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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Figure E5.5 - The Outcome under a Tenancy Contract
Deriving Angela's Optimal Choice in a Specific Example by Equating MRS and MRT
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A farmer, Angela, has a utility function over free time (t) and consumption (c) given by u(t, c) = 4√t + c. Her production of grain (which she consumes) is determined by the hours she works (h), according to the production function y = 2√(2h), where h = 24 - t. To find the technically efficient allocation of time and consumption, one must find the point where her subjective trade-off between free time and consumption equals the objective trade-off dictated by the production technology. What is the efficient amount of free time (t) for Angela?
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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?
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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 landowner wants to determine the maximum rent he can extract from a farmer. The farmer's preferences for free time (t) and consumption (c) are given by the utility function u(t, c) = 4√t + c. The production function for grain is c = 2√(2(24-t)), where (24-t) is hours of work. The farmer's next best alternative provides a utility of 21. Arrange the following steps in the correct logical order to calculate the landowner's maximum possible income.
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Calculating Economic Rent in a Specific Scenario
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?