1 Indifference Curves

2 Overview In this section we want to explore the economic model of labor supply. The model assumes that individuals try to maximize their happiness or utility. The basic choice people have in this context is find the dollar amount of consumption and amount of leisure time that gives them maximum utility. We will assume that time is either spent in leisure or labor. Thus, as the amount of leisure changes, the labor supply of the individual changes in the opposite direction.

3 Diagram used in analysis C Leisure AB Consumption is measured on the vertical axis. This is the same as when we had the budget constraint. Leisure is measured on the horizontal axis. As we move from A to B we are counting more hours of leisure(and less labor). Moving from B to A means we have more labor supplied.

4 Indifference curves Indifference curves are constructed as an attempt to get a feel for how much utility people receive from various combinations of the consumption and leisure they obtain. Plus the curves help us compare how an individual would rate different combinations. A person will either prefer combination A to B, prefer B to A, or be indifferent between the two (like the two equally well). Here we will focus on indifference curves relating to peoples views on consumption and leisure.

5 Indifference curves - definition u An indifference curve shows various combinations of consumption and leisure which will yield some specific level of utility or satisfaction for the individual. C leisure A B This is a typical looking indifference curve. The individual is equally happy at point A or B or any other point on this indifference curve.

6 Indifference curves - feature 1 u We assume more goods are preferred to less and thus indifference curves slope downward to the right C leisure Say the individual is at the point in the middle of the graph. Keep this in mind as we explore the following screens.

7 Indifference curves - feature 1 u If the individual is at the point in the diagram, then all those points in area 1 and on the boundary are more preferred because those points have either more of both items or more of one and the same amount of the other item compared to the point chosen. u Points in area 3 and the boundary are less preferred to the point in the diagram because the point chosen has more of both items.

8 Indifference curves - feature 1 u An individual may think that points in areas 2 and 4 are preferable, less preferred or equally desirable to the point indicated. u Since areas 2 and 4 are the only ones that could have a point of indifference to the chosen, the indifference curves must have negative slope.

9 Indifference curves - feature 2 C leisure Indifference Map Every point in the graph has one, and only one, indifference curve running through it. Curves farther out from the origin have more utility.

10 Indifference curves - feature 3 C leisure Indifference curves for an individual do not cross. Say they did, like in this diagram. Then individual would be indifferent to A and B, indifferent to A and C, and thus by logic should be indifferent to B and C. A B C But C has more of both goods compared to B and thus C is preferred to B. So the curves can not cross for an individual.

11 Indifference curves - feature 4 u Indifference curves are said to be convex. u Part of the reason for this is that it is assumed that the amount of consumption one is willing to give up to get more leisure holding utility constant depends on how much of each the individual starts out with.

12 Indifference curves - feature 4 C Leisure (this line is for the graph) A B You can tell that point A has more consumption than at B. As the individual moves to one more unit of leisure from either point A or B, some consumption must be given up. But more is given up if point A is the initial point. The point is the more you have of something(like consumption at point A compared to point B), the more you are willing to give up to acquire an additional unit of something else.

13 Indifference curves - feature 4 u The marginal rate of substitution(MRS) is the amount of consumption given up to obtain one more unit of leisure, while maintaining the same level of utility. u We an think of the MRS as a fraction: u MRS= (change in con)/(change in leisure) = ΔC/ΔL. u In this sense, the MRS is the slope of the curve at various points. Note the slope changes from point to point. In absolute value the fraction gets smaller the farther down the curve one moves. This is another way of saying the curve gets flatter.

14 Marginal rate of substitution L M C Leisure Note that as we move from point L to M we give up some consumption, but get back some leisure. The changes in consumption and leisure do NOT have to be of the same amount (in fact consumption is measured in dollars and L is measured in hours so they can NOT be equal). W

15 MRS continued Now when we give up consumption we lose utility and when we get more leisure we get more utility. Note that as we move along an indifference curve the changes in utility are equal in absolute value because in total utility does not change when we move along an indifference curve. Some definitions: MU L = the change in utility from an additional hour of leisure, holding the level of consumption constant. MU C = the change in utility from an additional dollar of consumption, holding the level of leisure constant.

16 MRS continued When you look back a couple of slides you can think of the change from L to M as separate moves from L to W and W to M. The change from L to W has less consumption – called change in consumption ΔC - and the utility lost from each unit of less consumption is MU C. So across the whole change in consumption the change in utility is ΔC MU C. The movement from W to M has more leisure – called a change in leisure ΔL – and the utility gained from each unit of additional leisure is MU L. So across the whole change in leisure the change in utility is ΔL MU L.

17 MRS continued Since the movement from L to M is on 1 indifference curve where the level of utility is the same, the two changes in utility must be equal and then ΔC MU C + ΔL MU L = 0 Or ΔC/ΔL = -MU L /MU C. The slope of the indifference curve is the negative of the ratio of marginal utilities. The MRS = MU L /MU C, or is the absolute value of the slope of the indifference curve.

18 Indifference curves - feature 5 u Different people can have different general shapes of indifference curves. Some are relatively steep and some are relatively flat. u On the next slide I will put two peoples’ indifference curves and they will cross. Before we said one individual’s curves could not cross.

19 Indifference curves - feature 5 C leisure Mr. A Mr. B more consumption to make up for the loss of leisure than Mr. B. Mr. A has a stronger preference for leisure than Mr. B. Perhaps we could say Mr.B is a workaholic and Mr. A a leisure lover. These are relative terms. Mr. B is relatively more of a workaholic. Note how Mr. A has a steeper curve than Mr. B. From the point where the curves cross if both give up a unit of leisure, note how Mr. A has to get back