Calculating Maximum Economic Rent in a Coercive Scenario
A landowner can make a take-it-or-leave-it offer to a farmer. The farmer's preferences for free time (t, in hours) and consumption (c, in bushels of grain) are represented by the utility function u(t, c) = 4√t + c. If the farmer doesn't work for the landowner, she has an outside option that gives her a utility of 21. The production of grain is determined by the function c = 2√(2(24-t)), where (24-t) is the hours of work. Assuming the landowner wants to maximize his own income (the economic rent), what is the maximum amount of grain he can receive while ensuring the farmer accepts his offer?
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A landowner makes a take-it-or-leave-it offer to a farmer. The farmer's preferences for free time (t) and consumption (c) are described by the utility function u(t, c) = 4√t + c. The amount of grain the farmer can produce is a function of her hours of work (h), given by y = 2√(2h), where h = 24 - t. If the farmer rejects the offer, her next best alternative provides a utility of 21. To maximize his income, how many units of grain should the landowner demand as rent?
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A farmer's preferences for free time (t) and consumption of grain (c) are described by the utility function u(t, c) = 4√t + c. The grain is produced according to the production function c = 2√(2(24-t)), where (24-t) is the hours of work. Suppose the farmer is currently working 10 hours a day, which gives her 14 hours of free time. Based on this situation, which of the following statements is correct?