1. Macroeconomic analysis of
technological change
Merit course – 2006
Production functions
Innovation and employment

2. Production functions
Today’s substitution possibilities are
yesterday’s technological innovations
Figure 1. Isoquants showing all possible combinations of production factors that will
yield a fixed amount of output

3. Characteristics of the production
function
Returns to scale
Decreasing marginal returns
These are crucial assumptions in modern
economic theory (e.g., without decreasing
marginal returns a supply curve would not be
upward sloping)
Traditional economics does not provide a
clear theory of these assumptions would hold;
can technology provide the answer?

4. Engineering production functions
Hollis Chenery, Vernon Smith in 1950s and
1960s
An example: heat transfer
H1 H0 H L .
Tout Tin
V St
HL ,
To raise the heat output level,
t
K
we may use insulation of the
kS
pipe, or produce more heat as
Tout Tin
H1 H0 .
input; these two alternatives are
V
K
substitutable production factors
kS 2
280
H1 H0 .
0.01381 0.000595V

5. The isoquants
Isoquants for the heat transmission process
70
output=10000 BTU/hr
60
insulation material (cubic feet)
50
output=15000 BTU/hr
40
30
output=5000 BTU/hr
20
10
0
0 5000 10000 15000 20000 25000 30000 35000 40000
Heat input (BTU/hr)

6. Functional forms of production
functions
α β
=
Cobb Douglas (widely used):
Constant Elasticity of Substitution (CES):
−ρ −ρ − ρ
= +
Elasticity of substitution:
σ= =
σ = 1 for Cobb-Douglas, 1/(1+ρ) for CES

7. Substitutability and localized
technological change
Localized technological
change (Atkinson & Stiglitz)
Figure 3. Isoquants shifting under the influence of
localized technological change

8. A bias of technological change
Bias of technological change (labour-saving
or capital-saving)
Figure 4. Technological change shifts the isoquant down: neutral technological progress
(left), capital saving technological progress (middle) and labour saving technological
progress (right)

9. Biased technological change – Hicks’
mathematics
∂ ∂ ∂ ∂
= −
For Cobb-Douglas a change in A is neutral
(B=0)
For CES, a change in AK or AL is non-neutral
(unless both change in the same proportion)
– The CES is a more flexible form than the Cobb-
Douglas

10. Endogenous bias (Kennedy’s model)
Figure 5. Kennedy’s model of an endogenous bias of technology

11. Growth accounting
Tinbergen/Abramovitz/Solow:
dQ dA dK dL
f A fK A fL .
dt dt dt dt
A fK K A fL L
ˆˆ ˆ ˆ
QA K L.
Q Q
ˆˆ ˆ ˆ
AQ L K.
L K
Figure 6. Substitution and technological change in the
production function
A measure of technological change or a
measure of our ignorance?

12. Growth accounting results (Solow)

13. TFP growth for the Netherlands, 1921-
2002
150
140
130
120
110
100
90
80
1920 1940 1960 1980 2000

14. Endogenous technological change –
R&D
Non-military R&D as Total R&D as a % of R&D researchers as a % R&D financed by
a % of GDP GDP % of total employment businesses
3.5 3.5 11 75
10
3.0 3.0 70
9
2.5 2.5 65
8
7
2.0
2.0 60
6
1.5
1.5 55
5
4
1.0
1.0 50
EU
EU
OECD
US
EU
OECD
US
OECD
EU
Japan
US
OECD
Japan
US
Japan
Japan
Q AR K 1 L ,

15. BERD and productivity
Country α ρ
France 0.860 (0.000) -0.031 (0.273)
United Kingdom 0.421 (0.023) 0.395 (0.067)
Japan 0.478 (0.000) 0.155 (0.000)
United States 0.521 (0.000) 0.237 (0.000)
Table 1. Estimations results for the equation including business R&D as a production factor,
1959 - 1999.
2.50
2.00
1.50
1.00
0.50
0.00
1950 1960 1970 1980 1990 2000 2010
France United Kingdom Japan United States

16. Issues – Ned Ludd and the Army of
Redressers
Ricardo: “The opinion,
entertained by the
labouring class, that
the employment of
machinery is frequently
detrimental to their
interests, is not
founded on prejudice
and error, but is
conformable to the
correct principles of
political economy”

17. The demand for labour - Two types of
innovation
Process innovation: technology replaces
labour? Compensation mechanisms:
– Lower prices, expanded demand (general
equilibrium)
– Demand for machinery (investment)
Product innovation: expanding demand
– New products substitute old ones?

