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# 经济代写|劳动经济学代写Labor Economics代考|ECON248 Graphic Portrayal of Income and Substitution Effects

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## 经济代写|劳动经济学代写Labor Economics代考|Graphic Portrayal of Income and Substitution Effects

Figure $2.7$ permits us to isolate graphically the income and substitution effects associated with a wage rate increase for a specific person. Remember that the substitution effect reflects the change in desired hours of work arising solely because an increase in the wage rate alters the relative prices of income and leisure. Therefore, to isolate the substitution effect, we must control the increase in income created by the increase in the wage rate. Recall, too, that the income effect indicates the change in the hours of work occurring solely because the higher wage rate means a larger total income from any number of hours of work. In portraying the income effect, we must hold constant the relative prices of income and leisure-in other words, the wage rate.

Consider Figure 2.7. As the wage rate increases and shifts the budget line from $H W_1$ to $H W_2$, the resulting movement of the utility-maximizing position from $u_1$ on $I_1$ to $u_2$ on $I_2$ is the consequence of the combined income and substitution effects. We isolate the income effect by drawing the budget line $n W$, which is parallel to $H W_1$ and tangent to $I_2$ at point $u_2^{\prime}$. The vertical distance $H n$ measures the amount of nonlabor income that would be required to make the individual just as well off (that is, attain the same total utility) at $u_2^{\prime}$ as at $u_2$. But by moving the individual from curve $I_1$ to curve $I_2$ with nonlabor income, we have left the wage rate (that is, the relative prices of leisure and goods) unchanged. ${ }^7$ No substitution effect is involved here. The movement from $u_1$ to $u_2^{\prime}$, therefore, measures or isolates the income effect. As noted earlier, this effect results in fewer work hours when analyzed from the vantage point of an increase in wage rates and hence an increase in income. Specifically, the income effect would result in the individual wanting to work $h_1 h_2^{\prime}$ fewer hours.
We isolate the substitution effect as follows. The substitution effect occurs solely because the slope of the budget line-the relative prices of income and leisure-has been altered by the assumed increase in the wage rate. We are concerned with budget lines $n \mathrm{~W}$ and $\mathrm{HW}_2$ because their comparison involves no change in the individual’s well-being; they pertain to the same indifference curve $I_2$. Line $n W$, however, reflects the original wage rate (also embodied in $H W_1$ ), whereas $H W_2$ mirrors the new higher wage rate. The movement from $u_2^{\prime}$ to $u_2$ on curve $I_2$ is the substitution effect. It is solely the result of a change in the relative prices of leisure and goods or, specifically, the fact that goods have become cheaper and leisure more expensive. It is no surprise that this prompts a substitution of work (goods) for leisure. For a wage rate increase, the hours of work rise (the substitution effect). In this case, the individual wishes to work $h_2^{\prime} h_2$ more hours.

## 经济代写|劳动经济学代写Labor Economics代考|Rationale for the Backward-Bending Supply Curve

From Figure $2.6$, we remember that wage rate increases are initially associated with the desire to work more hours. Specifically, for the wage increases that shift the budget line from $W_1$ through $W_3$ the absolute value of the substitution effects must be greater than that of the income effects, yielding the forward-rising segment of the labor supply curve. But further increases in the wage rate that shift the budget line from $W_3$ through $W_5$ are associated with the choice to work fewer hours. The income effects of these wage rate increases are greater than the substitution effects, yielding the backward-bending segment of the labor supply curve.

What is the rationale for this reversal? The answer is that points $u_1$ and $u_2$ are at positions on indifference curves where the amount of leisure is large relative to the amount of income (goods). That is, $u_1$ and $u_2$ are located on relatively flat portions of indifference curves, where MRS $L, Y$ is small because the individual is willing to give up substantial amounts of leisure for an additional unit of income or goods. This means that the substitution effect is large-so large that it dominates the income effect. The individual’s labor supply curve is forward-rising: Higher wage rates induce more hours of work. But points $u_3, u_4$, and $u_5$ are reached only after much leisure has been exchanged in the labor market for income. At these points, the individual has a relatively large amount of income and relatively little leisure. This is reflected in the relative steepness of the indifference curves. In other words, MRS $L, Y$ is large, indicating that the individual is willing to give up only a small amount of leisure for an additional unit of income. This means that the substitution effect is small and in this case is dominated by the income effect. Consequently, the labor supply curve of the individual becomes backward-bending: Rising wage rates are associated with fewer hours of work.

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