Microsoft Word - Econ 151 S23 Problem Set 2.docx1 Problem Set 2 P.6.2 [26 points] Consider workers who are able to choose their weekly work hours, in the standard setup of the...

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Microsoft Word - Econ 151 S23 Problem Set 2.docx 1 Problem Set 2 P.6.2 [26 points] Consider workers who are able to choose their weekly work hours, in the standard setup of the neoclassical model of “daily” labor supply. The horizontal axis shows up to 16 daily hours that the worker can allocate to leisure or work. Time spent commuting to work is time that is not enjoyable. With the right podcast or talk radio, it might be less awful, but let us model commuting time as a net loss of leisure time that is not formally compensated through work. Consider workers who live around a metro area called the San Bénézet Bay Area, who must spend 2 hours each day commuting around a large bay if they choose to work any amount of time, and there are no alternatives to commuting if any work is chosen. This hour of commuting is not paid, and the worker cannot telecommute. (Perhaps they work at Elon Musk’s Twitter.) But if the worker chooses not to work, they do not commute and do not spend time commuting. All workers receive the same moderately small amount of daily nonlabor income Y, perhaps $75, which creates a “kink” in the budget constraint in the usual way. Now imagine that policymakers propose building a new bridge over San Bénézet Bay, which will cut the daily commute time roughly in half. The proposal envisions funding the bridge with a large philanthropic donation, so it would come with no user fees (i.e., tolls) nor tax increases. (a) [2 points, no answer is incorrect] Before starting on this analysis, briefly explain what you think the impact of the new bridge would be on local labor supply. Would it increase labor supplied, reduce it, or not affect it? [No answer is incorrect. We will return back to this answer in order to examine how your intuition held up. I suggest you just write your honest “hot take” on this question here.] I think this new bridge will increase the labor supply. With a shorter commute time, workers would have more time available for leisure or work, and thus might choose to work more. Additionally, the reduced commuting time might make it more appealing for workers who previously chose not to work due to the burden of commuting. 2 (b) [2 points] Draw a budget constraint that shows leisure time (x) versus money income (y), showing the time cost of commuting, which is only relevant for workers who work strictly positive hours, and a wage rate w. Assume potential workers have 16 hours of daily time to split between leisure and work. Depict the budget constraint without the bridge, when the time cost of commuting is relatively large. (c) [2 points] Describe the two broad types of optimal labor supply choices that are likely to emerge with this budget constraint. In other words, there should be two qualitatively different spots on the budget constraint where two different sets of indifference curves are tangent. Identify and briefly discuss them. Corner Solution: At the first point of tangency between the budget constraint and an indifference curve, the worker maximizes their utility by choosing to work zero hours and consume all their available income and leisure time. This point lies on the horizontal axis 3 where the leisure time is at its maximum and there is no income from work. The income of laborers is completely determined by non-labor income Y. Interior Solution: At the second point of tangency, the worker chooses to work some positive hours, and at this point, the slope of the budget constraint equals the slope of the worker's indifference curve. At this point, the worker maximizes their utility by dividing their daily time between leisure and work. The optimal labor supply choice for a worker will depend on their preferences for leisure and consumption. If the cost of commuting is high, then the worker may choose to work fewer hours and consume more leisure time, leading to a corner solution. Conversely, if the cost of commuting is low, then the worker may choose to work more hours and consume less leisure time, leading to an interior solution. (d) [4 points] Take the perspective of a worker who supplies some labor to the market under the large, pre-bridge commuting time costs. Now consider what might happen when the bridge is built and commuting time costs are halved. Draw two budget constraints and two indifference curves below. (e) [2 points] Describe what you have drawn. What happens to hours of labor supplied by this class of worker when the bridge opens? Discuss income and/or substitution effects. The original budget constraint has a steeper slope, indicating that the worker has less flexibility in choosing how to allocate their time between work and leisure due to the high time cost of commuting. The new budget constraint, which results from the bridge halving commuting time costs, has a flatter slope, indicating that the worker has more flexibility in choosing how to allocate their time between work and leisure. The original and new indifference curve are tangent to the original and new budget constraint respectively. As a result of the bridge opening, the worker's budget constraint shifts outward, meaning they have more disposable income and more time available for leisure or work. This can lead to an income effect, where the worker may