Question

emmanuel enjoys growing zucchini in his garden and then selling his produce at the local farmers market. the table below shows his marginal benefit and marginal cost for each hour he spends in his garden per week. emmanuels marginal benefit and marginal cost of gardening table with hours spent gardening, marginal benefit (dollars), marginal cost (dollars) for 1 - 7 hours a. given the information above, what is emmanuels optimal amount of time spent gardening each week? 3 hours 4 hours 2 hours 5 hours b. if emmanuel were to spend 2 hours each week gardening: the marginal benefit would equal the marginal cost.

Explanation:

Step1: Identify optimal condition

The optimal time occurs where marginal benefit (MB) equals marginal cost (MC), or where MB > MC for the last hour and MB < MC for the next hour.

Step2: Match MB and MC values

Check each hour:

• 1 hour: $MB=24$, $MC=6$, $MB>MC$
• 2 hours: $MB=21$, $MC=9$, $MB>MC$
• 3 hours: $MB=18$, $MC=12$, $MB>MC$
• 4 hours: $MB=15$, $MC=15$, $MB=MC$
• 5 hours: $MB=12$, $MC=18$, $MB

Step3: Analyze 2-hour scenario

For 2 hours, compare MB and MC: $MB=21$, $MC=9$, so $MB≠MC$.

Answer:

a. 4 hours
b. (The provided option for part b is incorrect; the correct statement would be "the marginal benefit is greater than the marginal cost")