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Unformatted text preview: >> Chapter 12 Appendix: Indifference Curve Analysis of Labor Supply In the body of this chapter, we explained why the labor supply curve can slope down- ward instead of upward: the substitution effect of a higher wage rate, which provides an incentive to work longer hours, can be outweighed by the income effect of a high- er wage rate, which may lead individuals to consume more leisure. In this appendix we show how this analysis can be carried out using the indifference curves introduced in Chapter 11. The Time Allocation Budget Line Let’s return to the example of Clive, who likes leisure but also likes having money to spend. We now assume that Clive has a total of 80 hours per week that he could spend either working or enjoying as leisure time. (The remaining hours in his week, we assume, are taken up with necessary activities, mainly sleeping). Let’s also assume, initially, that his hourly wage rate is $10. His consumption possibilities are defined by the time allocation budget line in Figure 12A-1, a budget line that shows Clive’s trade-offs between consumption of leisure and income. Hours of leisure per week are measured on the horizontal axis, and the money he earns from working is measured on the vertical axis. The horizontal intercept, point X , is at 80 hours: if Clive didn’t work at all, he would have 80 hours of leisure per week but would not earn any money. The vertical inter- cept, point Y , is at $800: if Clive worked all the time, he would earn $800 per week. Why can we use a budget line to describe Clive’s time allocation choice? The budget lines found in Chapters 10 and 11 represented the trade-offs facing consumers decid- ing how to allocate their income among different goods. Here, instead of asking how 306 A time allocation budget line shows an individual’s trade-offs between consumption of leisure and the income that allows consumption of marketed goods. Figure 12A-1 80 40 $800 400 Income Quantity of leisure (hours per week) Y A X Time allocation budget line, BL Optimal time allocation choice The Time Allocation Budget Line Clive’s time allocation budget line shows his tradeoff between work, which pays a wage rate of $10 per hour, and leisure. At point X he allocates all his time, 80 hours, to leisure but has no income. At point Y he allocates all his time to work, earning $800, but consumes no leisure. His hourly wage rate of $10, the opportunity cost of an hour of leisure, is equal to minus the slope of the time allocation budget line. We have assumed that point A , at 40 hours of leisure and $400 in income, is Clive’s optimal time allocation. It obeys the optimal time allocation rule: the additional utility Clive gets from one more hour of leisure must equal the additional utility he gets from the goods he can purchase with one hour’s wages. Clive allocates his income, we ask how he allocates his time . But the principles under- lying the allocation of income and the allocation of time are the same: each involves...
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This note was uploaded on 10/31/2009 for the course BU BU224 taught by Professor Pakula during the Fall '09 term at Kaplan University.
- Fall '09