ECONOMIC RESEARCH CENTERDISCUSSION PAPER
E-Series

No.E16-5

Who Should Bear the Pain of Price Competition?
A Kaleckian Approachby
Shinya Fujita
Ryo Kato

July 2016

ECONOMIC RESEARCH CENTERGRADUATE SCHOOL OF ECONOMICSNAGOYA UNIVERSITY

Who should bear the pain of price competition?
A Kaleckian approach

Shinya Fujita†

Abstract
Ongoing globalization and the rise of neoliberalism have intensified price competition in both
domestic and international markets. If we consider a cost reduction owing to price competition,
the question inevitably becomes who suffers the pain of reducing costs. By constructing a
Kaleckian model with an intermediate goods sector and a final goods sector, we investigate
which economic agent, firms or workers in either sector, should take responsibility for the cost
reduction to maintain aggregate demand and growth. Our results show that firms in the final
goods sector should be targeted, as cutting the mark-up rate in that sector is likely to promote
capacity utilization and capital accumulation. Moreover, we show that forcing the burden of
the cost reduction onto workers in the intermediate goods sector is undesirable because it
decreases demand as well as the growth rate.
Keywords: Mark-up pricing, Vertical transaction, Cost reduction, Wage standardization
JEL Classification: E11, O41, J5†

Graduate School of Economics, Nagoya University. Furo-cho, Chikusa-ku, Nagoya-shi, 4648601, Japan. E-mail: fujita@soec.nagoya-u.ac.jp
1

1 Introduction
Behind the progress of economic globalization, emerging countries tend to dominate the goods
market, exacerbating the severity of international price competition. At the same time,neoliberalism, which relies heavily on the market mechanism, gains power, thus increasing thecompetitiveness of the market structures in advanced countries. Such an intensification ofprice competition in both domestic and international markets increasingly forces firms to
reduce their production costs. 1
When firms cannot avoid the pain of price competition, the problem inevitably becomes thequestion of who takes responsibility for the resulting cost reduction. In the absence oftechnological progress, such a cost reduction can only be accomplished at the expense ofsomebody’s income. For instance, let us consider the situation where firms in the final goods
sector aim to reduce their prices. Most final goods production passes through verticaltransactions in which intermediate goods-producing firms supply intermediate input goods tofinal goods-producing firms. It follows that to reduce the final goods price, any one of thefirms in the final goods sector, workers in the final goods sector, firms in the intermediate
goods sector, or workers in the intermediate goods sector is required to reduce its income.
Thus, the cost reduction owing to price competition is inseparable not only from the functional
income distribution between firms and workers but also from vertical relation between firms.
Studies that focus on the effects of price competition on the functional income distribution
are mainly based on the open economy version of the Kaleckian model. 2 By adding net
exports into the demand components, the pioneering work of Blecker (1989) shows that a fallin the wage share can strengthen international price competitiveness and positively affectaggregate demand. Missaglia (2007) assumes that the price equation of firms depends on thereal exchange rate (i.e., when the terms of trade deteriorate, firms control their prices) andinvestigates whether the paradox of cost is valid in the open economy. Blecker (2011) and
Cassetti (2012) indicate that it is effective to cut not only the nominal wage rate but also themark-up rate to survive in international price competition. This finding implies that firms aswell as workers have to share the pain of price competition. Sasaki et al. (2013b) show that,taking into account international trade, an increase in the negotiation power of firms does notraise aggregate demand even if the domestic economy exhibits a profit-led demand regime.
All these open economy models, however, are one-sector ones and thus abstract from the1

Such views on institutional change in the market structure are stressed mainly in the French
régulation school. See, for example, Amable (2004), Boyer (2000, 2005), and Nishi (2010).
2
Regarding the fundamental structure of the Kaleckian model, see Rowthorn (1981), Taylor (2004),
and Lavoie (2014). As for empirical studies that consider the functional income distribution andmacroeconomic performance in the open economy, see Bowles and Boyer (1995), Stockhammer andOnaran (2004), and Storm and Naastepad (2012).

