Lecture 5 - Unified Growth Theory

Question 1

What is the mystery of growth?

Answer 1

what are the roots of the dramatic
transformations in living standards in the past centuries, after
hundreds of thousands of years of stagnation

Question 2

What is the mystery of inequality

Answer 2

what are the origins of the vast
inequality in the wealth of nations?

Question 3

What did Romer predict

population size

Answer 3

that the size of the population drives innovations in the modern world

suggests that a lack of growth in the malthusian era in due to a lack of innovations which we know is false since innovations took place

Question 4

why is there a stagnation of living in Malthusian epoch

Answer 4

More innovations take place as the size of the population increases, however these innovations do not rasie the standard of living but the population size

Question 5

Malthus vs Romer

Answer 5

Malthus: technology progress, population expansion, no growth
Romer:population expansion, tech progress, growth

In Romer epoch there is a positive feedback loop between technology and population which eventually triggers accumulation of human capital and quantity-quality trade off: stagnation to growth and romer mechanism takes over malthusian

Question 6

What is the basic structure of the model

Answer 6

the Malthusian model with (1) human capital, determined by households’ decisions about the quantity and quality of their children, (2) endogenous tech.progress, driven by population size (because of nonrivalry - Romer) and quality (education)

There no not only land and technology as factors of prodcution but human capital as well

Question 7

What is the output equation and output per worker equation

Answer 7

Y_t = H_t^α (A_tX)^1-α and
y_t = h_t^α x_t^1-α

h_t = H_t/ L_t = human capital per worker
x_t = (A_tX) / L_t = effective resources per worker

Question 8

Assumption

What is technological progress a function of
and what is the equation

Answer 8

the size and composition of the population (with e the average level of education)

g_t+1 = (A_t+1 - A_t) / A_t = g(e_t, L_t)

Romer mechanism- when L increase,, g is going to increase too

Question 9

Assumption

What do the size and composition of population have on technological progress

Answer 9

positive and diminishing effect on the pace of technological progress
g_e(e, L) > 0 and g_ee(e, L) < 0 and
g_L(e, L) > 0 and g_LL(e, L) > 0

First derivative of h will respect to g is negative

The more you invest in your education the more human capital you have (which will help navigate changing technological advancements) but it will depreciate with how fast technological progress happens - whenever you increase e, h will increase as well but as g increases, h will become smaller

Question 10

Assmuption

What is the expression that shows that there is technological progress as long as humans exist

Answer 10

g(0, L) > 0 for L > 0

Question 11

Assumption

What is the human capital of an indivdiual in period t a function of

Answer 11

its education and the overall rate of technological progress
h_t = h(e_t, g_t)

Question 12

Assumption

What does human capital accumulate with and in what environment does it become obselete

Answer 12

• accumulates with investment in education
• becomes obselete in a changing, technologial environment
  h_e(e, g) > 0 and h_ee(e, g) < 0 - positive first derivative becuase whenever you increase education, human capital will increase as well
  and h_g(e, g) < 0 and h_gg(e, g) > 0 - negative first derivative, when the rate of technological progress accelerates, human capital is going to do down)

This is because human capital depreciates with how fast technology progresses

Question 13

Assumption

What does education help with

Answer 13

helps individuals better cope with a changing technological environment (lessens the obsolescence of human capital)
h_eg(e, g) > 0 (also h<0, g > 0)

When you increase technological progress AND education TOGETHER, human capital will increase

Question 14

Proposition

Relationship between education and technological progress

Answer 14

when technological progress is low, since demand for human capital is low, there is no investment in eduation. After technological progress reaches some threshold and starts accelerating, parents invest in the education of their children to help them cope with the changing technological envrionment

Question 15

What are preferences of an adult/ parent at the time

Answer 15

u_t = (n_th_t+1)^γ(c_t)^1-γ

with n_t = the number of children; h_t+1 = h(e_t+1, g_t+1) = the human capital of each child; c_t = consumption; and y_t = w_th_t = income

Question 16

What is the budget constraint for the preferences of an adult

allocation to time spent to raising children between quantity and quality is only determined by the rate of tech. progress

