Stabilization of Industrial Cycles by
Profit Sharing Policies
Localized near Stationary States
©Alexander V. RYZHENKOV
Ec. Faculty of Novosibirsk State
University, IEIE SB RAS,
17 Acad. Lavrentiev Avenue
Novosibirsk 630090 Russia
Abstract.
¢ This paper illustrates how dangerous
linear thinking and linear control could be if
overstretched.
¢ Effective stabilization of industrial cycles
by standard profit sharing policies is
feasible mostly near stationary states.
¢ The paper calls for organic profit sharing.
Ancestors
The R.M. Goodwin (1972) model M-1
“Neoclassical hijacking” of M-1 in P-1 in F. Ploeg (1985)
L. Aguiar-Conraria (2008) check of P-1 structural
Stability in P-2
The main variables are relative wage and employment
ratio, a ratio of investment to profit is constant. The
Spurious efficiency wage hypothesis supports
equations for a growth rate of output per worker.
Workers’ competition for jobs is stabilizing and their
fight for increased wages Is destabilizing. In each
model, a stationary state is LAS in a system of two
ODEs. Deceptively, there is no possibility for
endogenous industrial cycle.
Table 1. Main variables in Z-1 as generalization of P-1 and P-2
Variable Expression
Net product g
Fixed production assets k
Capital-output ratio s=kiq
Employment |
Employment in efficiency units L
Output per worker a=qll
Labour force n= nen ,B>0
Wage W
Total wage wl
Relative wage (unit value of labour power) | — u = w/a=wllq
P-1
Employment
P-2
Relative wage U< x
Gy
> Employment
Background
Z-1 reflects destabilizing cooperation and
stabilizing competition of investors. In a system of
three ODEs, rate of capital accumulation becomes
the new phase variable. Its targeted long-term
decrease raises profit rate together with reducing
relative wage and _capital-output ratio. Oscillations
imitating industrial cycles are endogenous. Crisis is
a manifestation of relative and absolute over
accumulation of capital.
Z-1 treats industrial cycles as capital accumulation
cycles. A limit cycle is born through super-critical
Andronov — Hopf bifurcation. Dual nature of
capital as the driver and barrier of capitalist
production is reflected.
Accumulation rate z and
profit rate (1-u)/s in the USA, 1951-2017
0.29 0.19
0.21 7 mi
0.13 4
0.05 re
1951 1967 1983 1999 2015 1951 1967 1983 1999 2015
Extension of P-2 in Z-1
In agreement with K. Marx (1867: 634) net
change of the share of investment in surplus
product has an opposite sign to relative wage
gains (bo >0, 0 <z, <z)< 1 < Z);
logic of logistic growth and
proportional control applied additionally (p > 0):
u
z=-b
zZ(4—2Z 2—-Z
l—u ( ) + PEb )
FT
Relative wage u=«
= Employment
ravi
Accumulation
rate 2
¢ Proposition. In Z-1, stationary state E, is
locally asymptotically stable for b < by; E,
loses its stability and Andronov — Hopf
bifurcation does take place at Doi; > Do.
¢ According to simulations, a supercritical
bifurcation occurs. The period of oscillations is
about ~7 (years).
¢ Fory =0.75 and b =byii-g, =57.4 > by = 54.4,
there is a transition to a limit cycle vicinity (up
to years 2200-2230) from the initial phase
vector x for 1958.
