the economics of ideas introduction. population human population growth has been exponential

The Economics of Ideas

Introduction

PopulationPopulation

Human population growth has been exponential

World Population Growth: 1000-2000

0

1000

2000

3000

4000

5000

6000

1000 1200 1400 1600 1800 2000

Year

Po

pu

lati

on

(m

illio

ns

)


Animal population growth fluctuatesTime-series data on Pandora moth populations inferred from the

number of trees infected during population fluctuations


Human populations also fluctuate with disease outbreaks, but these fluctuations haven’t been persistent the way they have for animal populations


So, we have a puzzle: why hasn’t human population growth been subject to the same kinds of checks that operate in animal populations?

Early thinkers on this subject – such as Thomas Malthus – were persuaded that finite economic resources together with diminishing returns must eventually drive wages down to subsistence levels, leading to checks in further population growth

But exactly the opposite has happened. Why?


The answer to the puzzle is IDEASIdeas evolve memeticallyGood ideas lead to increased economic productivity or general human betterment

These ideas get copied and become the basis for new ideas

Ideas lead to technology

TechnologyTechnology

The first good idea: agricultureObservation of plant reseeding patterns and understanding of the role of seeds led to plant cultivation

Random capture of buffalo calves led to the realization that animals could be domesticated

Subsequent innovation was largely devoted to the development of tools for farming

TechnologyTechnology The productivity improvements made possible first by simple

agricultural technologies, then by technologies for transportation by land or sea which opened up trade, and finally with the onset of industrialization in the 19th century, have not only allowed the human population to continue growing, but have also allowed for economic growth in excess of that of population growth, leading to a parallel growth in living standards over time as well.

So, in the first part of the course, we examine economic growth, its determinants, sustainability, and the role of technical innovation as a driver of growth

In the second part of the course, we will focus on how society manages the process of innovation, and the economic trade-offs implicit in this.

Growth BasicsGrowth BasicsExperiment: Tearing a sheet of paper

Take a sheet of paper and fold it in half, then tear it in half along the fold. Then take the resulting two pieces of paper, put them together, fold in half, and tear along the fold. Continue this process as long as you can (you can stop folding once the pile is small enough in area). Answer the following questions before you start tearing

Question 1: How many times do you think can you tear the resulting pile before it becomes too thick to tear?

Question 2: How many times would you have to tear the pile before it becomes a mile high? (Hint: a pile of 15,840,000 sheets of paper would reach a mile high.)

Growth BasicsGrowth Basics

Experiment: Suppose you find yourself reincarnated as a frog living in a pond with water lilies that double in number every day. At the beginning of the month, there is one water lily, and the pond is covered by water lilies in 30 days.

Question 1: On which day is the pond half covered?Question 2: On which day is the pond a quarter covered?Question 3: Suppose you and your fellow frogs start moving

dirt on the day the pond is only a quarter covered and manage to enlarge the pond to twice its original size. How much time have you bought yourselves in terms of having access to open water?


Exponential growthArises when the increase in quantity over a period of time is proportional to the quantity at that point in time :

If we let the time interval go to zero, we end up with the differential equation

trxx

rxxdt

dx


Exponential growth

rteX

Xrt

t

txdt

dtrx

0

0

tx

or

txln

get to respect to with integratecan we

lnx

x

Since


Exponential growth

Relationship to growth in discrete time

.0 have we,0at

because n integratio ofconstant thecalled We

0

0

Xxt

X

11

as equalities theseofany write-recan that weNote

111

:exampleinterest Compound

0

trPtPtP

PrtPrtP t


Exponential growthNow, subdivide the interval (say the year) into n subintervals and

compound n times instead of just once. This gives

Note that we divide the annual rate by the number of subintervals to convert it into a rate over the subinterval.

In the limit, as the number of subintervals goes to infinity, we get

nt

n

rtP

1

rtnt

ne

n

rtP

1 lim


Exponential growthRule of 70

When growth is exponential, there is an interesting relationship between the rate of growth and the time it takes for an initial amount to double:

i.e. the doubling time can be obtained by dividing 70 by the growth rate expressed in percent

%

70

rtdouble



The rule is derived from the fact that given some initial quantity N0 growing at rate (in fractional terms) r, the doubling time satisfies

2

or

2 00

rt

rt

e

NNe



Taking logs and solving for t yields

Multiply top and bottom by 100 to convert the growth rate to a percent and rounding up to 70 gives us the rule

rrt

6932.02 ln



Examples> “Asian tigers” – Hong Kong, S. Korea, Singapore and

Taiwan – experienced growth rates in the ’80’s and ’90’s in excess of 9% per year. Via the rule of 70, this means these economies were doubling in size every 8 years or so

> World population is growing at an average rate of 1.14% per year. Population doubling time is thus around 60 years



Examples> Gasoline prices in perspective: The U.S. inflation rate

from 1980 to 2005 has averaged roughly 3.5% per year

> At this growth rate, prices double every 20 years

> The current price of gasoline is about $2.50/gal., which would have been $1.25 in 1985

> In fact, in 1985, gasoline was slightly more expensive, running just under $1.50


Exponential growthConclusions

Exponential growth is relentlessHuman population growth has been exponentialSo how have we managed to stay ahead of our own

relentless needs?BRAINS

the economics of ideas introduction. population human population growth has been exponential

Documents

economic growth

population fluctuations

population human populations

technology slide

parallel growth

driver of growth

exponential slide

farming slide