Optimal Labor and Consumption Choice
A farmer's preferences for daily free time (t) and consumption of grain (c) are described by the utility function U(t, c) = 4√t + c. The farmer's production of grain (y) is a function of their hours of work (h), given by y = 2√(2h), where h = 24 - t. The farmer has an outside option that provides a utility level of 21, and will not accept any arrangement that provides less than this. A landowner, who owns the land, wants to offer the farmer a contract that maximizes the landowner's own share of the grain (the surplus, y - c). To do this, the landowner must find the allocation that is on the boundary of the feasible production set and provides the farmer with exactly their reservation utility. Calculate the optimal number of free time hours (t) for the farmer under this contract.
0
1
Tags
Economics
Economy
Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
CORE Econ
Social Science
Empirical Science
Science
Application in Bloom's Taxonomy
Cognitive Psychology
Psychology
The Economy 2.0 Macroeconomics @ CORE Econ
OpenStax Psychology (2nd ed.) Textbook
Related
Deriving Angela's Optimal Choice in a Specific Example by Equating MRS and MRT
An individual's preferences for consumption (c) and hours of free time (t) are represented by the utility function u = 4√t + c. Given a choice between two options, which one would this individual prefer?
Option A: 16 hours of free time and a consumption level of 10. Option B: 9 hours of free time and a consumption level of 15.
Interpreting a Utility Function
An individual's preferences for consumption (c) and hours of free time (t) are represented by the utility function u = 4√t + c. What is the marginal rate of substitution (the rate at which this individual is willing to give up units of consumption for an additional hour of free time) when they have 9 hours of free time?
Consider an individual whose preferences for consumption (c) and hours of free time (t) are described by the utility function u = 4√t + c. This individual's willingness to give up consumption for an extra hour of free time is the same regardless of how much consumption they currently have, assuming their amount of free time is held constant.
Evaluating a Policy Change
An individual's preferences for consumption (c) and hours of free time (t) are represented by the utility function u = 4√t + c. Consider two situations:
Situation A: The individual has 9 hours of free time and a consumption level of 20. Situation B: The individual has 9 hours of free time and a consumption level of 30.
How does the individual's willingness to trade consumption for an additional hour of free time (the marginal rate of substitution) compare between these two situations?
Analyzing Preferences from a Utility Function
An individual's preferences for consumption (c) and hours of free time (t) are represented by the utility function u = 4√t + c. This individual is indifferent between two bundles of goods: Bundle X, which consists of 16 hours of free time and a consumption level of 12, and Bundle Y, which consists of 25 hours of free time and an unknown consumption level. What must the consumption level be in Bundle Y for the individual to be indifferent between Bundle X and Bundle Y?
Evaluating a Job Offer
An individual's preferences for consumption (c) and hours of free time (t) are represented by the utility function u = 4√t + c. Which of the following statements accurately describes how this individual values an additional hour of free time?
Optimal Labor and Consumption Choice