NAME (Last, First): SID: Instructor: Ronald Lee May 10, 2010 Departments of Demography and Economics
University of California ‐ Berkeley
Demography/Economics C175 Final Examination Answer Key Please answer all parts of all questions, using the spaces on the examination itself, and writing on the back of the paper if necessary. WRITE YOUR NAME AND STUDENT ID NUMBER ON EVERY PAGE OF THE EXAM. -
2 points for putting name and SID on every page. 1 point for missing one page. 0 otherwise. You may spend up to 65 minutes on the exam. There are 63 points possible. The possible points are indicated in front of each question, and this is also roughly how many minutes you should spend on each question, which will leave you with two extra minutes. Make sure you completely label any diagrams you present. Final Exam w/Answer Key ‐ Page 1 of 11 NAME (Last, First): I.
SID: Multiple Choice and True/False [1 point each] 1. Which of the following statements, if true, would support the case for laissez faire policy regarding fertility? a. Markets exist for all present and future goods b. Individuals strive to maximize their own utilities. c. Parents invest optimally in their children’s education. d. Social welfare is the sum of the individual utilities of society’s members e. All of the above f. Three of the above 2. The following figure shows average labor income and average consumption by age. Which type of population do the data describe? [Circle one] a. Hunter‐gatherer b. Developing country c. Industrialized country Age profiles of Average Consumption and Labor Income,
standardized to average labor income
1.2
1.0
Ratio to Av yl(30-49)
labor income
0.8
0.6
consumption
0.4
0.2
0.0
0
20
40
60
Age
80
100
3. When applying his famous logic of the “Tragedy of the Commons” to fertility, Hardin would argue which of the following points? [circle one] a. Overbreeding brings its own “punishment” to the germ line b. Mutual coercion is an unnecessary evil c. The freedom for all individuals to reproduce can avoid locking the world into a tragic course of action d. All of the above e. Both (b) and (c) f. None of the above Econ/Demog C175 Final Exam with Answer Key Page 2 of 11 May 10, 2010 NAME (Last, First): SID: 4. According to Boserup, the choice of a food production system is about choosing an __________: a. appropriate pace of technological progress b. ideal population size c. appropriate factor mix d. annual cropping technique 5. Which of the following have been the main contributors to the decline in the age of retirement in the US? Circle one: a. Implicit taxes built into pension programs b. Lower demand for labor of the elderly c. Rising incomes d. Increasing health problems among the elderly e. Defined contribution pension programs are replacing defined benefit programs. f. Both (a) and (c) g. Both (d) and (e) 6. Which of the following measures would increase the implicit rate of return of a PAYGO pension system in the long run? Circle one: a. Increasing the amount of tax credits for families with children to encourage higher fertility. b. Increasing the age at which pension benefits can be accessed. c. Increasing the social security payroll tax rate. d. Investing in rising education to increase the rate of productivity growth for workers. e. Reducing the monthly benefits paid out during retirement. f. Both (a) and (b) g. Both (a) and (d) True/False 1. F When population is more dense, there is a shift to more extensive systems of food production that require less work per person but yield more output. 2. F The marginal product of labor (MPL) under a multi‐cropping food production system is greater than that under short fallow, according to Boserup. 3. T If pension accrual is positive, that is an incentive for a person to work one more year instead of retiring. 4. F Differences in population aging across countries in the developed world are largely due to differences in mortality. 5. F Social security accounts for the largest projected increases in public expenditures associated with population aging. 6. F In recent decades, the median retirement age of American men has stopped declining, but the median retirement age for American women has increased. 7. T The implicit rate of return for the Social Security system in the U.S. is higher for older generations compared to younger generations. 8. F The Social Security Trust Fund has already begun to decline. Econ/Demog C175 Final Exam with Answer Key Page 3 of 11 May 10, 2010 NAME (Last, First): II.
