Question

Two individuals, Sam and Barb, derive utility from the hours of leisure (L) they consume and from the amount of goods \((G)\) they consume. In order to maximize utility, they need to allocate the 24 hours in the day between leisure hours and work hours. Assume that all hours not spent working are leisure hours. The price of a good is equal to \(\$ 1\) and the price of leisure is equal to the hourly wage. We observe the following information about the choices that the two individuals make: $$\begin{array}{|cccccc|} \hline & & \text { SAM } & \text { BARB } & \text { SAM } & \text { BARB } \\ \hline \begin{array}{c} \text { PRICE } \\ \text { OF 6 } \end{array} & \begin{array}{c} \text { PRICE } \\ \text { OF L } \end{array} & \begin{array}{c} \mathbf{L} \\ \text { (HOURS) } \end{array} & \begin{array}{c} \mathbf{l} \\ \text { (HOURS) } \end{array} & \mathbf{G}(\mathrm{S}) & \mathbf{G}(\mathrm{S}) \\ \hline 1 & 8 & 16 & 14 & 64 & 80 \\ \hline 1 & 9 & 15 & 14 & 81 & 90 \\ \hline 1 & 10 & 14 & 15 & 100 & 90 \\ \hline 1 & 11 & 14 & 16 & 110 & 88 \\ \hline \end{array}$$ Graphically illustrate Sam's leisure demand curve and Barb's leisure demand curve. Place price on the vertical axis and leisure on the horizontal axis. Given that they both maximize utility, how can you explain the difference in their leisure demand curves?

Short answer

The leisure demand curves of Sam and Barb are the graphical illustrations of how the quantity demanded for leisure changes with changes in the wage rates. The difference in their leisure demand curves might be due to their personal preferences for leisure. For example, if Barb's demand curve is steeper, she likely values leisure time more than Sam and is less responsive to wage rate changes.

Step-by-step solution

Gather Data for Sam

Extract Sam's leisure hours and the price of leisure from the given dataset. The hourly wage is the price of leisure and quantity of leisure is simply Leisure (Hours) for Sam.

Plot Sam's Leisure Demand Curve

Using the data from Step 1, plot the leisure demand curve by placing the price of leisure on the vertical axis and leisure hours on the horizontal axis. The demand curve should be downward sloping, as the higher the price of leisure (higher wages), the less leisure time Sam will demand (work more).

Gather Data for Barb

Similarly, extract Barb's leisure hours and the price of leisure from the dataset. The quantity of leisure is the Leisure (Hours) for Barb.

Plot Barb's Leisure Demand Curve

Plot the leisure demand curve for Barb, analogous to Step 2. The leisure demand curve would likely be different from Sam's, reflecting her personal preferences.

Compare and Explain difference

Compare the leisure demand curves between Sam and Barb. Their curves might be different due to differences in preferences for goods and leisure. For instance, if Barb's curve is steeper than Sam's, it implies she is less responsive to changes in the wage rate in terms of her demand for leisure (i.e., Barb may value leisure time more than Sam).

Key concepts

Leisure Demand Curve

The Leisure Demand Curve is a valuable tool for illustrating how individuals choose between leisure and work based on their hourly wage. Imagine it as a graph with the hourly wage (price of leisure) on the vertical axis and leisure hours on the horizontal axis. This curve helps to understand that when wages increase, leisure time tends to decrease as individuals opt to work more in order to earn more money.

For instance, in Sam's case, as his wage rises, we observe a decrease in the number of leisure hours he enjoys. This is represented by a downward-sloping demand curve indicating that higher wages make leisure relatively more expensive, prompting Sam to substitute leisure with work hours.

Similarly, Barb's demand curve might differ due to her unique preferences. This variation helps highlight how individual choices on leisure time can differ based on personal circumstances and values. Sam might prefer more work when wages rise, while Barb may go for leisure, depending on their personal hobbies, family commitments, or lifestyle.

Price of Leisure

Understanding the Price of Leisure is crucial in economic decisions involving time allocation between work and leisure. Here, the 'price' refers to the potential earnings lost by choosing leisure over work. This is why it's equated to the hourly wage.

Higher wages increase the opportunity cost of taking an hour off work for leisure, making leisure 'more expensive.' For example:

• If Sam's wage is $8, the price of an hour of leisure is $8 lost in wages.
• When his wage increases to $9, the price of leisure is $9.

With a rise in wages, Sam must decide whether leisure is worth this increased cost. Similarly, Barb faces the same decision point as her wages change. The changes in these prices can dramatically alter how both individuals allocate their time between leisure and work.

It's essential to note how different people might price leisure differently based on their priorities and personal well-being. Regardless of the wage increase, if someone values personal time highly, like Barb, they might continue to choose more leisure.

Individual Preferences

Individual Preferences play a significant role in shaping how a person allocates their time between leisure and work. Each person has unique preferences influenced by factors like lifestyle, values, and immediate needs.

For Sam and Barb, their leisure demand curves reflect these personal likes and dislikes.

• If Barb's leisure demand curve is steeper, this suggests she is not as willing to reduce leisure even if wages rise. She might prioritize time for family or hobbies over additional income.
• Sam, on the other hand, might have a flatter curve, indicating a greater willingness to swap leisure for work when paid more.

Such differences can significantly impact their economic behaviors and ultimately their satisfaction or utility gained from balancing leisure and work. Understanding these preferences is key to analyzing their behaviors in a labor market context.

Wage-Leisure Tradeoff

The Wage-Leisure Tradeoff is a fundamental economic concept that individuals face when dividing their time between work and leisure. It involves making decisions based on the tradeoff between earning more income by working more hours and enjoying more leisure but earning less.

For Sam and Barb, this tradeoff varies based on their respective situations and preferences:

• A higher wage increases the cost of leisure time, making the tradeoff more significant. Sam might choose more work hours to capitalize on a higher wage.
• Barb might prioritize leisure due to personal values, even if it comes at a higher opportunity cost during a wage increase.

This tradeoff highlights a balance between choosing happiness and well-being through leisure, and economic gains through work. Each decision impacts their overall utility, showing the delicate balance between earning potential and living life according to personal values. Understanding this helps explain why people might make labor market choices that seem puzzling purely from a financial perspective.