Calculating Utility Under a Tenancy Agreement

A farmer's satisfaction is described by the function U(c, t) = c * t, where 'c' is bushels of grain consumed and 't' is hours of free time per day. The farmer has 24 hours available each day. For each hour worked (h), the farmer produces 2 bushels of grain. The farmer pays a fixed rent of 12 bushels of grain to a landowner, regardless of production. To maximize their own satisfaction, what is the farmer's final utility level?

A farmer works a piece of land under a tenancy contract that requires a fixed rent payment to the landowner, regardless of how much is produced. If the landowner increases this fixed rent, the farmer will choose to work more hours to compensate for the higher cost, assuming her goal is to maximize her own satisfaction from consumption and free time.

Impact of Rent on a Farmer's Choices

A farmer's satisfaction (utility) depends on their consumption of grain (c) and hours of free time (t). Consumption is determined by the total grain they produce minus a fixed rent payment. Starting from a given situation, match each independent change below to its direct consequence.

Analysis of a Rent Increase on a Tenant Farmer's Well-being

A tenant farmer pays a fixed amount of produce as rent. Their satisfaction depends on consumption and free time, and their preferences have a specific property: the marginal value of free time is independent of the level of consumption. Because of this property, the farmer's optimal choice of work hours is ______ of the amount of fixed rent.

A self-sufficient individual's satisfaction is determined by a function of their consumption and free time. They work to produce goods for consumption but must pay a fixed amount of their output as rent. To find their final level of satisfaction (utility) in this situation, what is the correct sequence of steps?

Evaluating Alternative Farming Contracts

Error Analysis in a Utility Calculation