Mathematically Deriving the Pareto Efficiency Curve for the Angela-Bruno Interaction

Tracing the Angela-Bruno Pareto Efficiency Curve by Varying Bruno's Share

In a model with a landlord and a tenant farmer, the farmer's preferences have a special property: her personal valuation of free time (the amount of grain she'd need to willingly give up an hour of it) only depends on how much free time she has, not how much grain she consumes. The production technology is such that the optimal arrangement, where the farmer's valuation of her time equals the grain she can produce in that time, occurs when she works 8 hours a day (i.e., has 16 hours of free time). Now, consider a different allocation where the farmer works for 7 hours (has 17 hours of free time). Why is this allocation not Pareto efficient?

Analysis of an Inefficient Proposal

Interpreting Movements on the Pareto Efficiency Curve

Consider an economic interaction between a landowner and a tenant farmer. The farmer's preferences are such that her willingness to trade free time for grain depends only on the amount of free time she has, not on her grain consumption. The total amount of grain produced is maximized when the farmer works 8 hours per day. A politician argues, 'Any policy that forces the landowner to give the farmer a larger portion of the harvest will necessarily result in a Pareto-efficient allocation.' Is this statement correct?

Evaluating a Policy Intervention

In an economic model with a tenant farmer and a landowner, the farmer's preferences are such that her personal valuation of an hour of free time depends only on her total hours of free time, not on her consumption of grain. The technically feasible set of production possibilities shows that the output from labor is subject to diminishing marginal returns. The point where the marginal rate of transformation (the slope of the feasible frontier) equals the farmer's marginal rate of substitution (the slope of her indifference curve) occurs when she works 8 hours per day, producing a total of 8 bushels of grain. Which of the following statements correctly describes the set of all Pareto-efficient allocations?

Efficiency and Distribution in a Landlord-Tenant Relationship

Preference Characteristics and Efficiency

Evaluating Economic Proposals for a Farming Community

In an economic model of a tenant farmer and a landowner, it is initially assumed that the farmer's preferences have a special property: her personal valuation of an hour of free time depends only on the amount of free time she has, not on how much grain she consumes. This specific assumption results in a set of all Pareto-efficient allocations forming a vertical line on a graph, where the amount of work (and thus total production) is constant across all efficient outcomes.

Now, suppose we change this assumption. The farmer's preferences are altered so that her valuation of an hour of free time now also depends on how much grain she consumes. Specifically, as she gets more grain, she values her free time more highly relative to grain. How would this change affect the shape of the Pareto efficiency curve?

Figure 5.21 - The Vertical Pareto Efficiency Curve in the Angela-Bruno Model

Allocation S as an Example of a Pareto-Efficient Distribution