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190 CHAPTER 5 THE THEORY OF DEMAND

$600

BL , w = 25
2
Daily income and units of the composite good $360 BL , w = 15 BL d J G I U 5
$480

1
$240

U
3
$120

A
0 12 13 15 24

Hours of leisure
FIGURE 5.26 Optimal Choice of Labor and Leisure
At the initial basket G on budget line BL 1 , the consumer has 13 hours of leisure (and works for
11 hours). At the final basket I on budget line BL 2 , the consumer has 15 hours of leisure (and
works for 9 hours). At the decomposition basket J on budget line BL d , the consumer has 12 hours
of leisure (and works for 12 hours). The substitution effect on leisure is 1 (the change in leisure
between G and J ). The income effect on leisure is 3 (the change in leisure between J and I).
Thus, the total effect on leisure is 2, and the corresponding total effect on labor is 2.

Now let’s examine the income and substitution effects of a wage increase from
$15 to $25. Figure 5.26 shows the initial budget line BL (with the wage rate of $15)
1
and the optimal initial basket G, with 13 hours of leisure and, therefore, 11 hours of
work. The figure also shows the final budget line BL (with the wage rate of $25) and
2
the optimal final basket I, with 15 hours of leisure and 9 hours of work. Finally, the
figure shows the decomposition budget line BL (which is tangent to the initial indif-
d
ference curve U and parallel to the final budget line BL ) and the decomposition
3
2
basket J, with 12 hours of leisure and 12 hours of work.
The substitution effect on leisure is thus 1 hour (the change in leisure as we
move from G to J). The income effect on leisure is 3 hours (the change in leisure as
we move from J to I). Since the income effect outweighs the substitution effect, the
net effect of the change in the wage rate on the amount of leisure is 2 hours. Thus,
the net effect of the increase in the wage rate on the amount of labor is 2 hours. This
accounts for the backward-bending shape of the labor supply curve in Figure 5.25 as
the wage rate rises above $15.
In sum, the labor supply curve slopes upward over the region where the substitu-
tion effect associated with a wage increase outweighs the income effect, but bends
backward over the region where the income effect outweighs the substitution effect.