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Evaluating Labor Contracts
A landowner is considering two different labor contracts for a worker. The landowner's share of the harvest depends on the worker's daily hours of free time, as shown in the data below, which reflects a known hump-shaped relationship:
- Worker has 10 hours of free time -> Landowner's share is 25 bushels.
- Worker has 16 hours of free time -> Landowner's share is 31 bushels.
- Worker has 20 hours of free time -> Landowner's share is 20 bushels.
Contract A requires the worker to have 10 hours of free time. Contract B requires the worker to have 20 hours of free time. Based on this information, which contract yields a higher share for the landowner? Is this the best possible outcome for the landowner? Explain your reasoning.
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Explaining the Landowner's Declining Share
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A landowner's share of a harvest is represented by a hump-shaped curve when plotted against a worker's daily hours of free time. Match each level of the worker's free time to the corresponding outcome for the landowner's share.
A landowner's share of a harvest is represented by a hump-shaped curve when plotted against a worker's daily hours of free time. The share is zero when the worker has 24 hours of free time, rises to a maximum, and then falls back to zero when the worker has only 7 hours of free time. According to this model, the landowner's share is maximized when the worker has ____ hours of free time per day.
A landowner's share of a harvest is represented by a hump-shaped curve when plotted against a worker's daily hours of free time. The landowner's share is maximized when the worker has 16 hours of free time. Currently, the landowner is forcing the worker to work long hours, leaving the worker with only 10 hours of free time per day. If the landowner forces the worker to work even more, reducing the worker's free time to 8 hours per day, what is the most likely effect on the landowner's share of the harvest?
Evaluating Labor Contracts
A landowner's share of a harvest is represented by a hump-shaped curve when plotted against a worker's daily hours of free time. The curve shows that the landowner's share is maximized when the worker has 16 hours of free time and is zero when the worker has only 7 hours of free time. True or False: The reason the landowner's share is zero when the worker has 7 hours of free time is that the worker is no longer producing any harvest at that point.