Technology and the Solow Model

Technology and the Solow Model

Econ 4960: Economic Growth

Extra credit assignment

! You have the option to make an in-class presentation

! 15 minutes, will answer questions ! Some papers cover topics that go (slightly)

beyond this course. ! Counts for a 7 point (%) bonus. ! Presentations if any will begin in 3-4 weeks ! Papers are allocated on an FCFS basis.

Econ 4960: Economic Growth

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Discussion questions from last lecture

! What does the basic Solow Model say about "Aid for Africa"? What modification do you need to make to alter this conclusion?

! Suppose we relax Inada condition 1: F(0,L)>0. How does that affect the steady states?

Econ 4960: Economic Growth

Overview: Introducing Technological Growth

! Previously, we saw that increasing savings rate does not lead to long-run growth. There is only transitional growth.

! In this lecture, we will add TFP growth which will generate long-run growth.

! But before we do that: ! Question: Is it possible that the transition is very very long,

so that the past 200 years countries have been going through one long transition without any technological progress? ! If the answer is yes, Solow model could be an interesting model of growth (and vice versa if no).

Econ 4960: Economic Growth

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Can Transitional Dynamics Be Important for Long Run?

! In principle, one can choose s, n, d, and especially to make the transition last as long as 400 years!

Econ 4960: Economic Growth

Solow Diagram for different Alfa values

Econ 4960: Economic Growth

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Solow Diagram for different Alfa values

Econ 4960: Economic Growth

Can Transitional Dynamics Be Important for Long Run?

! In principle, one can choose s, n, d, and especially to make the transition last as long as 400 years!

! Although this seems like an explanation, it fails miserably

in an important respect:

! If TFP did not grow, then all the growth is due to capital accumulation. For income per-capita to grow by 4 fold (being very conservative), capital-labor ratio must have grown by:

y2005 y1850

=

k 2005

k 1850

=4

k2005 = 41/ 101.6 k1850

taking =0.3

! What is wrong with this?

Econ 4960: Economic Growth

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Can Transitional Dynamics Be Important for Long Run?

? Capital is difficult to measure (for several reasons), so it is difficult to immediately reject that it could have gone up by 100 fold.

? But, there is another implication:

( ) R2005 ( ) ( ) R1850

=

k -1 2005

k -1 1850

+ +

1- d 1- d

101.6 = -(1- ) 1 25

? So, if the interest rate is 5 percent in 2005, it must have been 5 x 25 = 125% in 1850!

? Strongly contradicts Kaldor fact #1

? Therefore, we do need TFP growth to make sense of the

data

Econ 4960: Economic Growth

Introducing TFP Growth

! Recall that TFP is a catch-all term that includes not only

the technology level, but also the impact of regulations,

fiscal policy, commodity prices, etc. on production.

! The production function is: Y = F(K, AL) = K ( ) AL 1- g

! Assume that A grows at a constant rate: ! Output per-person is: y = k A1- .

A = A0egt

A=g A

! Capital accumulation implies: K = s Y - d

KK

! Differentiate y:

g

g

g

y = k + (1- ) A

yk

A

Econ 4960: Economic Growth

(2.9)

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