Question

Sam and Kim live in Coquitlam but work in Vancouver. They must commute to their place of work and back home during rush hours. Assume that there are 14 available hours in the day, that their wage rate is $25 per hour, and that they each have nonlabour income of $200 per day. The commute takes 2 hours each way (4 hours a day total), and it costs $80 in expenses for the round trip.

1. Draw Sam’s (or Kim’s, because they are the same) budget line (potential income constraint) in a work-leisure diagram. Clearly show all the numbers that describe the constraint.

2. Suppose Sam decides that he will go to work. Draw the indifference curve where he finds himself at his optimal labour supply choice (that is, show what preferences Sam would have that make him choose work).

3. Suppose Kim decides that he will not go to work. Draw the indifference curve where he finds himself at his optimal labour supply choice (that is, show what preferences Kim would have that make him choose work).

4. Let us say his boss agreed that Sam can work flexible hours and now Sam commutes before rush hours; his commute takes 1 hour each way (2 hours a day total). Everything else remains unchanged.

a. Draw Sam’s new budget line (potential income constraint) in a work-leisure diagram. Clearly show all the numbers that describe the constraint.

b. Would people like Sam be more likely or less likely to choose working (rather than staying home) when they are offered flexible hours compared to when they must work inflexible hours? Explain, with an illustration in a work-leisure diagram.

Answer 1

1. Plot leisure (in hours) on x-axis and consumption (in dollars) on y-axis.

Number of available hours in a day = 14 hours.

If Sam decides to go to work, then he would have 4 less hours (due to travel). So, available hours after Sam goes to work = 10

Wage rate = $25 per hour

Therefore, in 10 hours, Sam can earn $25 *10 =$250

nonlabour income = $200 per day

Cost of traveling to work = $80

If Sam decides to go work and work the entire day, then he would have $250 + $200 - $80 = $370 worth of consumption. Assume that P2 is the price of consumption, therefore, $370/P2 is the y-intercept (When leisure is 0, consumption = $ 370)

On the other hand, if Sam decides to not to go to work, he can have 14 hours that he can use for leisure. But he get $200 as non labor income. So, at this point, consumption = $200

Sam’s (or Kim’s, because they are the same) budget line (potential income constraint) in a work-leisure diagram is depicted in figure 1.

Figure 1

2. Suppose Sam decides that he will go to work. This means he value work more than he values leisure. Hence, he would consume less of leisure. His indifference curve would be flat because he values work more, he would require more of leisure if he is asked to forego a dollar of consumption in order to equally satisfied. Figure 2 depicts the indifference curve (ICs) where Sam finds himself at his optimal labor supply when Sam decides to go to work. Sam would still consume some amount of leisure (by not working the entire 10 hours). As is clearly seen, he works more.

Figure 2

3. Suppose Kim decides that he will not go to work.This means the only income that he has is the non labor income. His indifference curve would be steep because he values leisure more, he would require less of leisure if he is asked to forego a dollar of consumption in order to equally satisfied. Figure 3 depicts the indifference curve (ICK) of Kim decides not to go to work. Kim enjoys all leisure hours.

Figure 3

4.a If Sam commutes before rush hour and his commute takes 2 hour in total. Now, the maximum hours he can work = 12 hours.

Wage rate = $25 per hour

Therefore, in 12 hours, Sam can earn $25 *12 =$300

nonlabour income = $200 per day

Cost of traveling to work = $80

If Sam decides to go work and work the entire day, then he would have $300 + $200 - $80 = $420 worth of consumption. When leisure is 0, consumption = $ 420. Assume that P2 is the price of consumption, therefore, $420/P2 is the new y-intercept.

On the other hand, number of hours have not increased. He can still have a maximum of 14 hours that he can use for leisure. But he get $200 as non labor income. So, at this point, consumption = $200.

Sam’s new budget line in shown in Figure 4

Figure 4

4.b Sam would be less likely to choose working (rather than staying home) when they are offered flexible hours. This is because he already is consuming at a very high point. Since both consumption and leisure are normal good, he would try to increase the quantity of both. This has been represented in figure 5. Consumption increases from C1 to C2 and leisure increases from L1 to L2.

Figure 5