Economics 280
October 2011
1. Consider the following population pyramid.
a) Estimate the sex ratio for 0-4 year olds. Is it normal? (2 marks)
The sex ratio appears to be about 58.5 million to 56 million, or 1.04. This is normal.
b) What can you say about dependency in this population relative to the situation in
Canada? (2 marks) This population has higher child dependency and lower aged
dependency than Canada.
c) From the shape of this pyramid, at what stage of mortality transition is this
population? (2 marks) From the shape of this pyramid, childhood mortality is low and
fertility is falling. The population has passed out of the 1st stage of mortality transition where
infant mortality is very high. Mortality seems to be still quite high for old adults. We may not
yet be in the last stage of mortality transition where aging is delayed and many survive into
their 80s and 90s.
d) From the shape of this pyramid, what is happening to births?
(2 marks) The even-ness of the pyramid at the bottom shows that birth cohorts are
falling in size. Despite mortality during ages 0-4, the 5-9 cohort is the same size as the
newborn cohort.
The raccoon dog is a wild mammal found in Finland and elsewhere. Its pelts are sold to
the garment industry.
2. a) If the price of raccoon dog pelts is falling, does that mean that raccoon dogs are
becoming more plentiful? (2 marks)
If the price of raccoon dog pelts is falling, either supply is increasing or demand is decreasing.
Supply could even be decreasing, if demand is decreasing even faster.
b) What exactly does the price of one raccoon dog pelt represent? (4 marks)
The price of one raccoon pelt represents its value-in-trade at this present time to this
present generation. This value depends on marginal cost (i.e. supply) and marginal
willingness to pay (i.e. demand).
3a) If the Finnish government wants to protect wild raccoon dogs from hunters,
what policy might it adopt? Think of one and briefly explain how it would work. (2
marks)
The Finnish government might ban the hunting of raccoon dogs, imposing a fine on any
violators.
b) What/Who would the precise target of this policy be? Does this present any
problems? (2 marks)
This targets raccoon-dog hunters. It is targeted precisely on the behaviour we dislike, so it
should pose no problems in that respect.
c) What margin of behaviour does this policy influence? Does this present any
problems? (2 marks)
This policy impacts each and every raccoon dog a hunter might want to kill. It does not allow
even a low level of hunting which might be sustainable. Therefore its social costs might exceed
the benefits. On the other hand a no-kill policy has the best chance of resuscitating the raccoon
dog population.
d) Which constraints or incentives are changed by the policy? For which individuals is
this likely to be effective? (3 marks) The hunter's costs have now risen, so much so that
he/she may decide not to hunt. This policy will be effective for hunters for whom money is
scarce and who have alternative employment. It will be effective for hunters who are
conscientious and do not wish to break the law. Hunters who are wealthy and callous enough
to pay the fines or who are desperate to hunt raccoon dogs are now given an incentive to
poach.
e) Who will bear more of the cost of the policy, the hunters or the consumers of fur? (2
marks). Explain. With hunters' costs higher, hunters make less profit. They attempt to pass
the cost hikes onto their customers. This is only possible to the degree that customers are
relatively price-inelastic. The party that is least price inelastic will bear more of the cost.
Demand is probably fairly elastic because there are many substitutes for raccoon fur, so hunters
will bear most of the cost. Taxpayers – both consumers and hunters - are on the hook for the
cost of enforcing the program.
4. A population that doubles between 1990 and 2014 has what exponential
growth rate? State the answer as a per cent. Show your work. (2 marks)
2x = x exp(24r) r = 0.0289 The population grew at 2.89 percent.
5. In 1875, Queen's had 15 first-year students. Assuming that enrollment of firstyear students grew at an exponential rate of 3% per year, what would enrollment
of first year students have been after 20 years? State your answer in English as
well as math. Show your work. (2 marks)
N(1895) = N(1875)exp(20r) = 15exp(20r) = 15 exp(60)= 27.33 The number of frosh in
1895 would be roughly 27.
6. Again assuming that enrollment of first year students grew at 3% a year
exponentially, write an expression for the total number of students who enjoyed
a first year at Queen's during the 20 year period. (3 marks)
Integral from t=0 to t=20 15exp(0.3 t) dt
or Integral from t=1875 to t=1895 15exp(.03(t-1875)) dt
7. Consider the following partial Life Table for raccoon dogs in Finland.
Age
0
1
2
3
4
5
6
7
q,
probability
of dying
0.884
0.629
0.419
0.440
0.357
0.667
0.667
erased
l
100,000
11,600
4,300
2,500
1,400
900
300
100
e, expected
life years
remaining
0.712
1.319
1.709
1.580
1.429
0.944
0.833
0.500
a) What is the probability of dying in the last age category? Write the answer in your
booklet. (1 mark) The probability of dying in the last age category is always equal to 1.0 by
definition.
b) How many of the 100,000 newborn raccoon dogs die during their first year of life? (1
mark) The table shows that 88.4% of newborn raccoon dogs die during their first year of life.
c) What is the Paradox of the Life Table? How many instances of this paradox do you
see in this table? Describe briefly. (3 marks) The paradox of the Life Table exists whenever
an older individual has a higher expected-years-of-life-remaining than a younger individual.
For raccoon dogs, we see that 2 years olds have higher e than 1 year olds or newborns. We see
that 3 year olds and 4 year olds have higher e than newborns or 1 year olds. And we see that 1
year olds have higher e than newborns.
d) Working backwards from the Expected Life Years Remaining column,
what is the T for age 0, i.e. what is the total number of life years the 100,000 newborns
can expect to enjoy from birth onwards? (1 mark)
T(0)= e(0)*l(0) = 71,200.
e) Working from the "T"s, what is the number of life years the 100,000 newborns enjoy
during their first year of life? If you were unable to calculate T, make an assumption
and proceed. (2 marks)
L(0) = T(0) – T(1) = 71,200 – e(1)l(1) = 55,899.6 years of life as newborns.
f) What assumption have the researchers made about how soon after birth the average
non-surviving newborn dies? (3 marks)
L(0) = n l(0) – n f d(0) = 55,899.6
n is 1 year of life
l(0) = 100,000
d(0)=88,400 newborns who die
This implies that f = 0.4988 or 0.5
The researchers assumed that the average newborn raccoon dog who dies dies mid-way during
the first year of life.
g) If the population is stable at these mortality rates, what is the probability that a
newborn survives to age 2? State this as a percent. (1 mark)
The probability of surviving to age 2 is l(2)/100,000 = 4,300/100,000 = 0.043 = 4.3 percent.
You could also perform (1-.884)(1-.629) = 0.043.
Do not multiply .884 by .629. That would give you the probability that the dog died both as a
newborn and as a 1-year-old.
8. Consider the following fertility data for the typical female raccoon dog.
Age of female
Number of babies
0
0
1
5.5
2
6.6
3
8.6
4
7.9
5
8.8
6
8.8
7
8.8
Using this information plus the information given in question 7, what are the first 3 rows
of the Leslie matrix for the raccoon dog population? (6 marks)
The first 3 rows are:
0
2.25
3.3
0.118 0
0
0
0.371
0
4.3 3.95
0
0
0
0
4.4 4.4 4.4
0
0 0
0
0 0