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
idge over San Bénézet Bay, which
will cut the daily commute time roughly in half. The proposal envisions funding the
idge 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 inco
ect] Before starting on this analysis,
iefly explain what
you think the impact of the new
idge would be on local labor supply. Would it increase
labor supplied, reduce it, or not affect it? [No answer is inco
ect. 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
idge 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
idge, when the time cost of commuting is relatively large.
(c) [2 points] Describe the two
oad 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
iefly 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
etween 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-
idge commuting time costs. Now consider what might happen
when the
idge 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
idge 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
idge 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
espectively.
As a result of the
idge 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
elative 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-
idge commuting time costs. Now consider what might happen when the
idge is built and commuting time costs are halved. Draw two budget constraints and
two indifference curves below. [Hint: the
idge 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
idge 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 inco
ect.
5
In part (a), I point out that the new
idge 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
idge has a greater effect
on labor supply.
For workers who provide labor, the new
idge 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
idge 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 New
idge would increase labor supply was partly co
ect.
(i) [4 points] Based on everything you have done up to now, write a short policy
ief to the
political leaders of the San Bénézet Bay Area about the
idge 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
idge 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 cu
ently supply some of the workforce to the market,
idge 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 cu
ently provide labor to the market, the impact of
idge 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
idge 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
idge projects may also increase their labor supply due to the income and
substitution effects discussed above.
To measure the impact of
idge projects, it is useful to know the cu
ent labor market
participation rates of the predominant local working-age XXXXXXXXXXpopulation, as well as their
preferences and constraints on work and leisure. This information will help to more accurately
predict the
idge project's impact on labor supply and overall economic activity in the region.
In conclusion, we believe that the proposed
idge 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