An individual's feasible frontier shows the trade-off between their daily consumption (income) and hours of free time. Assume this frontier is a downward-sloping, concave curve (bowed in toward the origin), which reflects that each additional hour of work yields a smaller increase in consumption than the last. Let Point X be a point on the frontier with many hours of free time and few hours of work. Let Point Y be a point on the frontier with few hours of free time and many hours of work. How does the Marginal Rate of Transformation (MRT) of free time into consumption compare at these two points?

Evaluating an Offer with Variable Productivity

Work Hours and the Opportunity Cost of Leisure

Consider an individual whose productivity diminishes with each additional hour worked in a day. True or False: The amount of consumption (income) this individual forgoes by taking their 16th hour of free time (i.e., by working 8 hours instead of 9) is less than the amount of consumption they forgo by taking their 17th hour of free time (i.e., by working 7 hours instead of 8).

An individual's feasible set of outcomes is defined by the trade-off between their daily consumption and hours of free time. Consider two potential one-hour changes on this individual's feasible frontier:

• Change A: Giving up one hour of free time (from 18 to 17 hours) increases daily consumption from $100 to $130.
• Change B: Giving up one hour of free time (from 10 to 9 hours) increases daily consumption from $250 to $265.

Based on this information, which of the following statements provides the most accurate analysis?

An individual's ability to transform work into consumption is subject to diminishing marginal productivity. This results in a feasible frontier between consumption and free time that is a concave curve (bowed towards the origin). How does the opportunity cost of one additional hour of free time change as this individual works more hours (and thus has less free time)?

Analyzing Productivity and Opportunity Cost

An individual's ability to convert labor into consumption is subject to diminishing marginal productivity. This means that each additional hour of work generates less additional consumption than the previous one, resulting in a concave feasible frontier (bowed towards the origin) when plotting consumption against free time. Match each point on this frontier, described by the amount of daily free time, to the correct description of the Marginal Rate of Transformation (MRT) of free time into consumption at that point.

Evaluating a Work Opportunity with Diminishing Productivity

An individual's ability to generate income (consumption) is subject to diminishing marginal productivity for each additional hour worked. This relationship defines their feasible frontier between daily consumption and hours of free time. An analyst presents the following three combinations, claiming they all lie on this individual's feasible frontier:

• Point X: 16 hours of free time, $250 daily consumption.
• Point Y: 15 hours of free time, $260 daily consumption.
• Point Z: 14 hours of free time, $275 daily consumption.

Evaluate the analyst's claim based on the principle of diminishing marginal productivity.