# Backward bending slutsky equation

A backward-bending labor supply curve is depicted in Figure 9.

A Indifference curves B Labor supply curve Backward-bending labor supply. This follows from the Slutsky equation given in Chapter 8. First, at an intuitive level, it does not seem reasonable that increasing the wage would always result in an increased supply of labor.

If we apply the appropriate version of the Slutsky equation given earlier in this chapter, we get the following expression: Such a payment is known as an overtime wage. The change in demand resulting from a change in money income is an extra income effect—the endowment income effect.

What would happen to your demand for leisure? But R — R is positive as well, so the sign of the whole expression is ambiguous. Why does this ambiguity arise? Which is the larger effect is an empirical matter and cannot be decided by theory alone.

But when the wage rate increases, the value of the endowment goes up as well. When the wage rate is small, the substitution effect is larger than the income effect, and an increase in the wage will decrease the demand for leisure and hence increase the supply of labor.

For most people, the supply of labor would drop when their money income increased. And indeed in this case we have.

But if the wage rate changes, then money income must change as well. How can we reconcile this apparently plausible behavior with the economic theory given above?

If leisure is a normal good, then the supply curve of labor must be positively sloped. This is just like extra income, which may very well be consumed in taking extra leisure. As the wage rate increases, people may work more or less. Since leisure is a normal good, we would then predict that an increase in the wage rate would necessarily lead to a decrease in the demand for leisure—that is, an increase in the supply of labor.

The optimal choice describes the demand for leisure measured from the origin to the right, and the supply of labor measured from the endowment to the left. When the wage rate increases, leisure becomes more expensive, which by itself leads people to want less of it the substitution effect.

A normal good must have a negatively sloped demand curve. When the wage rate increases there are two effects: But for larger wage rates the income effect may outweigh the substitution effect, and an increase in the wage will reduce the supply of labor.The case where an increase in the wage rate results in a decrease in the supply of labor is represented by a backward-bending labor supply curve.

The Slutsky equation tells us that this effect is more likely to occur the larger is (R ~ R), that is, the larger is the supply of labor. Slutsky's equation holds. So if L # is the Hicksian demand function for leisure, we must have In theory, we may have a "backward bending labor supply curve" is the income effect is strong enough.

Note also that the magnitude of the income effect is proportional to H. People who work relatively few hours are unlikely to have backward bending.

Backward-bending labor supply When the wage rate increases, the substitution effect makes people want to work more to have more consumption (substitute consumption for leisure). However, when the wage rate increases, the value of endowment (or income) goes up. applications of the slutsky equation.

up vote 2 down vote favorite. Calculate the substitution and income effects for the following utility function: $$u(x,y)=\frac{x^a}{a}+\frac{y^a}{a}$$. LECTURE 1 REVIEW OF MICROECONOMIC THEORY I 1. Preferences and Choices When preferences are complete, re⁄exive, transitive, and con- Derivation of the Slutsky Equation: given the original bundle (x 1;x Backward-bending Labour Supply When R.

Lecture: Taxes and Labor Supply [email protected] EC Outline of Lecture: 1. Basic labor supply model with linear budget set (backward bending labor supply) Income effect parameter If leisure is a normal good, then negative equation is a function of .

Backward bending slutsky equation
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