SID: Short‐Answer Questions [18 points] 1. [4 points] In the May 2010 edition of Foreign Policy, Charles Kenny asserts Malthus’s predictions have been consistently proven wrong and that “the … model at the core of Malthusianism is way off base.” Describe how two of Malthus’ core assumptions have not stood the test of time. • Malthus did not anticipate increased productivity of land—for example, the green revolution or methods of intensive farming and agricultural production. • Malthus predicted that at higher incomes women would give birth to more children. This has not generally been the case; for example quality/quantity theory and VOT theory demonstrate why higher‐income parents generally have fewer children than their low‐
income counterparts. 2. The Children’s Health Insurance Program (CHIP) provides health insurance coverage to children in families with incomes that are low (although generally above poverty level), but too high to qualify for Medicaid’s health insurance which is for even lower‐income people. a. [2 points] Explain the public policy rationale for a government to establish such a program for child health. Your answer should be based on Becker and Murphy’s article, “The Family and the State”. Children could be better off in the longer‐run (i.e. obtain higher incomes) if they suffered less illness and were more productive during their working years. Parents with lower incomes are unlikely to invest the optimal amount in their children’s health due to tradeoffs with their own consumption. Parent may also be unable to force their children to repay if they loaned them the money. The lack of a market in health investments prevents children from borrowing enough to pay for their own health. Therefore, the government can force parents to pay taxes to finance public health programs for children. b. [1 point] Does such a public health program for children also strengthen the rationale for having a public pension system? Yes, there is also a rationale for a public pension system that forces children to repay their parents for their health investments by taxing them when they are working, and giving their parents consumption benefits when they become old. 3. The global population—currently about 6.8 billion people—is projected to surpass 9 billion by the end of this century. Imagine that to address this issue, the United Nations (UN) has convened an international summit to discuss population policy and government interventions for fertility. The UN has assembled a panel of experts, living and dead, to advise about the various facets of population policy. The speakers include: a) Thomas Malthus, b) Esther Boserup, c) Paul and Anne Ehrlich, and d) Jonathan Gruber and David Wise. Specifically, the UN is considering the merits of 3 government policies for regulating fertility: family planning programs, financial incentives to current or prospective parents, and the passage of coercive fertility laws. Econ/Demog C175 Final Exam with Answer Key Page 4 of 11 May 10, 2010 NAME (Last, First): SID: a. Malthus, as the 250‐year old elder statesman of the group, makes the first presentation. i.
[2 points] Malthus grumbles: “In my day, the need for government regulation of fertility wasn’t even worthy of study,” citing the preventive check as an important constraint on fertility. In 2 sentences or less, explain what Malthus means by the preventive check. The preventive check is a form of behavioral responses of individuals who decrease their fertility in anticipation of poor conditions in the future. In other words, the preventive check is a response of fertility to long‐run wages. This decline in fertility can result from married individuals choosing to lower their fertility or from people choosing to get married at later ages. In Europe it was customary for young people to wait until they could support their own household to get married. ii. [1 point] Malthus also weighs in on the issue of family planning programs. Does Malthus support family planning? Explain his reasoning in one sentence. No. Malthus views the avoidance of fertility by contraception as a vice. b. [2 points] Boserup speaks next. She calls into question Malthus’ dismal forecasts of human suffering as “so 19th century”. In 2 sentences or less, why would Boserup argue that Malthus overstates the negative effects of population growth on human welfare? Technological progress responds endogenously to population growth. As the population grows and becomes denser, food production techniques are likely to adjust and allow for greater output. c. The Ehrlichs aren’t convinced. They state: “Governments must go beyond family planning,” implying that financial incentives and/or coercion are necessary. i.
[1 point] What (one‐word) economic term describes the social costs that parents do not take into account when they make fertility decisions? Answer: Externalities ii. [2 points] Briefly explain how the Ehrlichs’ concept of natural capital justifies going “beyond family planning”. Natural capital includes renewable and nonrenewable resources that act as inputs into human production. Overpopulation diminishes the stock of natural capital. Thus fertility decisions may create environmental externalities which provide a rationale for using financial incentives or potentially coercion to limit fertility. d. Gruber and Wise shift focus to population aging as a rationale for government intervention. i. [2 points] Briefly describe how population aging affects the case for government intervention in decision making about fertility in industrialized countries. Industrialized countries are graying rapidly, increasing their old‐age dependency ratios. The elderly populations in these countries receive large public transfers from pay‐as‐you‐go pension systems, meaning that fewer workers will support a growing elderly population. Births provide a positive fiscal externality by contributing to the public transfers, providing a case for government intervention. ii. [1 point] Underline the correct word: Population aging provides a rationale for some industrialized governments to provide (positive / negative) financial incentives for prospective parents. Econ/Demog C175 Final Exam with Answer Key Page 5 of 11 May 10, 2010 NAME (La
ast, First): III.
