代做Economics 1 — Semester 2 — Tutorial Sheet 6 — Week 7 Labour调试R语言程序

Economics 1 — Semester 2 — Tutorial Sheet 6 — Week 7

Labour

Required reading:

-       Recent lecture notes

-      Frank & Cartwright, Microeconomics and Behaviour, Chapter 15

Homework:

-      To earn full credit for tutorial homework you must upload your attempt at tutorial homework to Learn by 5pm on the Sunday before the tutorials occur.

-      The attempt should be equivalent to at least two sides of handwritten A4 and should be clear enough to read.

-      Your homework does not need to be complete, and indeed it does not even need to be correct. You just need to show that you have made an honest attempt. As long as you have shown an honest attempt, you will get credit, and as long as you do this for 14 of the 18 tutorials during the year, you will get full credit.

Recordings:

-      Questions marked with an asterisk* have video solutions recorded by Sean, which will be released after the Sunday 5pm submission deadline. Because the asterisk questions are covered in video, they will mostly not be covered within the tutorials themselves.

Tutorial Questions

Q1. Eurostat estimates the following data on the average hourly labour costs across the European Union.

Comment on anything that strikes you in the graph. What do you think explains such large differences?

* Q2. The economy of Japan is widely considered to have had a “lost decade” starting in about 1991. GDP per capita had increased rapidly in the 1980s, but much more slowly in the 1990s (see the solid blue line in the graph below). But when we look at GDP per hour worked, we see a different picture – roughly the same pattern as GDP per capita before 1991, but a  much less pronounced  slowdown afterwards. Why  do you think the  series diverged? (Hint: why is this question being asked in a tutorial sheet about labour?)

* Q3. Suppose that there are two firms, one of which is in a competitive industry, and one of which is in an imperfectly competitive industry. What is different between these two firms in the way they value (and are willing to pay) a marginal (additional) worker?

*  Q4.  If  a  would-be monopolist acquired most of  the firms in a formerly competitive industry,   worked   to   construct   barriers   to   entry   against new   firms,   and gradually accumulated more and more market power, how would the quantity of labour employed be affected?

* Q5. What does economic theory suggest about the prevalence of unfair discrimination in perfectly vs. imperfectly competitive industries (or in public sector employment)?

* Q6. Members of two groups, the blues and the greens, each have productivity values that range from £10 to £30/hr. Even though the ranges are the same, however, the averages are different: the productivity of the blues is £12/hr and the corresponding average for the greens is £24/hr. It is easy for anyone to see whether an individual is blue or green, and it is common knowledge that the group average productivities are £12/hr and £24/hr, but it is not easy to see how productive any individual is. A new productivity test has been devised though, and 1/3rd of the time it is able to give a correct measurement of an individual’s productivity, but the other 2/3rds of the time it gives random productivity value drawn from the relevant colour-group distribution.

a) Assuming labour markets are competitive, how much will a blue with a test value of 18 be paid?

b)    How much will a green with the same test value be paid?

c) Is it correct to say that statistical discrimination accounts for why the greens, as a group, are paid more than the blues?

Q7. Given the information about the number of workers (L) compared to their marginal products  (MP) in the following table, fill in the value of the marginal product of labour (VMP) for price P = 4. Find the perfectly competitive firm’s optimal labour demand for a wage w = €4/hr.

L	MP VMP
0	4
10	3
20	2
30	1
40	0

Q8. In his current job, Smith can work as many hours per day as he chooses, and he will be paid €1/hr for the first 8 hours he works, €2.50/hr for each hour over 8. Faced with this payment schedule, Smith chooses to work 12 hr/day. If Smith is offered a new job that pays €1.50/hr for as many hours as he chooses to work, will he take it? Explain.

Q9. Consider the following two antipoverty programs: (1) A payment of €10/day is to be given this year to each person who was classified as poor last year; and (2) each person classified as poor will be given a benefit equal to 20% of the wage income they earn each day this year.

a) Assuming that poor persons have the option of working at €4/hr, show how each program  would  affect  the  daily  budget  constraint  of  a  representative poor  worker during the current year.

b)   Which programme would be most likely to reduce the number of hours worked?

* Q10. Suppose vacation time comes in one-week intervals, and that the total willingness to pay for total vacation time by younger and older workers in a competitive industry is as given in the following table:

Total Willingness to Pay
Total	Younger	Older
vacation	workers	workers
time, weeks
1	1000	2000
2	1900	3000
3	2700	3700
4	3400	4200
5	4000	4500
6	4400	4700

a) Suppose VMP = 750/wk for younger workers, 900/wk for older workers, and that existing firms give all their workers, young and old, five weeks per year of vacation time. Can these firms be maximizing their profits? If so, explain why. If not, say what changes they should make, and how much extra profit will result.

b)    Suppose that the government now taxes 1/3 of everyone’s wages and uses the money mostly  on  transfers  (pensions,  benefits etc.) and public goods (roads, defence,  the national broadcaster, etc.), and that these accrue to the public regardless of how much they work or how much tax they pay. Workers are still willing to pay the same amount per week of holiday (they don’t feel meaningfully any poorer because roughly the same amount of money is still spent on them), but now they only get at most 2/3 of their VMP in wages. What happens to the optimal amount of holiday time?

