1. ITFD Growth and Development
LECTURE SLIDES SET 6
Professor Antonio Ciccone
I did almost the first 70 of these slides in 2 lectures (one session).

2. Ideas and Economic Growth

3. Producing output versus ideas
Ideas: non-rival, accumulable input
Ideas: may be excludable (patents, secrecy) or not
Ideas: producing them lowers current, but increases future output

4. Producing output versus ideas
Question 1: what is the growth process for a given allocation of inputs between producing output and producing ideas?
 Characterize the join evolution of ideas and output in the “spirit” of Solow

5. Producing output versus ideas
Question 2: how much of inputs is allocated to producing ideas in decentralized equilibrium?
Difficulties:
In these models there are at least 3 inputs: capital, labor, and ideas
Holding ideas constant, our “reproduction argument” implies that there are at least constant returns to capital (K) and labor (L)
HENCE, there are increasing returns to K,L, and ideas!
 It took quite a while to develop a set of models (“toolbox”) where the decentralized dynamic general equilibrium could be characterized

6. 1. A FRAMEWORK FOR ANALYZING GROWTH WITH RESEARCH AND DEVELOPMENT
Quantity of output produced
fraction of total capital stock used in production
fraction of total labor force used in production
taken to be exogenous; in the “spirit” of Solow

7. = level of technology
= stock of ideas
ideas: non-rival inputs
= new ideas, which are created by using capital, labor, and old ideas in the RESEARCH AND DEVELOPMENT (R&D) process

8. Production of new ideas Research and Development (R&D) technology
fraction of total capital stock used in R&D
fraction of total labor force used in R&D
taken to be exogenous; this is in the “spirit” of Solow

9. Returns to scale to K and L in production of IDEAS could be increasing or decreasing:
DECREASING: replicating inputs could lead to same discoveries being made twice
INCREASING: doubling inputs could lead to more than twice the discoveries because of interactions among researchers (“the whole is more than sum of its parts”)

10. Also, what is the link between stock of ideas and new ideas?
presumably : OLD ideas are useful for developing new ideas
: doubling stock, doubles discoveries holding inputs L and K constant
: effect of stock of ideas on creation less than proportional
: effect of stock of ideas on creation more than proportional

11. q=1: ideas keep growing at same rate even if resources allocated to R&D constant
q>1: growth of ideas accelerates when resources allocated to R&D constant
q<1: to keep growth of ideas constant, more and more resources must be allocated to R&D

12. 2. GROWTH WITH RESEARCH AND DEVELOPMENT: THE CASE WITHOUT CAPITAL
Quantity of output produced
Production of new ideas
Population growth (exogenous):

13. Growth of ideas ( )

14. CASE 1:
Balanced (constant) growth path

15. Is the BGP stable?
Graph on the vertical axis against on the horizontal axis
Check that is increasing when below and decreasing when above

16. STABILITY OF BGP

17. Note that implies that a faster population growth n translates into faster growth of ideas in the balanced growth path.
Is there empirical support for the positive relationship between n and the long run growth rate?
 Hard to test as we need long time series for that; but Michael Kremer 1993, QJE used population growth data going back to 1 Million B.C.

18. Why does an increase in not raise the long run growth rate?
Reason analogous to why increase in savings rate s in the Solow model does not increase long run growth: “Decreasing returns”
Note that yielded
Increase in al increase the short-run growth rate of ideas
But when q<1 we get that maintaining the same growth rate of ideas becomes harder and harder as the stock of idea increases (“fishing out the pond effect”)
In the long-run we get a level effect only
 The fraction of resources allocated to R&D is IRRELEVANT for long-run growth rate !!

