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ECON 151 Spring 2023

Problem Set 2 ANSWERS

Problems loosely based on Ehrenberg, Smith, and Hallock 14e (2021):

Topic Question Points

6. Labor Supply 1 P.6.2

P.6.7

8. Compensating Wage Diffs Q.8.1

9. Human Capital P.9.1

10 .

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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 it’s likely that most would expect a reduction in commuting time costs to raise labor supply. Exactly why is less clear, but I think what “seems obvious” is that a reduction in commuting costs should probably raise the returns to working, and that ought to increase labor supply.

As we will see, a reduction in commuting time costs looks like a pure income effect for workers who are working. Although this looks like something that would usually decrease hours worked, and although it does increase leisure time enjoyed, it also increases labor supply. For those working, the 1 hour gained in reduced commuting time will be split between leisure and earning. For those not working, a reduction in commuting time costs might push them into supplying some labor.

(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.

With a 2 hour time cost of commuting, if the worker supplies any labor, they must also pay a 2

hour time penalty, which shows up as a leftward shift of the budget constraint.

(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.

Broadly speaking, this budget constraint will reveal two worker types: one that supplies labor, and another that does not because utility is highest at the “kink” where no commute time is required.

(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 reduction in commuting time costs is a pure income effect for workers who are already working. This is because the flat amount of time surrendered to commuting has fallen, which is a rightward shift in the budget constraint, and that is equivalent to an upward shift. Leisure rises, and so does money income. What’s complicated is what happens to working time: because the commuting time cost fell, the worker splits that extra hour between work and leisure

(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.

If a worker was originally at zero hours worked, it seems likely that the bridge, which shifts the budget constraint rightward or upward, would induce some labor supply, as shown. Although there technically are income and substitution effects, you could refer to this as a pure substitution effect that raises work for those who are not supplying labor originally. Those folks are moving from a place where the wage is effectively zero to a place where the wage is positive. There is no obvious income effect at play for such workers, but if you diagram out the income effect, you would find a small one.

(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.

Both classes of workers that we’re looking at here are likely to increase their work time, one class by a little and the other by a lot. For those not already working, the “pure substitution effect” of parts f and g associated with opening the bridge would raise labor supply by a lot. For those who were already working, the reduction in the time cost is actually a pure income effect that increases the amount of leisure time consumed and also increases the amount of work time by a little.

(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?

A policy brief should touch on how the magnitude of the net effect depends on whether the individual is already working and commuting. It turns out that a bridge is a pure income effect for those workers, which is likely to increase their leisure time and money income, raising their labor supply a little. For workers who were not working, the reduction in commuting time cost is by contrast likely to raise labor supply by a lot.

The important parameter here is the labor force participation rate: the share of the working- age population 25-64 who are in the labor force: either working or unemployed and looking for work. If many are neither employed nor looking for work, it is possible that building a bridge would draw in new workers and raise labor supply.

Otherwise, it would appear that a bridge project would improve the lives of workers who are already supplying labor, and it might not have a large impact on their labor supply.

P.6.7. [8 points] Teddy’s daily budget constraint is shown in the following chart. Teddy’s employer pays him a base hourly wage rate plus overtime if he works more than the standard hours, and the “overtime wage” is defined as the sum of those, or the total hourly wage earned during overtime.