Answer 16

n_t(τ + e_t+1)y_t + c_t ≤ y_t

τ + e_t+1 = time to raise a child with education e_t+1
(τ + e_t+1)y_t = opportunity cost of raising a child with education e_t+1

Question 17

what is the subsistence consumption constraint

Answer 17

c_t ≥ c squiggle

this is the consumption enough for survival

When this binds, c_t = c squiggle, individuals allocate whatever is left of their income to children

Question 18

What if there was no subsistence constraint

Answer 18

then the optimal expenditure on consumption would be a fraction 1 −γ of income; while time spent raising children would be a fraction a γ of parental time

n_t(τ + e_t+1)y_t + c_t ≤ y_t where
n_t(τ + e_t+1)y_t is γy_t and c_t is (1 −γ)y_t

Question 19

Optimization graphs

Answer 19

1. a fixed time spent raising children no matter if you are rich or poor
2. if too poor you cannot spend that same fraction of time with children because you would die, you wouldn’t work sufficiently to afford to consume above subsistence so less time is spent raising children
3. when income increases, budget constraint rotates
4. when income increases more time is spent with children and number of children will increase but because fertility increases, income decreases (malthusian epoch)
5. because size of population increases there is more technological progress so income increases a little more
6. pace of technological progress will slowly acclereate over time until the point where you reach your desired fertility (that allows you to spend γ time with children
7. trade of between quantity and quality will drive transition from stagnation to growth

Question 20

Proposition

Malthusian and Post-Malthusian epochs

Answer 20

1. if income is low (and subsistence constraint is binding) the time devoted to raising children increases with technological progress
2. when tech progress is low there is no investment in education and only fertility increases with tech progress (malthusian era)
3. once tech progress reahces threshold g hat and starts accelerating, both fertility and education will increase as long as the subsistence constraint is still binding (post-malthusian era)

c_t^* = c squiggle and n_t^*(τ + e_t+1) = 1 - c squiggle/y_t

1 - c squiggle/y_t is positive because technological progress will increase income which will decrease the overall fraction. However this is going to increase the share of time people can allocation to raising children
Income effect > Substituion effect

Question 21

Proposition

Modern Epoch

Answer 21

When income is sufficiently high (subsistence constraint is non-binding), the time spent raising children remains a fixed fraction γ of parental time, but parents substitute quantity for quality as technological progress accelerates since the returns to education increase too

c^* =(1- γ)y_t and n_*(τ + e_t+1^*) = γ

since tech. progress only affects the quantity- quality trade- off n^*_t(τ + e_t+1)y_t = γy_t

income effect < subsititution effect when subsistence constraint is non-binding

Question 22

Summary

Modern Epoch

Answer 22

• negative relationship between pace of technological progress and fertility: sustained decline in fertility (demographic transition) takes place and human capital becomes main driver of technological progress and econ growth

Question 23

The evolution of the economy

Malthusian Epoch

Answer 23

Effect of g on n +
Effect of g on e 0

positive feedback loop between tech and population: standards of living is stagnant, tech progresss slowly accelerates over time driven by population growth
population size, tech progress, population size

Question 24

The evolution of the economy

Post- Malthusian Epoch

Answer 24

Effect of g on n +
Effect of g on e +

Tech progress reaches critical threshold: investment in HC becomes necessary to help individuals cope with rapid technological change
population size and quality , tech progress, population size and quality

Question 25

The evolution of the economy

Modern Epoch

Answer 25

Effect of g on n -
Effetc of g on e +

Tech progress becomes so rapid that human capital formation triggers a decline in fertiliity
high growth, tech progress, low fertility, mass education

Question 26

Resolution of Mystery of Growth

Answer 26

transition from stagnation to growth is an inevitable by product of the process of development
human capital formation triggered a demongraphic transition, enabled economies to convert a larger share of the fruits of factor accumulation and tech progress into growth in income per capita

Question 27

Contribution to Mystery of Inequality

Answer 27

Identifies the orgins of differential timing of the transition acorss the globe and the origins of vast inequality in income per capita