Question

Sasha has 60 hours a week she can work or have leisure. Wages are \(\$ 8 /\) hour. [LO 16.3] a. Graph Sasha's budget constraint for income and leisure. b. Suppose wages increase to \(\$ 10 /\) hour. Graph Sasha's new budget constraint. c. When wages increase from \(\$ 8 /\) hour to \(\$ 10 /\) hour, Sasha's leisure time decreases from 20 hours to 15 hours. Does her labor supply curve slope upward or downward over this wage increase?

Short answer

Sasha's labor supply curve slopes upward with the wage increase.

Step-by-step solution

Define the Budget Constraint

Sasha has a total of 60 hours per week, which she can allocate between work and leisure. Her income depends on her hourly wage and the number of hours worked. At a wage of \( \\(8 / \text{hour} \), her income can be represented as: \[ \text{Income} = 8 \times (60 - L) \] where \( L \) is the number of leisure hours. The budget constraint equation is \( 8(60 - L) + L \cdot 0 = \\)480 \), giving points (0, 480) when all hours are working and (60, 0) when all hours are leisure.

Graph Sasha's Initial Budget Constraint

Plot the budget constraint for when the wage is \( \\(8 \) per hour. The Y-axis represents income, and the X-axis represents leisure hours. The line connects point (60, 0) on the X-axis (all leisure, no income) to point (0, 480) on the Y-axis (all work, \\)480 income). This linear line shows all possible combinations of work and leisure that Sasha can choose.

Define New Budget Constraint for Increased Wages

When the wage increases to \( \\(10 / \text{hour} \), the new income function becomes: \[ \text{Income} = 10 \times (60 - L) \] This changes Sasha's maximum possible income to \( \\)600 \) if no leisure is taken. The budget constraint equation is \( 10(60 - L) = \$600 \), which gives the new points: (0, 600) when working all hours and (60, 0) when taking all leisure hours.

Graph the New Budget Constraint with Increased Wages

With the wage increase to \( \$10 \) per hour, plot the new budget constraint. The new line connects point (60, 0) on the X-axis to point (0, 600) on the Y-axis. This line is steeper than the original, reflecting the higher wage rate and potential income.

Analyze the Change in Leisure Hours

When the wage increased from \( \\(8 \) to \( \\)10 \), Sasha's leisure hours decreased from 20 to 15. This indicates she chose to work more hours as the wage increased, allowing her to earn more even with less leisure.

Determine the Slope of the Labor Supply Curve

Since Sasha's leisure hours decreased as her wage increased, she supplied more labor. This behavior reflects an upward-sloping labor supply curve, as higher wages lead to more hours worked.

Key concepts

Income-Leisure Tradeoff

The income-leisure tradeoff is a fundamental concept in microeconomics. It involves the choices individuals make between working (earning income) and taking leisure (enjoying free time). Sasha's situation exemplifies this tradeoff. She has 60 hours each week that she can allocate to either work, earning an income, or leisure, enjoying her personal time.

Initially, at a wage of $8 per hour, Sasha is able to choose how to divide these hours. The more she works, the more income she earns, but at the expense of less leisure. Conversely, the more leisure she takes, the less income she earns. Her decision reflects her personal preferences between income and leisure. This tradeoff is represented using budget constraints, helping her visualize how different allocations affect her income.

When her wage increases to $10 per hour, this tradeoff becomes more enticing because more income can be achieved with each additional hour of work. Economists use this tradeoff to understand labor supply decisions and to predict how changes in wages might influence work and leisure choices.

Labor Supply Curve

The labor supply curve is an important analytical tool in economics. It demonstrates the relationship between the wage rate and the quantity of labor an individual is willing to supply. In Sasha's case, when her wages increased from $8 to $10 per hour, her decision to work more illustrates this relationship well.

With the wage increase, Sasha decreased her leisure time from 20 hours to 15 hours per week. This behavior reflects the typical nature of an upward-sloping labor supply curve - as wages rise, the quantity of labor supplied increases. More people are inclined to provide additional labor because the reward, in terms of income, is higher.

Economists are very interested in these behaviors because labor supply curves help indicate how individuals respond to changes in wage rates. The slope and elasticity of these curves can vary among different people, depending on their preferences and income needs.

Wage Effects

Wage effects are the outcomes that arise from changes in the wage rate. This includes changes in hours worked, income, and lifestyle. Sasha's case provides a practical example.

Initially, with a wage of $8 per hour, Sasha's maximum possible income is $480 if she dedicates all 60 hours to work. When her wage increases to $10 per hour, her potential maximum income rises significantly to $600, provided she works all available hours.

Such a wage increase usually results in two major effects on individuals:

• Substitution Effect: As the wage increases, working becomes more attractive than leisure because each hour worked now provides more income. Therefore, individuals might substitute leisure hours for work hours.
• Income Effect: With a higher wage, individuals can achieve the same income with fewer hours worked, which might lead some to enjoy more leisure while maintaining their desired income level.
  

In Sasha's case, the substitution effect dominates, leading her to work more hours and enjoy less leisure to benefit from the increased wage.

Microeconomic Modeling

Microeconomic modeling is used to simplify and understand individual economic behavior. By analyzing Sasha's decision-making process, economists can model how people choose between working hours and leisure, influenced by wage changes.

These models use budget constraints and factors like wage rates, preferences, and available time to simulate real-life scenarios. They provide predictions and offer insights into how economic agents respond to different stimuli.

In Sasha’s example, the model predicts a reaction to wage changes that many individuals in the labor force might exhibit. This helps to understanding broader economic trends, especially concerning labor supply, income distribution, and even policy making. Microeconomic models are thus, pivotal in constructing policies that affect labor markets and general economic well-being.