Post Keynesian Economic Policy session at 12th International Conference

1. Towards a ‘Classical-Keynesian’ Analysis
of Effective Demand in the Long Period
Man-Seop Park, Korea University
The 12th Post Keynesian International Conference
UMKC
25 Sept 2014

2. • To provide a framework for the (long-period) analysis
of (Keynesian) effective demand which is compatible
with the Classical/Sraffian perspective
(Arising from criticisms of the Cambridge and
the Kaleckian approaches)
• (To show how the ‘given’ quantities of output in the
Sraffa system can be interpreted as those being
determined in accordance with Keynes’s principle
of effective demand)
1
The objective(s)

3. • Part I: main ideas in terms of the aggregate economy
• Part II: a formalisation for the aggregate economy
• Part III: a multi-sector model
2
The paper(s)

4. Part I
3

5. Effective demand in the long period:
the Classical-Keynesian perspective
• given
- the methods of production
- the ‘normal’ real wage rate (or the ‘normal’ rate of profits)
- the saving propensities of social classes
the ‘normal’ rate of accumulation is determined:
• the principle of effective demand: generating saving through
changes in the size of capital stock
 I  scrK
4
c g  s r
c g s r 

6. r  f (w)
w g
r
Effective demand in the long period
5
r
c g s r 
g *
* r * r
w
g
K
g *
I  gK
0 I
1 I
0 K
1 K

7. • The ‘long period position capital equipment’ /
A ‘fully-adjusted position’
• ‘The long period position exists in the present’
• Two parts of a long-period analysis
• Three states of the economy for the first part of
a long-period analysis
6
Key ideas/concepts
for a ‘Classical-Keynesian’ approach

8. The long-period position capital equipment
t K
*
1 t K 
Kt1
Kt
time
log K
log Y
*
t Y
t Y *
t I
It
7
warranted investment
autonomous investment
long period position
capital equipment

9. The long-period position capital equipment
The size (and composition) of the capital equipment ( ) that
would have been utilised at the normal level for a given level of
investment
• the autonomy of investment  not necessarily
' K
' K K 
• why ‘long period’ ?:
(1) ‘fully-adjusted’ to the level of output (= utilised at the normal
level) [the first part of the long-period analysis]
(2) regarded ‘normal’ with respect to the current state of effective
demand, thus guiding investment in the next period
(‘reference point’ /‘centre of gravity’) [the second part]
8

10. The long-period position capital equipment
t K
Kt1
*
Kt2
'
Kt
time
log K
log Y
*
1 t Y 
t Y
*
1t I 
1t I 
'
Kt1
1 t Y 
2 t K 
9
WG
‘realised’
LP

11. Two parts of the long-period analysis
First part:
analysis of the long-period position ‘existing in the present’
Second part:
analysis of the sequence of the long-period positions existing in
the present
10

12. The long-period analysis (first part):
three states of the economy
Kt
'
Kt
time
log K
log Y *
t Y
t Y
*
t I
It
The Warranted
Growth state
The state of
effective demand
The long-period
position
The ‘realised’ state
11

13. Effective demand in the long period
t K
Kt
time
log K
log Y
12
WG
rLP
eLP

14. 0K
0 K
WG
rLP
eLP
warranted
investment
0 T time
capacity
autonomous
investment
13

15. ‘erasing the traces of output loss’:
‘[t]he elasticity of the capitalist economy … in reacting to
incentives for a more rapid growth by bringing about additional
productive capacity, or, symmetrically, by … erasing the visible
traces of the losses in output due to a low such incentive’
(Garegnani, 1992, p. 53)
• the observed tendency, if any, to the ‘normal’ utilisation of the
existing productive equipment is a result of the adjustment of
supply to demand
14
Effective demand in the long period

16. Policy implications
(against neoclassical)
• No existence of spontaneous market mechanism which would
lead to the optimal use of available resources
• No welfare properties of the paths that the system
spontaneously realises
• No trade-off between consumption and investment
• No trade-off between public and private expenditure
• No unique set of prices compatible with (output) equilibrium
• No unique path of optimal growth  wide scope for policy
action
15