19. IMPORTANT TO NOTE:
Balanced growth path growth rate:
there can only be long run growth of ideas and output if:
n>0
if n=0, there is NO long run growth

20. R&D and endognous growth
Hence, there can be long run growth even without exogenous technological progress
BUT the growth rate is linked to population growth, which we don’t usually think of as a “policy parameter”

21. CASE 2:
Hence implies ever accelerating growth

22. In this case, a small increase in ends up having a very large effect on the stock of ideas in the long run
An increase in implies
short term increase in growth of ideas (as before)
these additional ideas further increase the growth of ideas when
 for any future time t, the growth rate will be higher after the increase in

23. CASE 3:
NOW, there is long run growth even if n=0!!!

24. 3. GROWTH WITH RESEARCH AND DEVELOPMENT: THE CASE WITH CAPITAL
Quantity of output produced
Production of new ideas

25. +
standard assumptions of Solow model:
constant savings rate s
constant population growth rate n
no depreciation of capital

26. The idea and capital growth equations

29. CASE 1: (i.e or )
-ISOCLINE ( )
Above this line: falls
Below this line: increases

30. -ISOCLINE ( )
Above this line: falls
Below this line: increases

31. ISOCLINES in GROWTH RATES space

32. EVOLUTION OF GROWTH RATES

33. DYNAMICS

34. DYNAMICS plus INITIAL CONDITION
STARTING POINT

35. Starting point of dynamical system is GIVEN by INITIAL
capital, technology, and labor force

36. IMPORTANT TO NOTE:
there can only be long run growth of ideas, capital, and output if:
n>0
if n=0, there is NO long run growth

37. CASE 2:
we are interested in whether IN THIS CASE there will be long run growth even if n=0
hence ALSO assume n=0

38. -ISOCLINE

39. -ISOCLINE
HENCE:
The two isoclines lie on top of each other
NOW, there is long run growth even if n=0!!!

40. beta+theta=1 CASE WITHOUT POPULATION GROWTH

41. Michael Kremer's model

42. Michael Kremer's model
"Population Growth and Technological Change One Million B.C. to 1990", Q.J.E. 1993
Michael Kremer's intuition was that in a Malthusian world, i.e. a world in which population is just big enough to survive, there is a link between the state and technology and the amount of population: If everyone consumes just a "subsistence" amount, societies with more advanced technology (say, better agriculture) will be able to support larger populations
Hence, we could infer from the level of

43. The framework Assume the following production function: where:
indicates the level of technological progress
is population
is land
At least for a pre-industrial society, it may make sense to have only labour and land as production inputs. Note that the production function has constant returns to scale: the replication argument is valid! (ie, double the amounts of input, and you double output)

44. Malthusian case
Now express the production function in per-capita terms:
and assume that population increases when is above some subsistence level
This will reduce output per capita, so that it is reasonable to assume - if population growth reacts fast enough - that population will constantly adjust such that always holds.

45. Malthusian case
We can solve for the population level that corresponds to
What does it mean?
In the absence of changes in , population will be constant
Ceteris paribus, population will be proportional to land area
If separate regions have different levels of technology , population or population density will be increasing in

46. Technological progress
Now: enter technological progress. Assume that What does this imply for population growth?
Take logs and derivatives of
and obtain
population will grow at a constant rate. True?

50. More than exponential growth
So population growth appears to be increasing in population. This implies faster than exponential growth, which is what you would achieve with
Why?
Key insight: Each person has a constant probability of inventing a new technology. But because "ideas" (insights, designs. . . ) are nonrival, the whole society should profit from it.

51. Ideas as public goods
"As for the Arts of Delight and Ornament, they are best promoted by the greatest number of emulators. And it is more likely that one ingenious curious man may rather be found among 4 million than among 400 persons."
William Petty
"If I could redo the history of the world, halving population size each year from the beginning of time on some random basis, I would not do it for fear of losing Mozart in the process."
Edmund Phelps

52. Modelling growth and ideas
So, because every individual has the same probability of inventing something new, should be proportional to population size:
Insert this into:
Result:
population growth is itself proportional to population.
Aside: Results don't change substantially if we assume ,
i.e.

53. A natural experiment Could we somehow test the model?
Kremer suggests to consider a "natural experiment": the end of the last ice age around 10'000 B.C., when previously connected land masses (Eurasia+Africa, the Americas, Australia, Tasmania) were separated and technological diffusion wasn't possible any more.
Assumptions:
These 4 regions had shared the same basic technology up to that point (same ).
Hence, their populations must have been proportional to the land areas

54. 4 (or 5) separated regions

55. A natural experiment Prediction:
11500 years of separation (until 1500) should have lead technology levels to diverge
Growth rates of technology will be proportional to initial
population:
Higher growth rates of translate into larger populations
or, given constant area of land masses, into higher densities

56. The natural experiment: results