18. Labour markets and unemployment
Keynesians and neoclassicals: flexible wages
or sticky wages?
We focus mainly on demand for labour (fall
leads to either unemployment or wage
pressure)

19. Models - Katsoulacos
Process innovation and the demand for
labour
Product innovation (supply-side of the labour
market)
Structural issues (skills bias)

20. Process innovation and the demand
for labour
Restrictive assumptions:
– Homothetic demand
– One production factor: homogenous labour
– Two sectors/goods
Setting: investigate the impact of a change in
the labour coefficient (productivity) in one
industry

21. Goods markets
Profit maximization in goods market
Qi pi
1
pi (1 ) wai, where .
ii
pi Qi
ii
Totally differentiation this w.r.t. time:
( 1) a1 (
ˆ 1 e22) e12 ( 1) a2
ˆ
11 22 22
p1
ˆ ,
( 11 1 e11)( 22 1 e22) e12 e21
( 1) a2 ( 11 1 e11) e21 ( 11 1) a1
ˆ ˆ
22
p2
ˆ ,
( 1 e22)( 1 e11) e21 e12
22 11

22. Consumers – Utility function
Ces functional form:
1 1
1
U C1 C2 ,
Leads to demand functions:
Y
d 1 1
Qi , where A p1 p2 ,
pi A
With price elasticities:
pi Qi 1
1) s i, 1) sj (i j), where si
( (
ii ij
Y 1
1 (pi /pj)
Because of homothetic demand:
1
11 12 22 21
12 21 21 12
e 11 e12 , e22 e 21 .
11 22

23. Model closure
Differentiate demand function:
ˆ ˆ ˆd ˆ
Li aj Q i ai p
ˆ p.
ˆ
ii i ij j
Which leads to:
2
( )( ( ))
ˆˆ 22
22 11 11 22 12 22 11
L a1 .
( )( )
11 22 22 11 21 11 21 22
Hence everything depends on relative
elasticities η11 and η22

24. Model conclusions
Process innovation leads to an increase in
overall demand for labour if the sector where
the innovation takes place has a high price
elasticity
But in the model, price elasticity is an
endogenous variable, it depends on the share
of a sector in GDP
With persistently higher process innovation in
a sector, the share of this sector in GDP will
grow, and hence it’s price elasticity will
decline, hence the impact of process
innovation eventually becomes negative

25. Product innovation and the demand for
labour
A similar setup, but
– Labour productivity fixed and constant between
sectors
– Number of goods/sectors is n, and expands as a
result of product innovation
– Labour supply is modeled explicitly

26. Model – consumers and workers
Ces utility function
1 1 1
1
U C1 C2 .. Cn .
V j = U - ω j, where ω j is worker j’s disutility from work
when Vj < 0 (U < ω j), worker j will make the rational decision not to
take a job
ω j is a random variable distributed uniformly between 0 and ¯ , with
total density equal to N (the number of workers)

27. Model solution
Demand functions become:
Y
d 1 1 1
Qi , where A p1 p2 .. pn .
pi A
( 1) ( 1)
, ,
d c
n n
Profit maximization condition becomes:
1
p(1 ) w.
d
This leads to:
Each workers that has a job receives w income, which is spent on the n
w ( 1) (n 1)
. goods. Thus, the budget constraint is w = npC*, where C* is the quantity
p (n 1) 1
consumed of each good
Substituting in the utility function leads to:
1
1
n ( 1) (n 1)
V ,
(n 1) 1

28. Labour supply
V*determines labour supply:
1
1
Nn ( 1) (n 1)
L .
¯ (n 1) 1
2
1
(1 1/n) n 1 (
L Nn 1)
.
n ¯ 1)2
(n
This derivative is always positive, but it is
declining in θ

29. Conclusions (in words!)
Product innovation (increasing number of
products) always leads to a higher labour
supply
The extent two which this happens declines
with the elasticity of substitution between the
products
In the limit, when products become complete
substitutes, there is no effect on labour supply
(product innovations completely substitute old
products)

30. Structural unemployment
Industries (Schumpeter’s creative
destruction)
Skills (skills-bias of technological change and
the skills-premium)

31. A model of the skills-bias (structural
unemployment)
A ces production function with skilled and
unskilled labour (homogenous output):
1 1
1
QT s (As L s ) u (Au L u) .
Profit maximization:
1
1
Aj L j wi
1
Q 1 j
Ai T 1 , i, j s,u (i j)
i
Li Si Li p
i
Labour demand functions:
1
1 1
Q Li (Ai T)
T Ai Aj L j i
si .
j i
Li .
Li Q 1
(wi/p)
1
1 1 1
(wi/p) Ai T
i

32. Model solution
From this one may derive:
ˆ ˆ ˆˆ
Lu /s s T ( /s s 1) As Ls ,
ˆ ˆ ˆˆ
L /s u T ( /su 1) Au Lu,
s
ˆ ˆˆ ˆˆ
Lu > 0 iff /s s (T Au) > Au As ,
ˆ ˆˆ ˆˆ
Ls > 0 iff /su (T A s) > As Au.
ˆˆ ˆ
Suppose that all three rates of innovation (T, As , Au ) are positive, but
that innovation primarily replaces unskilled technical change, i.e.,
ˆˆ
Au > A s .
– Then, demand for skilled labour will always
increase
– But demand for unskilled labour is ambiguous,
only when elasticity of substitution is high it may
increase

33. Conclusions
With a skills-bias of technological change,
unskilled labour is at a disadvantage
(unemployment or skills-premium)
But this depends on how easy unskilled
labour may substitute for skilled labour