1 To Supply Labor or Not to Supply Labor This is the question to which we turn.

2 Utility Maximization C leisure Recall the budget constraint. The individual searches along the line to find the best option, where best is that one that maximizes the utility of the individual. Remember that movement along the line from one spot to another will mean a gain in utility from the item gained and a loss from the item given up. So, a person will move from a spot if the gain in utility is higher than the lose in utility component and the person will stop moving when the lose component is bigger than the gain component.

3 Utility Maximization u The individual would like to get to the highest indifference curve possible (because then they would maximize utility – that is the utility they can obtain), but the budget constraint restricts the individual’s options to the budget line. u On the next slide let’s see what is the best the individual can do.

4 Utility Maximization C leisure a b c u1 u2 u3 Because of the budget line, u3 can not be reached u1 can be reached at points c and b, but even more utility would be obtained if the individ. went to point a on u2. The utility associated with u2 is the maximum this person can achieve given the wage rate and the nonlabor income they have.

5 Utility Maximization b Note why b from the previous screen was not the best point. To give up a unit of leisure and maintain the same utility the person needed to get back a certain amount of consumption. But the market actually gives back more consumption than the individual requires for the same level of utility. This trade is beneficial. The individual would thus give up the unit of leisure and be happier for the trade. C L

6 Utility Maximization Note why c from two screens ago was not the best point. To take a unit of leisure and maintain the same utility the person is willing to give up a certain amount of consumption. But the market actually requires the individual to give up less. This is a beneficial trade. The individual would thus take the unit of leisure and be happier for the trade. c C Leisure

7 Utility Maximization In the final analysis, the individual maximizes utility when the MRS=wage(this means the indifference curve is tangent to the budget line). Distance ab is the amount of leisure this individual would take. Distance ad is the amount of consumption the person would take. Distance Tb would be the amount of labor the individual would supply. a b T c d C Leisure

8 Interior Solution When the individual maximizes utility (given the budget constraint) and does not end up at the endowment point of the intercept we say the solution is an interior solution. At the interior solution the slope of the indifference curve equals the slope of the budget. This means (-MU L /MU C ) = -w, or MRS = w. This means the rate at which the individual is willing to give up leisure for consumption equals the rate the market allows or requires one to give up leisure for consumption.

9 Another interpretation Since at an interior solution (-MU L /MU C ) = -w, we can rewrite this as MU L /w = MU C /1. Recall that the MU’s are the marginal utilities of leisure and consumption. w is the wage and is the “cost” of a unit of leisure. Each unit of consumption costs $1. MU L /w is the extra utility from leisure per dollar spend. (Say the mu = 15 and the wage is 10. thus 15/10 = 1.5, or for each dollar of the wage 1.5 units of utility are added.) MU C /1 is the extra utility from consumption per dollar spent. So, the interior solution can also be interpreted as the marginal utility per dollar spent must be equal across both consumption and leisure.

10 At the same wage, why two people supply different amounts of labor Note the solid line indiff. curve is for the workaholic. At the workaholics optimal point, the leisure lover finds it beneficial to take on more leisure because or their willingness to give up much more inccom to get more leisure than the market requires. Note that at each persons optimal point MRS=wage. A workaholic is a person with a relatively weak preference for leisure because little income is needed to give up a unit of leisure