2219 2221 2223 2225 2227 2219) = 2221) 2 2223-0 222522227
170 32 0.08
joy
5 A A
g -q -M 0.06 7 \ rete nat \
3 /
160 +4 | 30 0.04 —Surplus valuefhat :
2 --Profithat /
002 A\
150 - | 28
0
140 - | 5670-02
-0.04
130 -+—+—_+—+—_+—_+—_ +_ +++ 24-0.06
Employment 1 and net output g in Z-1:
1 (1), g (2) on the left,
their growth rates (1) and (2) on the right
0.84 0.06
170 0.06
0.03
0.03
0
0
0.8 -0.03
130 -0.03
2218 2H 218 2222 2226 223(
Index of intensity of workers’ competition for
jobs at stationary state y =f '(v,)v, as control
parameter and accumulation rate z in Z-ly
12 /
5! y,
re)
£ 08 7
0.6
085 0.87
Vb
1)
1)
1)
AAS
1958 1966 1974
Measures of intensity of workers’ competition for
jobs at stationary state Abs(J ,) and yw =f '(X)X;
accumulation rate z and Z,,, in Z-ly for X =0.95
A()
10)
0.890
0.920
X
0,950
15
1d
0
0
1958
1963 1968
Time (Y ear)
Z +
Z.goal
Z-1 extended by standard profit
Sharing (SPS) is Z-2
SPS (mechanistic) is ¢ GR of wage
reflected by additional becomes the sum
terms in an extended of bargained and
Phillips equation Stimulating terms
Stationary state in Z-2
New stationary employment ratio is
|,
,-Y—-T0
4h
Stationary relative wage u,, accumulation rate z,
and other stationary magnitudes remain the
Same as in Z-1.
(aah
Z-2., SZ >| Relative wage u
Net mt of 1 relative wage \
GR of on bo Profit rate
GR Rot output per
‘N1) ee a “ed
GR of
wy vege ~—_ GRof wage
stimulating term
w b hat
GR of wage
bargained term
w m hat
Stabilization of industrial cycles trom Z-1 (2) by
SPS in Z-2n (1) forsame v,: P (I.), z (r.), v (c.)
1.4 0.6
14 oe
0.3
0.3
0.9
0
0.9 0
1958 1963 1968 1973 1978 1958 1963 1968 1973 1978
0.91
0.91
0.88
0.88 + 2S) + +f
0.85 \ Sf
0.85
10523 3109063 190683 319073 19078
0.96
0.96
0.93
0.93
09
09
Decorative role of SPS in in Z-2
compared with Z-ly (2): v
eee
Lo
Lo
1958 1963 1968
V(l.), z
(r.) in
n (1)
avo runs
1958
1963
1968
Super adjustment speed in P-2 (I.) and Z-1 (r.):
relative wage u (1), capital-output ratio K/L (2),
accumulation rate z (3) as employment ratio v
jumps from v, =0.9 to X =0.95 during 1 quarter
0.83
2.1
1)
1958.25
0.83
21
Lo
1958
1958.25
Employment ratio v and capital intensity K/L
relative wage u and accumulation rate z (r.
in the USA, 2010-2016
0.96
0.93
wv —K/L $ 2012
0.9
2010
2011
2012
2015
2016
0.21 0.67
0.65
2010
2011.
2012
2013 |
2014
2015 |
2016 |
V),
0.1
0.08
0.06
Conclusion on stabilisation policies
Model of industrial cycles Z-1 contains strongly
non-linear Phillips Eq. that is crucial for dynamics.
Stabilization of industrial cycles can be locally
achieved through moderate increases in workers’
competition for jobs y =f '(V,)V,. This tool fails for
elevated employment target v = X in Z-lw.
SPS with opportunistic targeting of
employment ratio stabilizes industrial cycles in Z-20.
SPS fails when employment targeting strives
to ambitious goal v =X under improper structural
setting. Intensity of workers' competition for jobs is
then immensely strengthened in Z-2X as in Z-lvy.
Organic profit sharing is recommended solution.
References
Marx K. Capital. A Critique of Political Economy. Vol. I.
Arrow K., Chenery H., Minhas B., and Solow R. 1961.
Capital-labor substitution and economic efficiency //
Rev. of Ec. and Stat.43 (3): 225-250.
Goodwin R.1972. A growth cycle, in: C. Feinstein (ed.).
Ploeg F. Van der. 1985. Classical growth cycles /
Metroeconomica 37 (2): 221-230.
Forrester]. 2007. System dynamics — the next fifty
years / System Dynamics Rev. 23 (2/3): 359-370.
Aguiar-Conraria L. 2008. A note on the stability
properties of Goodwin's predator-prey model / Rev. of
Radical Political Economics 40 (4): 518-523.
Ryzhenkov A. 2015. Socially efficient stabilization
policies for growth cycles / Advances in Economics
and Business 3 (11): 502-527.