SID
D: Population, LLand Use and Wages [2
21 points] In 1626, P
Peter Minuit, the Director‐‐General of th
he Dutch colo
ony of New Neetherland purchased Manhattaan Island from
m the Native A
American Len
nape people ffor a price of 6
60 guilders. IIn the analysis that follow
ws, assume th
hat, at the tim
me of purchasse, Manhattaan was uninhaabited and that the island would be settled in the
e near future by Dutch colonists. Furth
her assume th
hat: •
•
•
•
•
Th
he colonists u
use two inputts (land and laabor) to produce a single o
output (food)) Th
here is no tecchnological prrogress Th
here is no cap
pital accumulation (and th
hus no saving or investmen
nt) Upon reachingg a certain population, there are diminishing returnss to labor on tthe island. Th
he amount off labor supplied does not cchange according to the w
wage level a. [1
1 point] Manh
hattan Island consists of approximatelyy 23 square m
miles of land. Assume that the optimal size off a farm is onee square milee and that, as colonists arrive in Manhattan, each on
ne mal size which yields an amount of food,, w*. How many individuaals esstablishes a farm of optim
caan emigrate tto Manhattan
n before the m
marginal prod
duct of labor ffalls below w
w*? Answer: 23 peeople 4 points] Draaw a graph that plots Manh
hattan’s popu
ulation on thee x‐axis against total outpu
ut on b. [4
th
he y‐axis. Draaw a second ggraph that deepicts the marrginal producct of labor and
d the averagee product of labor for Manhaattan’s populaation. The po
opulation should be plotted on the x‐axxis aggainst outputt per worker o
on the y‐axis.. Clearly labeel all axes, currves and the p
point, p*, at w
which diminishing maarginal return
ns to labor set in. Econ/Demog C175 Final Exa
am er Key with Answe
Page 6 of 11
1 May 10, 2010 NAME (La
ast, First): SID
D: O
OR Econ/Demog C175 Final Exa
am er Key with Answe
Page 7 of 11
1 May 10, 2010 NAME (Last, First): SID: c. [1 point] Briefly explain why labor productivity declines at p*. After 23 people arrive in Manhattan and establish farms of optimal size, the 24th immigrant to the island will cause land to be re‐allocated in such a way that the average farm size is no longer optimal. Another possibility is that the 24th immigrant to the island will become a worker on one of the pre‐existing farms. Either way, the marginal contribution of this immigrant to the island’s total output will be lower than that of the 23rd immigrant. d. [2 points] Can Manhattan’s average product of labor (APL) fall below its marginal product of labor (MPL)? Briefly explain why or why not. No. With diminishing marginal returns to labor, each immigrant to the island adds to the island’s total output by a smaller amount than the immigrant who came before him. If MPL > APL, then there would have to be increasing marginal returns to labor. e. [2 points] Assume that Manhattan’s economy is competitive such that the wage is given by the marginal product of labor. Find the maximum population size where the marginal product of labor equals the average product of labor. For this population size, what part of total output will accrue to landowners in the form of rents? Briefly explain why this is the case. Answer: Zero. This is because at this population size or sizes land is relatively abundant and labor is relatively scarce. Econ/Demog C175 Final Exam with Answer Key Page 8 of 11 May 10, 2010 NAME (La
ast, First): f.