choose to work less and enjoy more leisure time given the increased income. Alternatively, it can also lead to a substitution effect, where the worker may choose to work more and enjoy more income given the lower time cost of commuting. The actual effect on labor supply will depend on the specific preferences of the worker and the relative wages for leisure and work. 4 (f) [4 points] Take the perspective of a worker who supplies NO labor to the market under large, pre-bridge commuting time costs. Now consider what might happen when the bridge is built and commuting time costs are halved. Draw two budget constraints and two indifference curves below. [Hint: the bridge is also likely to affect this class of worker as well, except under extreme assumptions about their indifference curves.] (g) [2 points] Describe what you have drawn. What happens to hours of labor supplied by this class of worker when the bridge opens? Discuss income and/or substitution effects. (h) [4 points] Return to your answer to part (a) and compare and contrast what you stated then with what you have found in parts (b)-(g). Remember: no answer to part (a) can be wrong. But you may find that your earlier intuition was either incomplete or incorrect. 5 In part (a), I point out that the new bridge may increase labor supply by reducing the cost of commuting time. However, after studying the budget constraints and indifference curves for workers who supply labor and those who do not, I find that the new bridge has a greater effect on labor supply. For workers who provide labor, the new bridge leads to an increase in the labor supply time due to income and substitution effects. The income effect comes from an increase in disposable income, as commuting time costs less, and the substitution effect comes from the flatter slope of the new budget constraint, which provides more flexibility in how time is allocated between work and leisure. For workers who do not provide labor, the impact of the new bridge on labor supply is less pronounced. Assuming that this group values leisure time more than potential income from work, would this significantly influence their decision to enter the labor market. But if the value of leisure time is not high enough, a reduction in the cost of commuting time may make work more attractive, leading to an increase in the labor supply. Overall, my previous hunch that Newbridge would increase labor supply was partly correct. (i) [4 points] Based on everything you have done up to now, write a short policy brief to the political leaders of the San Bénézet Bay Area about the bridge project. To gauge the impact, what might be important to know about the local prime working-age (25-64yo) population? We conduct an analysis of proposed bridge projects aimed at halving daily commute times. Our findings suggest that the project will have a significant impact on the labor supply choices of workers in the region. For workers who currently supply some of the workforce to the market, bridge work may increase their labor supply. This is due to the income effect, as reduced commuting time increases their disposable income, making work relatively more attractive, and the substitution effect, as workers now have more flexibility in choosing how to allocate their time between work and leisure. For workers who do not currently provide labor to the market, the impact of bridge projects is less pronounced, as it depends on their specific preferences and circumstances. Assuming this group values leisure time more than potential income from work, the new bridge may not significantly influence their decision to enter the labor force. But if the value of leisure time is not high enough, a reduction in the cost of commuting time may make work more attractive, leading to an increase in the labor supply. Our analysis thus suggests that bridge projects may also increase their labor supply due to the income and substitution effects discussed above. To measure the impact of bridge projects, it is useful to know the current labor market participation rates of the predominant local working-age (25-64) population, as well as their preferences and constraints on work and leisure. This information will help to more accurately predict the bridge project's impact on labor supply and overall economic activity in the region. In conclusion, we believe that the proposed bridge project has the potential to significantly increase labor supply and overall economic activity in the San Bénézet Bay region. However, further analysis and data collection are required to fully understand the project's impact. 6
Answered Same DayMar 06, 2023

Answer To: Microsoft Word - Econ 151 S23 Problem Set 2.docx1 Problem Set 2 P.6.2 [26 points]...

Himanshu answered on Mar 07 2023
37 Votes
D.
The budget line will spin outward as the wage rate rises, unleashing two opposing forces and hav
ing an uncertain impact on the worker's demand for leisure time.
The wealth (income) effect: An increase in pay inevitably raises u since it enables the employee to spend more on c and l. The need for leisure time tends to rise as a result of this effect, which causes the worker to work less hours overall.
If the wealth effect is predominant, the person will put forth less effort after a pay raise.
The substitution effect: As wages rise, the opportunity cost of leisure likewise rises. The worker may substitute other activities for...
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