17. Scope for policy action
• Demand policies: both short-run and long effects
• Industrial policies: to remove growth constraints
• Economic growth is figured partly by the relative power of the
different groups of the society: the conscious social choice of
policies
16

18. Part II
17

19. A fully-adjusted position
The relation between the quantities of the means of production
and the quantities of output in the respective industries is such
that
(1) output is produced at the normal utilisation of the means of
production
(2) each type of output is produced of the quantity that is
exhausted for gross investment and consumption in the
economy as a whole (supply = ‘(effectual) demand’)
• The Warranted Growth state (WG)
• The long-period position (LP)
18

20. 19
The Warranted Growth state
WG
r r
r  f (w) / c s r  S K  g
* r
w /, S K g * g

* 
(1)
  (u) K  J / (  g)
* * (J ,  , K)
K
K
* u g g max 1 u

21. The Warranted Growth state
20
• normal utilisation
*   (u), u  1  
Y*  K / v
* * * Y  (  r )K  wlY
* * * Y  (  g )K  C
- depreciation:
- output:
• price equation
• quantity equation
• saving
* * * * * Y C  S  (sr   )K

22. The state of effective demand
– autonomous investment decision in individual industries
21
*
i,t i,t i,t J  z J
- (the volume of gross investment)
- the capacity-generating effect:
J
*
i,t - the effective-demand-constituting effect:
- the autonomy of investment: not necessarily
i,t z
, 1 i t z 

23. (The recurrence relation)
(4) zt+1 =1+ 1- 1 zt ( ) é
ë
ù
ûz
Some examples:
(1) zt1  zt 1
(2) zt1  zt  z (1)
(3) zt1 zt K K  1        
(5) zt+1 =1+a K K ( ) -1 é
ë
ù
û
(Supermultiplier)
22
(6) zt+1 = z +a K K ( ) -1 éë
ùû
(WG)
(Kaleckian)
(Harrod)
{ -1}
+b ri r(å i / n) éë
ùû
(7) too complex to formalise (completely autonomous)

24. 23
The effective long-period position (eLP)
WG
r  f (w)
/ c s r  S K  g
r r
* r
w /, S K g * g

* 
(1)
  (u) K  J / (  g)
* * (J ,  , K)
K
K
K * eLP (JJ,,d*, K)
* u g g max 1 u

25. The effective long-period position (eLP)
24
• normal utilisation
- depreciation:
- output:
• price equation
  (u), u  1  *
Y = K / v
Y = (d* + r)K + wlY
• quantity equation
Y = (d* + g)K + wlY + (1- s)rK
• autonomous investment
(d* + g)K º J = z(d* + g*)K

26. 25
The notional long-period position (nLP)
WG
r  f (w)
/ c s r  S K  g
r r
* r
w /, S K g * g

* 
(1)
  (u) K  J / (  g)
* * (J ,  , K)
K
K
K (J , d eLP *, K)
* max u g g 1 u
u
d
= (J , d, K)
(u) r
nLP
g
g

27. The notional long-period position (nLP)
26
Y = u(K / v)
d = d(u)
(d + g)K = J = zJ*
Y = (d + r)K + wlY
Y = (d + g)K + wlY + (1- s)rK
• utilisation
• depreciation
• autonomous investment
• price equation
* quantity equation not holding

28. 27
WG
r  f (w)
/ c s r  S K  g
r r
*r
w /, S K g * g

* 
(1)
  (u) K  J / (  g)
* * (J ,  , K)
K
K
eLP K
(J , d*, K)
* u g g max 1 u
u
d
= (J , d, K)
(u) r
nLP
The realised long-period position (rLP)
u

g
g
()u
r
g 
g
(J , , K) rLP

29. The realised long-period position (rLP)
28
Y '  u '(K / v)
'  (u ')
Y '  (' r ')K  wlY '
Y '  (' g ')K  wlY ' (1 s)r 'K
* (' g ')K  J  zJ
* * * (1) (u ')  u '  r '  zr , g '  zg
* * * * * * * (2) (u ')    r '  z(  r )   , g '  z(  g )  