SID
D: 2 points] Now
w assume thaat every Manh
hattan resideent needs an aamount of food, s, to survive [2
an
nd reproduce
e. Draw a graaph that depiccts the maxim
mum populatiion size that ccan be sustain
ned on Manhattan. OR g. [1
1 point] Name a condition which gives tthe maximum
m sustainablee population ssize under eggalitarian inco
ome distributtion assumingg every resideent needs an amount of fo
ood, s, to survvive. Answer: s = AP
PL Econ/Demog C175 Final Exa
am er Key with Answe
Page 9 of 11
1 May 10, 2010 NAME (La
ast, First): •
SID
D: Assum
me that afterr a period of o
one year, thee population o
of Manhattan
n is in demog
graphic equiliibrium such tthat populatio
on size and w
wages are sta
ationary. h. [3
3 points] Usin
ng the Malthu
usian model, in the space p
provided belo
ow, draw and
d completely llabel a diagram of th
his equilibrium
m. Be sure to
o label the equilibrium wagge level (w0) and equilibriu
um po
opulation levvel (P0) and th
he axes. i.
j.
[4
4 points] Now
w assume that Manhattaniites raise the legal minimu
um age at first marriage to
o sttrengthen the
e preventative check and p
protect against overpopulaation. Depictt the changess ab
bove with a n
new birth curvve (b1), a new
w population size (P1) and a new wage (w1). In worrds, briefly describe how these changes occu
ur to form a n
new long‐run equilibrium. Do residents have higher or lowe
er wages than
n before? W
When the age at marriage iis higher, ferttility is reduceed, thus leadin
ng to a fall in
n the crude birrth ra
ate curve and
d a correspond
ding movemeent along the crude death rate curve. In
n the long run
n, the w
wage rises. [1
1 point] In the
e Malthusian model, which of the following changess will increasee real wages iin M
Manhattan in t
the long run?? (circle one) i.
A ttechnological advance thaat shifts the laabor demand curve outward ii.
A ssudden population influx
iii.
A permanent in
ncrease in thee crude death
h rate at all wage levels iv.
A permanent in
ncrease in thee crude birth rate at all waage levels Econ/Demog C175 Final Exa
am er Key with Answe
Page 10 of 11
1 May 10, 2010 NAME (Last, First): IV.
SID: Pension Theory [10 points] In their article, Gruber and Wise discuss the trend in which many workers now retire earlier than they did a few decades ago, and labor force participation at older ages has declined. Consider the welfare of a population characterized by very high life expectancy in which: •
•
•
•
People begin working age 20, the normal retirement age is 80, but social security benefits begin at age 50 and no one dies until age 110. Thus there are workers, Wt, young retirees, YRt, and old retirees, ORt. Each generation is twice as large as the previous one. The worker population of size W at time t produces 20 units of a perishable good per person. However, the younger retiree population aged 50‐79 of size YR at time t, can still produce 5 units per person. However, the “oldest old” retirees aged 80‐109 of size OR at time t cannot produce anything at all due to health conditions. [Show all your work!] 1. [3 points] What is the dependency ratio? YRt = Wt‐1 YRt = 2ORt Wt = 2Wt‐1 Wt = 4ORt Wt = 2YRt DR = (# Young Retirees + # Old Retirees)/#Workers = (YRt+ORt)/Wt = (2ORt+ORt)/4ORt = 3/4 2. [3 points] Derive the social budget constraint. YWWt + YYRYRt + YORORt = CWWt + CYRYRt + CORORt 20Wt + 5YRt + 0ORt = CWWt + CYRYRt + CORORt 20(4ORt) + 5(2ORt) = CW(4ORt) + CYR(2ORt) + CORORt 90 = 4CW + 2CYR + COR 3. Suppose the government introduced a defined benefit program where each young retiree under the normal retirement age receives 5 units of consumption in addition to what they can produce themselves, while each old retiree above the normal retirement age receives 10 units of consumption. a. [2 points] What would be the amount of tax levied on workers? CYR = (5+5) = 10 COR = 10 90 = 4CW + 2(10) + 10 4CW = 60 CW=15 Transfer = 5 Tax = transfer/amount produced = 5/20 = 25% b. [2 points] What is the rate of return to this pension system? [5 + 10]/5 – 1 = 15/5 – 1 = 2 Æ 200% Note: 100% is also acceptable since this is just a convention about whether you include getting back what you put in as part of the rate of return. Econ/Demog C175 Final Exam with Answer Key Page 11 of 11 May 10, 2010