Practice Problem Set 2 (ANSWERS)

Transcription

1 Economics 370 Professor H.J. Schuetze Practice Problem Set 2 (ANSWERS) 1. See the figure below, where the initial budget constraint is given by ACE. After 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 ABCD, which intersects the old constraint at point C the original combination of income and working hours (10 hours of work in this example). b) Initially earnings were = 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 ACE) at point C. Since the new budget constraint (along segment BD) 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 C. Instead, there will be a new point of tangency along segment CD, and hours of work must increase tangency points along CD lie to the left of point C. (Income in the vicinity of point C is effectively being held constant, and the substitution effect always pulls in the direction of less 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. 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 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. a) This is just a simple labour- choice diagram, where the heavier line represents the budget line after childcare costs. Person A would choose A1 hours of without child care costs, but with the costs, will work more (pure income effect) and choose A2 hours of. Person B has a higher marginal rate of substitution (steeper curves) and without child-care costs would choose B1 hours of. Your first thought might be that similar to person A, with costs they will work more and choose B3 hours of. However, utility will be maximized by dropping out of the labour market at B2 and therefore not incurring the cost of childcare.

3 800 A2 A1 B3 B1 B2 b) Now the budget line has several kinks in it. The diagram below indicates the budget line with child-care costs, but with (heavier line) and without the subsidy program c) First, it s important to remember that working 50 hours implies consuming 10 hours of, since = 10. Thus, in the above diagram we see that the new budget line is flatter, but has moved outward. Thus, the substitution effect implies that is cheaper, and thus you should buy more of it and work less. The income effect implies that there is more income available to buy all normal goods, including, so you should buy more of it and work less. Thus, both the income and substitution effects for an individual that was working 50 hours without the program imply working less with the program. For someone who would work 30 hours (i.e consume 30 hours of ) without the program, the budget line has moved out parallel, so it is a pure income effect implying working less. d) Person A, with a lower marginal rate of substitution (flatter indifference curves) is now better off working 20 hours per week then not working, as they did without the program. Person B is still best off not working.

4 800 A B a) An increase in the wage will never cause a participant to exit the labour market. This answer is sufficient to give you full marks: Agree. 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 (work less) Income Effect. At the same time, the opportunity cost of has gone up (for each hour of the worker must give up more income). This will cause the worker to substitute away from (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 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: Agree. 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) An increase in the wage increases the opportunity cost of labour. Because of the increased price of the worker s reservation wage will increase.

5 Disagree. It is true that increases in the wage rate raise the opportunity cost of time. An 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 (T). (You may wish to draw a diagram here to illustrate the reservation wage). An increase in the wage will not alter the worker's preferences for or consumption. She/He is still willing to give up for income at the same rate. The rate the market pays for the worker s has changed. c) Higher take-home wages for any group should increase the labour force participation rate for that group. Agree: The rationale behind this lies in the facts (shown in class) that an increase in the wage will never result in a labour force participant exiting the labour market (this is also shown above in part a) AND that an increase in the wage may entice a non-participant into the labour market. Here you should (similar to part a) prove that this second statement is also true (this is not done here). For example, if the wages of women were increased as a result of equity legislation, we would need to consider the impacts of the wage change on both women in the labour market and those out of the labour market. For women in the labour market, the increase in the wage may result in some of these women to work fewer hours but this will not result in a complete withdrawal. For women out of the labour market, the increase in the wage makes it more likely that the market wage will exceed the reservation wages of some of these women (you should illustrate this).