Figure E5.5 - The Outcome under a Tenancy Contract

Deriving Angela's Optimal Choice in a Specific Example by Equating MRS and MRT

Optimal Labor and Consumption Choice

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?

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?

Calculating Consumption on the Reservation Indifference Curve

Calculating Maximum Economic Rent in a Coercive Scenario

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?

Evaluating a Tenancy Contract

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.

Evaluating the Efficiency of a Labor Contract

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?