Practice Problem Set 2 (ANSWERS)
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1 Economics 370 Professor H.J. Schuetze Practice Problem Set 2 (NSWERS) 1. See the figure below, where the initial budget constraint is given by E. fter the new legislation is passed, the budget constraint bends upward after 8 hours of work. Thus, the new wage rate and overtime constraint is given by B, which intersects the old constraint at point the original combination of income and working hours (10 hours of work in this example). b) Initially earnings were $11 10 = $110. The new earnings formula is 8W W, where W = the hourly wage. Pick W so that this total equals $110. Since 11W = $110, we calculate that W = $10 per hour. c) See the figure above. If the workers were initially at a point of utility maximization, their initial indifference curve was tangent to the initial budget constraint (line E) at point. Since the new budget constraint (along segment B) has a steeper slope ($15 per hour rather than $11 per hour), the workers initial indifference curve cannot be tangent to the new constraint at point. Instead, there will be a new point of tangency along segment, and hours of work must increase tangency points along lie to the left of point. (Income in the vicinity of point is effectively being held constant, and the substitution effect always pulls in the direction of less leisure whenever the wage rate rises.)
2 2. The following are very brief outlines for your answers. You should be able to fill in the blanks. a) Increased education will lead to a few years of reduced labour force participation while these individuals are in school. You may represent this in your graph as a change in preferences for leisure. However, the main impact is likely to be on wages. With more education wages will rise and could increase or decrease hours for women already in the labour market but will definitely increase participation among those who were not previously in the labour market. b) This will likely lead to a decrease in the value of leisure time for wives as household responsibilities, such as children, are taken care of by husbands. Thus, the reservation wage would decrease and we would expect to see an increase in participation among married women. c) This will also reduce the value of non-market time. That is to say, having fewer children is associated with a higher participation rate. This reflects the lower value of the mother s work at home, and the commensurate increase in her reservation wage. d) The effect of a tendency to have children more closely together would be to increase labour force participation among married women. This is a simple timing issue. There is now a longer period of time over which married women have a reduction in the value of non-market time (lower reservation wage). e) This is a pure income effect. The higher the husband s wage rate, the lower the participation to the labour market of the wives. f) This obviously increases the value of non-labour time. In this case the increase in value is easy to quantify. We can think about this policy as a pure income effect as it would increase the non-labour income component of earnings. 3. The income-leisure diagram will look as follows: $1000 B l 0 T l (leisure) The budget constraint is vertical at T representing the cash grant (in this case $1000). If the implicit tax rate is 0 on the first few hours worked, then the budget constraint has the same slope as the initial budget constraint. If there is a 100% implicit tax rate imposed on all hours of work beyond T-l 0, then the budget constraint becomes horizontal.
3 b) With a reduction in the cash grant and an increase in the amount of income allowed before the income is taxed back the diagram will look like the dashed line in the following diagram: F $1000 B E l 1 l 0 T l (leisure) The cash grant is reduced from B to E, but the individual can receive his/her full wage for up to T-l1 hours of work now. These changes are expected to increase labour supply. s the cash grant is lowered, less leisure is consumed because of the income effect. The wage applies to a greater number of hours, so the positive substitution effect is allowed to work over longer hours for each individual. c) The benefits of such a change are obvious given our answer to part b. There will be more workers who would have collected welfare and chose not to work working (at least those who are able to work). These workers will gain valuable labour market experience which will hopefully result in an increase in their wages. This will increase the probability that these individuals leave the welfare roles over the long run. The problem with such a change is that those who can t work (are unable for some reason or are willing to work at the going wage but can t find work) will experience a reduction in their standard of living. Most of these individuals are barely above the poverty level if they are at all. It may also induce workers with relatively low wages and few hours of work to go on welfare. 4. a) n increase in the wage will never cause a participant to exit the labour market. This answer is sufficient to give you full marks: gree. For a participant, an increase in the wage rate has both income and substitution effects, because these are opposite in sign, hours of work may either increase or decrease. The increase in the wage leaves the individual with more real income with which to purchase more leisure (work less) Income Effect. t the same time, the opportunity cost of leisure has gone up (for each hour of leisure the worker must give up more income). This will cause the worker to substitute away from leisure (work more) Substitution Effect. However, even if the income effect dominates the substitution effect so that hours of work decline, an increase in the wage rate can never cause a participant to withdraw from the labour force. The reason for this is that in order to receive any of the gains from the increased wage the individual must spend at least
4 some time in the labour market. For example, if the wage were increased to a million dollars an hour the worker would still have to work at least one hour to get the million dollars. On the other hand, an increase in the market wage may cause some non-participants to enter the labour market if the increase if the wage is sufficiently large that the now higher market wage exceeds the reservation wage. This answer would not get you full marks: gree. For a participant, an increase in the wage rate has both income and substitution effects, because these are opposite in sign, hours of work may either increase or decrease. However, even if the income effect dominates the substitution effect so that hours of work decline, an increase in the wage rate can never cause a participant to withdraw from the labor force. b) n increase in the wage increases the opportunity cost of labour. Because of the increased price of leisure the worker s reservation wage will increase. isagree. It is true that increases in the wage rate raise the opportunity cost of leisure time. n increase in the wage directly affects the budget constraint. The increased "price" is represented by the increased slope of the budget constraint. However, the individual's reservation wage will not change. The reservation wage, which gives the wage at which the worker is indifferent between working and not working, can be represented by the slope of the worker s indifference curve passing through the point of maximum leisure (T). (You may wish to draw a diagram here to illustrate the reservation wage). n increase in the wage will not alter the worker's preferences for leisure or consumption. She/He is still willing to give up leisure for income at the same rate. The rate the market pays for the worker s leisure has changed. c) Suppose a simple welfare program offers a cash grant to eligible individuals but reduces the cash grant by 50 cents for each dollar earned in the labour market. Such a program will create a disincentive to work. gree: Slope = -10 $500 F Slope = -5 E U 1 l* l W T B U 0 l (leisure)
5 Without the welfare program - budget constraint is B With the program - budget constraint is B We can show in this case that both the income and substitution effects will lead to a reduction in work. Income effect: (cash grant) will leave the household with more money to purchase goods. If leisure is a normal good, the household will purchase more leisure or work less. Substitution effect: s we can see from the diagram the wage is lower due to the "tax back" aspect of the simple welfare program. Thus, the opportunity cost of leisure is lower and the household will substitute towards more leisure (work less).
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