* Q11. Based on the discussion in the textbook, what do you think might be some reasons why unemployment has on average been so much higher in Europe in the 21st century than it was in the late 1960s and early 1970s? Note particularly the comparison of three continental countries (Sweden, France and Italy – bold lines in green/blue) with the USA and UK (thin lines in orange/red).

* Q12. Goto Marginal Revolution University’s website and watch the 4-minute video3 “The Missing Men” by Tyler Cowen.

(a)  What was the main finding about participation rates discussed in the video?

(b) Which factors were given as related to the change in male participation rates?

(c)  Which factors were dismissed as explanations for the change?

* Q13. In contrast to America’s ‘missing men,’ Japan has made great strides in increasing female labour force participation in recent years. As recently as the year 2000, Japanese female labour force participation was about 10 percentage points lower than the US rate. Now, though, the Japanese rate is significantly higher (see graph below).

For an explanation of why the Japanese female participation rate has risen, please read the article “Japanese women are working more, but few are getting ahead” (from the

Economist on 18/11/2017 – reproduced along with this tutorial sheet).

a)    What are some of the factors given in the Economist article to explain the increased female participation rate?

b)   What are some non-explanations for the fact that Japanese women are more likely to be in the labour force than American women? (I.e. things you might have thought would explain it, but which don’t actually explain it.)

c) Given your answers to parts (a) and (b), can you understand why these issues might not be discussed in the textbook? Discuss.

* Q14. A monopsonist’s demand curve for labour is given by w = 12 − 2L, where w is the hourly wage rate and L isthe number of person-hours hired.

a) If the monopsonist’s supply (AFC) curve is given by w = 2L, which gives rise to a marginal factor cost curve of MFC = 4L, how many units of labour will they employ and what wage will they pay?

b) How would your answers to part (a) be different if the monopsonist were confronted with a minimum wage bill requiring them to pay at least €7/hr?

c) How would your answers to parts (a) and (b) be different if the employer in question

were not amonopsonist but a perfect competitor in the market for labour?

* Q15. Please read the Economist article “What harm do minimum wages do?” to answer the questions below.

a) On the question: “What harm do minimum wages do?”, how (and why) has the consensus among economists changed since the early 1990s?

b) Are there any structural reasons why the real effect of the minimum wage on employment might have changed overtime?

Q16. A monopolist can hire any quantity of labour for €10/hr. If their marginal product of labour is currently 2, and their current product price is €5/unit, should they increase or decrease the amount of labour hired?

Q17. Acme is  the sole supplier of security systems in the product market  and the sole employer of locksmiths in the labour market. The demand curve for security systems is given by P = 100 − Q, where Q is the number of systems installed per week. The short-run production function for security systems is given by Q = 4L, where L isthe number of full - time locksmiths employed per week. The supply curve for locksmiths is given by W = 40 + 2L, where W is the weekly wage for each locksmith. How many locksmiths will Acme hire, and what wage will it pay?

Q18. The Ajax  Coal Company is the only employer in its area. Its only variable input is labour, which has a constant marginal product equal to 5. Because it is the only employer in the area, the firm faces a supply curve for labour given by w = 10 + L, where W is the wage rate and L isthe number of person-hours employed. This supply curve yields the marginal factor cost curve MFC = 10 + 2L. Suppose the firm can sell all it wishes at a constant price of 8.

a)    How much labour does the firm employ, how much output does it produce, and what is the wage?

b) Suppose now the firm sells a special kind of coal such that it faces a downward-sloping demand curve for its output. In particular, assume that Ajax faces the demand curve given by P = 102 − 1. 96Q. How much labour does the firm employ, how much output does it produce, what price does it set for the output, and what is the wage?

c) Assume that Ajax still faces the demand curve P = 102 − 1. 96Q, but now further assume that Ajax has five labourers under contract to produce coal at a wage of 15. If Ajax has the option of hiring additional labourers at a higher wage without increasing the wage to the five labourers already under hire, will Ajax increase its labour force? Explain.

Q19. A firm produces output according to the production function Q = K2/1 L2/1 . If it sells its output in a perfectly competitive market at a price of 10, and ifK is fixed at 4 units, what is this firm’s short-run demand curve for labour?

Q20. How would your answer to the preceding problem be different if the employer in questionsold his product according to the demand schedule P = 20 − Q?

Q21. A and B face the choice of working in a safe mine at €200/wk or an unsafe mine at €300/wk. Output is the same at each location, and the wage differential between the two mines reflects the €100/wk costs of the safety equipment in the safe mine. The adverse consequence of working in the unsafe mine is that life expectancy is shortened by 10 years (assume  there  is  no other adverse effect) .  A and B have utility functions of  the  form ui [xi,si, R(xi)] = xi + si + R(xi) for i = A, B, where xi is i’s income per week in euros, si is 200 if the mine is safe and 0 otherwise, and R(xi) = 200 if xi  > xj, 0 if xi  = xj and −250 if xi  < xj.

a)    What does it mean for workers to have preferences like the ones characterised by the R(xi) function just described? Why might workers have such a preference?

b) If the two workers choose independently, which mine will they work in? Explain. (Hint: Use the utility function to construct a game theory payoff matrix like the one described in the text.)

c)    If they can negotiate binding agreements with one another at relatively low cost (e.g. by forming a union), will their choice be the same as in part (a)? Explain.