Question

Suppose there are 8,000 hours in a year (actually there are 8,760 ) and that an individual has a potential market wage of \(\$ 5\) per hour. a. What is the individual's full income? If he or she chooses to devote 75 percent of this in come to leisure, how many hours will be worked? b. Suppose a rich uncle dies and leaves the individual an annual income of \(\$ 4,000\) per year. If he or she continues to devote 75 percent of full income to leisure, how many hours will be worked? c. How would your answer to part (b) change if the market wage were \(\$ 10\) per hour instead of \(\$ 5\) per hour? d. Graph the individual's supply of labor curve implied by parts (b) and (c).

Short answer

In summary, an individual's labor supply is affected by changes in their market wage and additional income. We calculated their full income, working hours, and leisure hours under various scenarios. When their total income increased due to non-labor income, they chose to spend more time on leisure and reduced their working hours. When the market wage increased, they chose to work more hours. The labor supply curve shows the relationship between the market wage and the number of hours worked, indicating that as the market wage increases, the number of hours worked also increases.

Step-by-step solution

Part (a): Calculating the full income and hours worked

First, let's determine the individual's full income if they work all available hours. Full income can be calculated by multiplying the market wage ($5 per hour in this case) by the total number of working hours (8,000 hours). Full income = Market wage * Total working hours Full income = \(5 * 8,000 = \)40,000 Now, let's find how many hours the individual needs to work to devote 75% of their full income to leisure. Leisure income = 0.75 * Full income Leisure income = 0.75 * \(40,000 = \)30,000 Since the individual's market wage is $5 per hour, we can calculate how many leisure hours they can take by dividing the leisure income by their market wage. Leisure hours = Leisure income / Market wage Leisure hours = \(30,000 / \)5 = 6,000 hours Since there are a total of 8,000 hours available in a year, we can now calculate the number of working hours: Hours worked = Total hours - Leisure hours Hours worked = 8,000 - 6,000 = 2,000 hours

Part (b): Incorporating the non-labor income

Now, let's consider the scenario in which the individual receives an additional annual income of $4,000 from their late uncle. Their new full income will include this non-labor income: New full income = \(40,000 (previous full income) + \)4,000 (non-labor income) New full income = $44,000 Now, we will calculate the hours worked if the individual still devotes 75% of their new full income to leisure. New leisure income = 0.75 * New full income New leisure income = 0.75 * \(44,000 = \)33,000 We can now calculate the new leisure hours with the updated leisure income. New leisure hours = New leisure income / Market wage New leisure hours = \(33,000 / \)5 = 6,600 hours As before, we will calculate the new number of working hours: New hours worked = Total hours - New leisure hours New hours worked = 8,000 - 6,600 = 1,400 hours

Part (c): Changing the market wage

Now, we will analyze the situation with a market wage of \(10 per hour instead of \)5. We will use the new full income obtained in the previous step ($44,000). First, we need to recalculate the new leisure hours with the new market wage: New leisure hours = New leisure income / New market wage New leisure hours = \(33,000 / \)10 = 3,300 hours Now, let's calculate the new hours worked: New hours worked = Total hours - New leisure hours New hours worked = 8,000 - 3,300 = 4,700 hours So, with a market wage of $10 per hour, the individual will work 4,700 hours.

Part (d): Graphing the labor supply curve

To graph the labor supply curve, we will use the number of hours worked as a function of the market wage. We have two points on the labor supply curve from parts (b) and (c): Point 1: Market wage = $5, Hours worked = 1,400 Point 2: Market wage = $10, Hours worked = 4,700 Plot these points on a graph, with the market wage on the y-axis and the number of hours worked on the x-axis, and draw a straight line through these points. This is the labor supply curve for the individual. The labor supply curve has a positive slope, indicating that as the market wage increases, the number of hours worked also increases.

Key concepts

Full Income Calculation

Understanding full income calculation is key when examining labor economics. Full income represents the total amount an individual can potentially earn by allocating all their available time to work. It is calculated by multiplying the market wage rate by the total number of hours available for work over a period, such as a year. In our example, the individual's full income is calculated based on a \(5 hourly wage and 8,000 working hours, resulting in \)40,000. This represents the individual's purchasing power before considering any leisure time.

Full income serves as a baseline for further decisions regarding work and leisure. By quantifying the trade-offs between earning income and enjoying leisure, individuals can make informed choices about how to allocate their time. If our individual assigns a value of leisure to be 75% of the full income, they are effectively choosing personal time over the equivalent dollar amount in earnings. This perspective is crucial in illustrating the concept of opportunity costs within the labor-leisure decision-making framework.

Leisure vs. Labor Hours

The leisure versus labor hours debate reflects an individual's choice between income-generating activities and non-paid activities such as rest or hobbies. Every individual has a fixed amount of time, and must choose how to allocate it. The labor supply dilemma centers around deciding how many of those hours to sell for wages versus how many to reserve for personal time.

For instance, our example shows an individual working 2,000 hours when they decide to enjoy 75% of their full income as leisure. This implies 6,000 hours are dedicated to leisure, indicating a high value placed on personal time. The labor-leisure choice model assumes that this valuation is influenced by personal preferences and external factors, such as income from other sources or the prevailing wage rate. By understanding this trade-off, economists can predict how changes in these factors may alter the quantity of labor supplied to the market.

Impact of Non-Labor Income on Labor Supply

When discussing the impact of non-labor income on labor supply, we are examining how additional income that is not earned through labor affects an individual's decision to work. Non-labor income can include inheritances, gifts, or investments and can provide financial comfort, thus potentially reducing the need to supply labor.

In our scenario, the bequest of \(4,000 from a relative is seen as non-labor income, which increases the person's full income to \)44,000 without additional work. If the individual maintains their preference for leisure at 75%, they work fewer hours (1,400 hours) as a result of the supplemental income — demonstrating a phenomena economists call the income effect. The income effect suggests that, as people become wealthier, they may choose to ‘purchase’ more leisure and therefore offer less of their time for work, assuming leisure is a normal good.

Effect of Wage Changes on Labor Supply

The effect of wage changes on labor supply is pivotal in understanding individual responses to different wage levels. As wages rise, workers are faced with a decision: work more hours to take advantage of the higher per-hour earnings, or work fewer hours because they can maintain their desired level of income by working less.

In the given exercise, when the wage rate increases from \(5 to \)10, the individual works more hours (up from 1,400 to 4,700). This represents the substitution effect, where an increased wage makes leisure more costly in terms of foregone earnings, therefore incentivizing more hours worked. Economists often represent this relationship graphically with a labor supply curve, which slopes upwards to show that higher wages typically lead to more labor supplied. Plotting points (1,400 hours at \(5 and 4,700 hours at \)10) and drawing a line through them as described in step 4, provides a visual representation of the labor supply response to changing wage rates.