2

following point: final goods-producing firms not only share the pain of the cost reduction
between themselves and their workers, but also shift the burden to firms that produce
intermediate goods. In the real economy, final goods-producing firms are likely to impose acost reduction on intermediate goods-producing firms.
Taking into account this point, we construct a two-sector Kaleckian model with anintermediate goods sector and a final goods sector. In our model, there are four ways in which
to reduce the final goods price: cutting the mark-up rate in either sector and cutting nominal
wage rate in either sector. Our model clarifies which economic agent should take responsibility
for the cost reduction in order to maintain aggregate demand and growth. In contrast to theabove studies, however, we do not consider the factors of an open economy because pricecompetition does not appear only in the international goods market. Consumers have areservation price that they are willing to pay and producers such as manufacturing firms set the
product price/cost target that is required for market success by applying the “target costing”
method.3 Accordingly, even domestic or Kaleckian oligopolistic firms give top priority to
reducing the goods price/cost below its target.
In line with Kaleckian tradition, some two-sector models investigate the impact of a change
in the sectoral mark-up rate on macroeconomic performance. 4 Dutt (1987) considers a modelwith an investment goods sector and a consumption goods sector and shows that a rise in themark-up rate in the latter sector reduces the rate of capital accumulation, whereas the effect ofa rise in the mark-up rate in the former sector on capital accumulation is ambiguous. Lavoie
and Ramírez-Gastón (1997), using a two-sector model with target-return pricing, show that
increases in the mark-up rates in two sectors negatively affect both sectors’ rates of capacity
accumulation and the macroeconomic rate of capital accumulation. However, these studies
abstract from the role of the intermediate goods sector for the sake of simplicity, which differsfrom the contribution of our model.
Our findings are summarized as follows. First, provided that certain realistic conditions are
satisfied, a relative fall in the mark-up rate in the final goods sector tends to increase theshort-run rate of capacity utilization, which implies that firms in the final goods sector shouldtake responsibility for reducing costs. Second, workers in the intermediate goods sector should
not bear the pain of price competition; compared with cutting the mark-up rate in either sector,
3

As for the cost targeting method, see, for example, Hiromoto (1988) and Fujitmoto (2012).
There are other interesting two-sector models. Dutt (1988, 1990) demonstrates that in a Kaleckian
monopoly economy the sectoral rate of profit never converges to the equal rate of profit, even in thelong run. Taylor (1989) supposes that one sector produces goods purchased from wages, while anotherproduces investment goods as well as goods purchased from profits, and considers how a demand
composition change affects capital accumulation. Franke (2000) introduces the optimal use of capitaland the financial sector in the price adjustment economy to conduct a stability analysis.

43

cutting the nominal wage rate in the intermediate goods sector is likely to reduce the rate ofcapacity utilization in the short run. Third, owing to the short-run effects, cutting the mark-up
rate in the final goods sector is likely to increase long-run capital accumulation on thebalanced growth path (BGP). Thus, to promote economic growth, firms in the final goods
sector should reduce costs.
The remainder of the paper is organized as follows. Section 2 presents the proposed
two-sector model. Section 3 assumes that capital stocks do not accumulate and investigates theshort-run effect of changes in the mark-up rate and in the parameter representing wage
standardization on capacity utilization. Section 4 assumes that capital stocks accumulate andinvestigates the long-run effect of the same parameter changes on capital accumulation andcapacity utilization. Section 5 concludes.
2 Model
2.1 Basic settings
We consider a closed economy with no government sector. The economy is composed of anintermediate goods sector (sector 1) and a final goods sector (sector 2). Sector 1 produces
intermediate goods by using fixed capital stocks and labor. Sector 2 produces final goods for
consumption and investment by using fixed capital stocks, intermediate input goods, and labor.
Each sector is assumed to have a Leontief-type fixed coefficient production function. Fixed
capital stocks and labor are sector-specific, which implies that there are sectoral differentials inboth the rate of profit and the rate of nominal wage. In addition, there are no labor supply
constraints.
Moreover, we assume that oligopolistic firms control each market and adopt mark-up
pricing in both sectors. Both sectors also have excess capacity, and the supply of output can be
immediately adapted to demand. Value added is distributed to workers as wages and to firms
as profits. Workers spend all their wage income on final goods, whereas firms save all theirprofit income. 5 Neither sector’s investment behavior necessarily coincides because each is anindependent economic agent. Finally, we ignore technological progress and the depreciation of
fixed capital stocks.
Let us consider the price system. We assume that the prices in each industry are marked up
on prime costs as follows: 6
5

