Intermediate Macroeconomics Questions, due on April 29, 3:00pm (UTC+8)

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d) (8 pts.) In a single properly labeled graph in () space, illustrate the labour market equilibria for skilled and unskilled workers.

e) (4 pts.) Calculate the cumulative income distribution for each labour market by reporting the cumulative shares for the following percentiles: 50 % and 100 %.

f) (4 pts.) In a single graph, construct the Lorenz curves representing labour income inequality for each labour market. Construct the cumulative shares for the following percentiles: 50 % and 100 %.

g) (2 pts.) Briefly explain why the declining share of labour income in recent decades could entirely be attributed to the shape of the labour supply curve.

A flatter labour supply curve results in a larger increase in capitalists’ income and a smaller increase in workers’ income. As a result, the labour share of income, defined as the share of labour (or workers’) income over total (capitalists’ and workers’) income, declines.

h) (2 pts.) Briefly explain why the temporary foreign workers program run by the federal government influences the shape of the labour supply curve but the permanent residence program does not.

The temporary foreign workers program commonly permits a worker to work only for a specific employer, which reduces their opportunity cost. This effect is represented by a flatter shape of the labour supply curve. In contrast, permanent residents face no such restrictions with respect to being tied to a specific employer.

Question 2 (14 pts.)

Suppose that the wage of skilled labour equals 30 and the wage of unskilled labour equals 20. The total labour force is 35. In addition, the number of unskilled workers who are employed is twice as large as the number of skilled workers who are employed. The markets for skilled labour and unskilled labour are defined as in the lecture notes.

a) (2 pts.) Calculate the opportunity cost of skill acquisition as a function of the probability of finding a job in the skilled sector.

Opportunity cost of skill acquisition = Net gain from not acquiring skills – Net gain from skill acquisition

b) (2 pts.) Briefly describe the nature of the trade-off faced by an unskilled worker.

An unskilled worker faces the prospect of a higher wage in the skilled sector but there is uncertainty in the actual outcome, i.e., they receive unemployment with probability and are unemployed with the remaining probability.

c) (4 pts.) Calculate the number of employed workers in the skilled sector if unskilled workers are paid just enough to forego skill acquisition. Show ALL steps.

First, we must determine the probability of finding a job such that unskilled workers are paid just enough to forego skill acquisition.

Secondly, we could use that and also that since .

To solve this equation, we must use two facts. First, there is no unemployment in the unskilled sector, i.e., . In addition, it is given in the question that . Replacing with gives us a linear equation with one unknown.

d) (2 pts.) Briefly explain why neither of the two labour markets is in equilibrium if the probability of finding a job in the skilled sector is 80 %.

A probability of finding a job in the skilled sector larger than 2/3 induces unskilled workers to acquire skills.

Consequently, the labour supply in the skilled sector is increasing, while the labour supply in the unskilled sector is decreasing. This implies that neither of the labour markets are in equilibrium (stable outcome).

e) (4 pts.) Briefly discuss the validity of the statement: “New jobs in the skilled sector increase unemployment in the skilled sector if the probability of finding a job in the skilled sector is 80 %.”

The statement is correct for the following reasons.

First, for the probability of 80 %, unskilled workers have an incentive to acquire skills since average income in the skilled sector exceeds average income in the unskilled sector.

In addition, each new vacancy each new vacancy entices more than one unskilled worker to acquire skills.

Since only 80 % of those who acquire skills end up finding a skilled job, unemployment in the skilled sector increases.

Question 3 (18 pts.)

Answer the following set of questions about Figure 1 and Figure 2 in the Appendix found on pp. 5 – 6 of the exam.

Word limit for the entire question: 400 words. Penalties for non-compliance will be imposed.

Figure 1, panel c) is more appropriate as it includes information on both employed and unemployed women. Mothers often face the choice of working and sending their kid to childcare vs. not working at all.

b) (2 pts.) Briefly explain why the decomposition of the total variance into between-variance and within-variance is useful in determining how the childcare policy in Quebec affected women’s earnings.

This decomposition is useful to determine whether it is mothers of different skill levels or of the same skill level are more affected by the introduction of the childcare policy. For instance, a reduction of the between variance will be indicative that less skilled mothers benefited more from the introduction of the childcare policy.

c) (2 pts.) Briefly explain why the opportunity cost of working for a mother with no post-secondary education was more likely to be impacted by the size of the childcare subsidy relative to a mother with post-secondary education.

A mother without post-secondary education would on average have lower income. The reduction in the cost of childcare is more likely to be pivotal in switching her decision to work and send her kid to childcare.

d) (2 pts.) Briefly describe and interpret the between-group variance curve (Figure 1, panel c) with respect to the general relationship observed in the time trend over the examined period.

The between-group variance curve has decreased from approx. 1.8 to approx. 1 during the examined period meaning that income inequality between more educated vs. less educated mothers has decreased.

e) (2 pts.) Briefly explain how the introduction the childcare policy in Quebec has contributed to your answer in part d).

Some mothers are likely to have started working instead of taking care of their kids at home.

f) (2 pts.) Briefly explain why we need to group female workers of the same educational attainment and age group for the within-group variance to be a meaningful concept.

The within-group variance is a meaningful concept if we could compare the earnings of people with the same level of schooling and work experience.

g) (2 pts.) Briefly explain why we may view as problematic a large within-group variance if measured as noted in part f).

This would suggest that there is a sizable income inequality among workers with the same level of schooling and work experience. That is, factors other than one’s skill level contribute to substantial differences in earnings.

h) (2 pts.) Briefly describe and interpret the within-group variance curve (Figure 1, panel c) with respect to the general relationship observed in the time trend over the examined period.

The within-group variance curve is flat at approx. 7.5 meaning that within-group inequality among women has remained fairly constant over the examined period.

i) (4 pts.) Suppose that the only difference between the changes in the males’ and females’ within-group variance is the impact of introducing the childcare policy in Quebec. If we use the within-group variance of the male earnings as the control group (Figure 2 panel c) and that of the female earnings as the treatment group (Figure 1 panel c), briefly describe the impact of the childcare policy on the within-group income inequality.

It is important to have a control group because factors other the introduction of the childcare policy could have impacted both males and females. Comparing the time trends of the treatment and the control groups provide us with the opportunity to disentangle the impact of the childcare policy from those other factors.

The within-group variance curve is flat for both women (treatment group) and men (control group). This would imply that the childcare policy has had virtually no impact on within-group income inequality among women.

APPENDIX

Figure 1

Source: IRPP (2016)

Figure 2

Source: IRPP (2016)

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