Profit-Maximizing Condition under Coercion: MRT = MRS
To maximize his share of the grain under coercion, Bruno selects the specific allocation on Angela's reservation indifference curve where its slope is identical to the slope of the feasible frontier. This point of tangency satisfies the condition that the Marginal Rate of Transformation (MRT) equals Angela's Marginal Rate of Substitution (MRS), ensuring the highest possible surplus for Bruno. The condition is formally stated as:
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Ch.5 The rules of the game: Who gets what and why - The Economy 2.0 Microeconomics @ CORE Econ
The Economy 2.0 Microeconomics @ CORE Econ
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Bruno's Profit Incentive to Increase Angela's Free Time When MRS > MRT
Bruno's Profit Incentive to Decrease Angela's Free Time When MRS < MRT
Bruno's Reservation Option and Economic Rent in the Coercion Model
Bruno's Profit-Maximizing Allocation D (16, 15) and His Economic Rent
A powerful landowner controls a plot of land and can dictate the working hours of a tenant farmer. The tenant has a 'survival threshold' which represents the minimum combinations of grain and free time they are willing to accept. The landowner's goal is to maximize their own share of the grain harvest while ensuring the tenant remains at this survival threshold.
Currently, the tenant is working a certain number of hours. At this specific allocation:
- The rate at which an additional hour of the tenant's labor can be transformed into grain is 3 bushels.
- The rate at which the tenant is willing to give up an hour of free time for more grain (while staying on their survival threshold) is 2 bushels.
What should the landowner do to increase their own share of the grain?
Profit Maximization with a Participation Constraint
Optimizing Surplus under a Participation Constraint
Optimizing Surplus under a Participation Constraint
A landowner seeks to maximize their share of grain from a tenant farmer, who must be kept on their reservation indifference curve (their minimum acceptable outcome). If, at the current allocation, the rate at which the tenant's labor produces additional grain is greater than the rate at which the tenant is willing to trade free time for that grain, the landowner can increase their own share by granting the tenant more free time.
Surplus Maximization under a Participation Constraint
A landowner seeks to maximize their share of a grain harvest produced by a tenant farmer. The landowner can determine the tenant's work hours but must ensure the tenant receives a combination of grain and free time that meets their minimum acceptable living standard. At the current allocation of work hours, the following is true:
- The rate at which an additional hour of the tenant's labor is transformed into grain is 2 bushels.
- The rate at which the tenant is willing to give up grain for an additional hour of free time (while maintaining their minimum living standard) is 4 bushels.
To increase their own share of the grain, what action should the landowner take?
A landowner seeks to maximize their share of a grain harvest produced by a tenant farmer. The landowner can dictate the farmer's working hours but must provide the farmer with a combination of grain and free time that meets the farmer's minimum acceptable living standard. Which of the following scenarios describes the allocation that maximizes the landowner's share of the grain?
A landowner is deciding on the work hours for a tenant farmer. The landowner's goal is to maximize their own share of the grain harvest, while ensuring the tenant's combination of grain and free time keeps them at their minimum acceptable living standard. The landowner is considering three potential allocations:
- Allocation X: The rate at which an hour of the tenant's labor can be transformed into grain is 4 bushels. The rate at which the tenant is willing to trade an hour of free time for grain is 2 bushels.
- Allocation Y: The rate at which an hour of the tenant's labor can be transformed into grain is 3 bushels. The rate at which the tenant is willing to trade an hour of free time for grain is 3 bushels.
- Allocation Z: The rate at which an hour of the tenant's labor can be transformed into grain is 2 bushels. The rate at which the tenant is willing to trade an hour of free time for grain is 4 bushels.
Which allocation should the landowner choose to maximize their share of the grain?
Explaining the Surplus-Maximizing Condition
Profit-Maximizing Condition under Coercion: MRT = MRS
Learn After
Bruno's Optimal Choice at 16 Hours of Free Time
Maximizing Surplus under Coercion
A landowner, who can compel a tenant farmer to work, seeks to maximize their own share of the harvest. At the current arrangement, the amount of extra grain produced from one more hour of the farmer's labor is greater than the amount of grain the farmer requires as compensation to give up that hour of free time (while remaining at their minimum survival level of well-being). To maximize their surplus, what should the landowner do?
Evaluating a Coercive Labor Contract
Evaluating a Coercive Labor Contract
An economic advisor tells a landowner, who has the power to compel a tenant farmer to work, the following: "To maximize your own surplus, you should force the farmer to work the number of hours that results in the largest possible total harvest." Evaluate this advice.
A landowner has coercive power over a farmer and wants to choose a work requirement that maximizes the landowner's own surplus (the grain left over after giving the farmer just enough to survive). The landowner knows two things for any given level of work: 1) The rate at which an extra hour of the farmer's work can be transformed into additional grain. 2) The rate at which the farmer, at their survival level, is willing to trade an hour of free time for grain. How should the landowner identify the surplus-maximizing number of work hours?
A landowner, who can compel a farmer to work, wants to maximize the amount of grain they keep. At the current arrangement, the amount of extra grain produced if the farmer works one more hour is greater than the amount of grain the farmer would need to be compensated to willingly give up that hour of free time (while remaining at their survival level). True or False: The landowner has found the arrangement that maximizes their own surplus.
A landowner with coercive power over a farmer aims to maximize their own grain surplus. The farmer is provided with just enough grain to survive. At the current work arrangement, the amount of additional grain that would be produced from one more hour of the farmer's labor is 2 bushels. However, the amount of grain required to compensate the farmer for that lost hour of free time (to keep them at their survival level of well-being) is 3 bushels. Based on this information, what should the landowner do to maximize their surplus?
Analyzing the Surplus-Maximizing Condition under Coercion
Evaluating a Landowner's Profit Strategy