Answer to end of chapter questions:
2.The labour force is calculated as the sum of the employed and the unemployed, which in this case is 22,000,000 + 1,000,000 = 23,000,000. The labour force participation rate is calculated as the ratio of the labour force to the working age population: 23,000,000 / 30,000,000 = 77 %. The unemployment rate is calculated as the ratio of the number of unemployed workers to the size of the labour force: 1,000,000 / 23,000,000 = 4.3 %. 4.a)The poor who are at minimum subsistence and who aspire to middle class consumption patterns: This group values income highly relative to leisure, so the indifference curve is relatively flat. As the wage increases, the income constraint line rotates clockwise, and we would expect a relatively large increase in hours worked. This response is dominated by a substitution effect, but there may be a small income effect working in the direction of increased leisure.
b)The wealthy who have acquired an abundance of material goods and who now aspire to be members of the idle rich: This group values leisure highly relative to income earned from wages, so the indifference curve is relatively flat. They would presumably have high non-labour income, which would shift the income constraint line upward in parallel fashion from the bottom right-hand corner. As the wage increases, the income constraint line rotates clockwise, and we would expect a decrease in hours worked. In this income range — high up and to the left in the leisure-income diagram — very strong income effects work to outweigh the substitution effect. Recall that for this labour supply model, the two effects always work in opposite directions. This group is on the backward bending part of their labour supply curve.
c)Workers who have a strong attachment to the labour force and who are reluctant to change their hours of work: This situation can be depicted by the intersection between the upper left-hand corner of the income constraint and the highest indifference curve along the vertical axis (provided that the total time endowment available for working is feasible). The indifference curve is flatter than the income constraint line, so the marginal rate of substitution exceeds the wage. For a certain range, an increase in the wage will not cause a change in hours worked, and we could say that the wage elasticity of supply is perfectly inelastic.
d)Workers who have a weak attachment to the labour force and have viable alternatives to labour market work: This case is very similar to case b. If the wage falls, they might drop out of the labour force.
e)Workaholics are defined as those who have very strong preferences for labour market work: They have very flat indifference curves. One can expect a tangency near the vertical axis. Answer to end of chapter problems
2.This question pertains to the estimated linear equation of aggregate labour force participation for women. You are asked to interpret the coefficients. It is important to pay attention to the units that are given for each variable, which in turn is very important for the interpretation of the coefficient.
a)Ceteris paribus, this effect is -7 percentage points. As the husband’s expected earnings increase, there is a fairly strong negative effect on the wives’ participation rate, which is called a cross-income effect.
b)Ceteris paribus, this effect is +18 percentage points. As the wife’s expected earnings increase, there is a very strong positive effect on the wives’ participation. This is primarily attributable to a substitution effect.
c)We can interpret the effect of the husband’s income as a pure effect stemming from non-labour income. Assuming that this cross-income effect is the same as the wife’s own-income effect stemming from her own earnings, the substitution effect is +25 percentage points, which is partially offset by an income effect of -7 percentage points. This means that as the wife’s earnings increase, the opportunity cost of them not working increases, which induces her to work longer. At the same time, they become richer, and can maintain the living standard while purchasing more leisure. That effect pushes her to work less. The net effect of +18 induces them to work more.
d)According to this equation, it would lead to a net increase of 25 percentage points. The pay cut for the husband would increase the labour force participation of wives, as they have to work more to maintain living standards.
e)We are given no information on the hourly wage, so technically we cannot answer this question. The variables which appear in this equation for expected earnings include both wages and hours worked. For the less precisely defined quantities of uncompensated and the pure elasticities for expected income, the former is 18*(6/35), and the latter is 25*(6/35). We use only the coefficient pertaining to the wife for these ‘own’ elasticities.
f)Yes it does. The total effect of the expected earnings of women on their labour force participation far outweighs the negative income effect of non-labour income earned by their husbands. As the returns from working for women increased a lot in recent decades, the labour force participation rate increased. The main reason is a substitution effect that dominated the income effects from both earners on women’s labour force participation. 6.a)For this case, we assume that the husband continues to work 40 hours per week, or 8 hours per day. This implies that his labour income falls from $160 to $120 per day. For the income-leisure choice diagram of the wife, refer to figure 2.7b. The initial value of Yn is $160, and the coordinates of point A are (T, $160). The budget line has a slope of – 10. There is a solution at point E0. Next, the budget shifts down in parallel fashion such that the coordinates of the right endpoint are (T, $120). There is a new equilibrium that lies to the south-west of the original one. It involves a lower amount of labour income and a higher number of hours worked for the wife.
b)In this case, we allow for the possibility that the husband might react to having his wages cut by altering the number of hours that he works. In his income-leisure choice diagram, the slope of the budget line changes from -20 to -15, which means that it becomes flatter. If the substitution effect dominates the income effect, he will work fewer hours, and he will earn much less income than before. If the income effect dominates the substitution effect, he will work longer hours, and he will be able to recoup some or all of his lost income. We are not given the information that is required to solve this problem. Until we know what his labour income is, we do not know what the wife’s non-market income is, so we cannot say much about how she reacts to the wage cut that is imposed on her husband.
c)If the husband collects unemployment insurance (UI), he has to stop working on the labour market. The wife’s non-labour income falls from $160 to $40 per day, and we repeat the analysis in part a) with a major downward shift in the wife’s budget line. She is likely to work many more hours. On the other hand, the husband does gain 8 hours of leisure per day by going on UI. 8.a)For the income-leisure choice diagram, refer to figure 2.7b in the textbook and the accompanying graph. The initial value of Yn is $100, and the coordinates of point A are (T = 60, $100). The budget line has a slope of -5. There is a solution at point E0, which in this case is the point (leisure = 20, $300) Labour market income is 40*5 = $200.
b)For the income-leisure choice diagram, refer to figure 2.7b in the textbook. As the effective wage is now cut in half, the budget line has a slope of -2.5, but it still has the right endpoint (T = 60, $100). There will be a tangency at an indifference curve which is lower than the original indifference curve. Call this final point of tangency E1. We do not know exactly what the resulting number of hours worked will be, but we do know that he will be worse off than before. Draw a hypothetical (dashed) budget line with slope -2.5 which is tangent to the higher, original indifference curve at point E’. The horizontal distance between the two points of tangency on the higher indifference curve gives the substitution effect, and its direction is left to right. The horizontal difference between the final tangency E1 and the hypothetical tangency E’ is the income effect, and its direction is right to left. The horizontal distance between the original and the final tangency points is the total effect of the wage cut on his labour supply, or the difference between the two equilibria that we observe.
c)This event is not depicted on the graph because it becomes very crowded. George will pay only one of these taxes at a time, so the problem asks us to compare their effects on his labour supply using the same diagram. The poll tax has the effect of shifting the original budget line down in parallel fashion. It is the equivalent of cutting George’s allowance. Taking the original budget line with a slope of -5, shift it down by the amount of taxes that George was paying in part b). This is given by the net income level that he was earning in part b). (Recall that he kept half of his earnings and forked over the other half to his caretaker.) The equilibrium should lie to the left of the equilibrium in part b), with more hours worked and less leisure taken. George will be worse off than he was in part a. The idea is that the poll tax gives George greater incentives to work. It produces only an income effect, which will actually raise work effort if leisure is a normal good. There is no substitution effect in this case.