Optimum
An economic agent is choosing an optimal level of an activity where the marginal benefit of the activity is a strictly decreasing function of its level, and the marginal cost is also a strictly decreasing function of its level. True or False: Under these conditions, there cannot be a unique level of the activity where marginal benefit equals marginal cost.
An economic agent determines the optimal level of an activity by finding where the marginal benefit (MB) equals the marginal cost (MC). Match each scenario describing the relationship between the MB and MC functions with the correct implication for the number of potential optimal solutions.
Uniqueness of a Firm's Optimal Output
A firm is determining its optimal production level. The marginal revenue (the benefit from one more unit) is found to be an increasing function of output, as early units help build market presence and brand recognition. The marginal cost of production is also an increasing function of output due to resource scarcity. Based on these characteristics, what can be concluded about the number of production levels where marginal revenue equals marginal cost?
Graphical Guarantee of a Unique Solution
An individual is deciding on the optimal number of hours to study for an exam. The marginal benefit of each additional hour of study is a strictly decreasing function, as the easiest material is learned first. The marginal cost of each additional hour of study (in terms of fatigue and foregone leisure) is a strictly increasing function. Which of the following statements best describes the graphical representation of this scenario and the implication for finding a unique solution?
Evaluating Conditions for a Unique Optimum