1. Chapter 23: The Economics of Resources Lesson Plan
Growth Models for Biological Population
How Long Can a Nonrenewable Resource Last?
Sustaining Renewable Resources 1

2. Chapter 23: The Economics of Resources Growth Models for Biological Population
Use of resources involves a complex intermixture of biological, ethical, practical, technical, and economic issues:
How many people will there be in the world in another 20 or 40 years, and how will those numbers affect resources available to you and to them?
What should we consume for our own use, give to others more needy, or leave for future generations, in terms of wealth, well-being and wilderness?
Will our standard of living keep getting better, or it is not maintainable, even at current levels, in the long run?
How long will it be, at current patterns of use, until we exhaust some particular resources? 2

3. The Balance Between Consumption and Conservation
Chapter 23: The Economics of Resources Growth Models for Biological Population
Use of resources - continue
Can we develop more efficient technology, so that we can get more out of the resources that we use?
How do we balance economics, the needs and desires of individuals, with other important considerations? How much would it cost – how much is it worth – to assure that we do not let some things go extinct?
The Balance Between Consumption and Conservation 3

4. Chapter 23: The Economics of Resources Growth Models for Biological Population
Geometric growth model is used to make rough estimates about sizes of human populations.
Birth, death, and migration rates rarely remain constant for long, so projections must
be made with care.
Using the model for short-term projections may be useful.
Rate of Natural Increase
The annual birth rate minus the annual death rate. 4

5. Chapter 23: The Economics of Resources Growth Models for Biological Population
Predicting the H.K. Population
The H.K. population was 7.18 million in It is increasing at an average growth rate of 0.8% per year. What is the anticipated population end-2021?
Answer: Apply the compound interest formula, A = P(1 + r)t
with P = 7.18 million, r = 0.008, t = 10
A = P (1 + r)t = 7.18 million ( )10
= 7.18 (1.008)10
= million
Population in 2021 is rounded off and estimated to be 7.78 million.
Using Compound Interest
Formula for Population
Growth –
A = P (1 + r) t
Where:
A = Amount owed after interest is added (future population amount after growth rate)
P = Principal amount (initial population)
r = Interest (growth) rate
t = Years where r (growth) rate is applied 5

6. Chapter 23: The Economics of Resources Growth Models for Biological Population
Comparing Growth Rates in Different Nations
Rate of increase of U.S. was estimated at 1.0%
The rates of increase in most developing nations are much higher than in industrialized nations.
Nigeria, Africa’s most populous country, has an estimated growth rate of 2.8%, and will grow from 135 million in mid-2007 to 231 million in mid-2030.
This is an increase of more than two-thirds within this period.
These projections raise concern over providing sufficient food and resources for all people.
Also, population structure (subgroups of the population) may change in poorer countries. It is likely the life expectancy of poorer nations will increase, resulting in the proportion of the older population to increase.
In poorer countries, the proportion of the population over 60 years of age will be 20% by 2050, compared with 8% now. 6

7. Chapter 23: The Economics of Resources Growth Models for Biological Population
Limitations on Growth
Population growth is eventually constrained by the availability of resources such as food, shelter, and psychological and social “space.”
Carrying capacity of the environment is the term for the maximum population size that can be supported by the available resources.
Logistic Model
A particular population model that begins with near-geometric growth but then tapers off toward a limiting population (the carrying capacity).
The logistic model reduces the annual increase r P by a factor of how close the population size P is to the carrying capacity M:
Growth rate P ′ = r P (1 – ) = r P (1 – )
population size carrying capacity
P M 7

8. Chapter 23: The Economics of Resources Growth Models for Biological Population8

9. Chapter 23: The Economics of Resources How Long Can a Nonrenewable Resource Last?
A resource that does not tend to replenish itself and of which only a fixed supply S is available.
Important examples include gasoline, coal, and natural gas.
Example: How long will the supply of a resource last?
As long as the rate of use of the resource remains constant; say for example, we use a constant U units per year, then the supply will last S/U years.
Example: U.S. recoverable coal reserves will last 250 years.
For most resources, its consumption or rate of use tends to increase with population and with a higher standard of living.
To determine how long the supply will last, we can manipulate the savings formula (similar to making regular withdrawals [with interest] from a fixed supply of the nonrenewable resources).
The terms we use to describe this calculation are referred to as the static reserve and the exponential reserve. 9

10. Chapter 23: The Economics of Resources How Long Can a Nonrenewable Resource Last?
Static Reserve
Static reserve is how long the supply S will last at a particular constant annual rate of use U.
The length of time that a static reserve will last is S/U years.
Exponential Reserve
Exponential reserve is how long the supply S will last at an initial rate of the use U that is increasing by a proportion r each year.
This length of time (the number of years, t) is determined by evaluating the following expression:
Where ln is the natural logarithm and can be evaluated easily on a calculator.
ln [1 + (S/U) r ] ln (1 + r )
years
t = 10

11. Chapter 23: The Economics of Resources How Long Can a Nonrenewable Resource Last?
Example: Suppose that you begin retirement with $1 million in savings, and you don’t invest your money and just keep it in a safe.
If it costs you $180,000 per year to live at your accustomed standard of living and there is no inflation, the static reserve is $1,000,000/$180,000 = 5.5 years.
If the inflation rate is 3% per year, then it will cost you increasingly more per year to live, so the exponential reserve: 11

12. Chapter 23: The Economics of Resources Sustaining Renewable Resources
Renewable Natural Resource
A resource that tends to replenish itself (fish, wildlife, and forests).
We would like to know how much we can harvest and still allow for the resource to replenish itself.
We concentrate on the subpopulation with commercial value.
We measure the population size as its biomass.
Biomass is the physical mass of the population and is written in common units of equal value.
Examples of biomass can be measuring fish in pounds rather than in number of fish and in forests counting the number of board feet of usable timber rather than the number of trees. 12

13. Chapter 23: The Economics of Resources Sustaining Renewable Resources
Annual scholarship = $10,000 per year
Investment return rate: 5%
The one-time donation = $10,000/0.05 = $200,000
The inflation rate is 3%
The one-time donation = $10,000/ = $515,000
g = 1.942% 13