30. Short period
• in the short period, the rate of real wages is not necessarily at
the ‘normal’ level
• the short period rate of real wages is determined in reference to
- the given money wage rate
(determined by short-period wage bargaining)
- the short-period price level
(determined by some short-period price setting procedure
such as mark-up pricing)
29

31. Y (P; J ,W)  Y *
Y   Y (w, J ) Y
 
  
 
W
P
 
  w

 
Short period
30
LP for
SP for
SP for
W
P
w
(w, J ,W)
Y (P; J ,W)  Y *

32. (SP-1) 푌′′ = ( 퐾/푣)푢′′
(SP-2) 푌′′ = (훿′′ + 푔′′) 퐾 + 퐶′′
(SP-3) 푌′′ = (훿′′ + 푟′′) 퐾 + 푤′′푙푌′′
(SP-4) 푌′′ − 퐶′′ ≡ 푆퐺
′′ = 푠푐 푟′′ 퐾 + 훿′′ 퐾
(SP-5) (훿′′ + 푔′′) 퐾 = 퐽 = 푧(훿∗ + 푔∗) 퐾
(SP-6) 훿′′ = 훿(푢′′)
(SP-7) 푤′′ = 푊 /푃
31
Short period

33. 32
푃 푏
푃 퐴
퐴
푎
푏
푃 푎
Short period
풀

34. • the ‘employment curve’:
d L lY
- from the rLP, one obtains for each w
• The ‘wage bargaining curve’
33
The normal real wage rate
/ ( ) d L L  e  e w
0
( ); (0
( )
) 0, 0 1
w w e
w if e e
w f e f f if e e
  
 
     



35. 34
The normal real wage rate
푤
1
퐴
푤퐵
푒퐴
푤푚푎푥
푤 = 푤(푒)
푒퐵
퐵
푒 = 푒(푤)
the existence

36. 35
The normal real wage rate
′′
푤
1
푒 = 휀(푤′′)
퐴
푒퐴
the stability
푤푚푎푥
푤 = 푤(푒)
푒 = 푒(푤)
푤푚푎푥

37. Part III
36

38. Multi-sector model
• The prices of production
• The financial market for allocating aggregate saving
37

39. a11 a1n
an1 ann
æ
ç
ç
ç
è
ö
÷
÷
÷
ø
A fully-adjusted position
* * * * * * * * * *
i i i i x r w x x      
[ ]([ ] ) [ ] [ ]
I A p l B p
*
1


dp
 * * * * * * [ ] i ix   g A p  S
* * * * * * * [ ] i i x B  x   g A  h d
38

40. The Warranted Growth state
* * * * * *
* [ ]([ ] ) [ ] [ ]
i i i i  x   r  w x  x

 
I A l Bp
*
1
p
dp
* * * * * ( ) i i i i i J    g x a p
* * * * * [ ]i ix B  x   g A  h d
* * * * * [ ] i ix   x Ap  S
39
*
i i i k  x a

41. The effective long-period position (eLP)
p Bp
p
40
* [ ]( ) [ ] [ ]
i i i i  x   r  w x  x

 
xB  xA  x[gi ]A  hd
I A l
1
d
(1 ) i i i i i  g x a p  z J
x[gi ]Ap = S

42. The notional long-period position (nLP)
Ap l Bp
dp
41
i i i i i x r x w x      
[ ][ ] [ ] [ ]
 1


 
( ) i i i i i i   g x a p  z J
* ( ) i i i i    x x

43. The realised long-period position (rLP)
 xi i  ri   w xi  xi 

A p l B p
42
[ ][ ] [ ] [ ]
 1


dp
 ( ) i i i i i i   g xap  z J
* ( ) i i i i    x x
[ ]i x g Ap  S
[ ]i xB  xA  x g A  hd