We assume that firms’ propensity to save out of profits is unity because we do not consider theparadox of thrift. Even if firms were assumed to consume a constant proportion of profits, our resultschange little.
6
See Lavoie (1992), Lee (1998), and Coutts and Norman (2013) on post-Keynesian price theory. For
the sake of simplicity, we assume the most familiar pricing rule.

4p1 = (1 + µ1 ) w1b1 ,(1)p 2 = (1 + µ 2 )( p1 a12 + w2 b2 ) ,(2)where pi denotes the price of good i , µ i the mark-up rate in sector i , and wi thenominal wage rate in sector i . In addition, a12 is the coefficient of intermediate inputs in
sector 2 and bi is the labor input coefficient in sector i .8 µ i , a12 , and bi are assumed to
be positive constants. In the following, i = 1 represents the intermediate goods sector andi = 2 represents the final goods sector.
The mark-up rate represents the monopoly power in the market as well as the relative
bargaining power of the firm. The higher the monopoly power or stronger the bargaining
power of the firm, the higher the mark-up rate is (Kalecki, 1971; Sen and Dutt, 1995). Thus,
the level and transition of the mark-up rate vary by industry.
In equations (1) and (2), we assume w1 ≠ w2 . However, in the case where the labor union
becomes centralized, one sector’s nominal wage rate can be affected by that in another sector.
Taking into account this respect, we assume that there exists proportionality between both
sector’s nominal wage rates: 7

w1 = θw2 ,(3)

where θ represents the degree of wage standardization. It is appropriate to assume that thispositive parameter is smaller than unity, that is, 0 < θ < 1 . This is because the final goods
sector is the main customer of the intermediate goods sector and thus the latter is inclined todecrease the nominal wage rate because of the former’s request for a cost reduction. Thus, thenominal wage rate in sector 1 is smaller than that in sector 2. Moreover, the smaller θ
implies that the responsibility for the cost reduction is shifted to the workers in sector 1.
Next, we consider the quantity system. Demand for intermediate goods is equal tointermediate demand in sector 2:

p1D1 = p1a12 X 2 ,(4)where Di denotes real aggregate demand and X i real output.
Demand for final goods is composed of investment and consumption demand:

p 2 D2 = p 2 ( I 1 + I 2 ) + p 2 C ,(5)where I i denotes real investment and C real consumption. Here, we assume thatinvestment is independent of firms’ saving (Keynes, 1930; Kalecki, 1971).
We assume that workers spend all their wage income on final goods, whereas firms save all
their profit income, which implies that macroeconomic consumption is equal to workers’ wage
income:7

We hardly find a Kaleckian model that considers the sectoral wage differential. By contrast, Lavoie(2009) and Sasaki et al. (2013a) consider the wage differential between two types of workers in themacroeconomy. Our model refers to their formulations.

5

p 2 C = w1b1 X 1 + w2 b2 X 2 .

(6)

These price and quantity equations are summarized in Table 1.
(Table 1 here)
2.2 Price system
Equations (1), (2), and (3) provide the following relative price and real wage rate:p≡p1(1 + µ1 )b1θ=,
p 2 (1 + µ 2 )[b2 + (1 + µ1 )a12 b1θ ]

(7)

ω1 ≡

w1
θ
=
,
p 2 (1 + µ 2 )[b2 + (1 + µ1 )a12 b1θ ]

(8)

ω2 ≡

w2
1
=
,
p 2 (1 + µ 2 )[b2 + (1 + µ1 )a12 b1θ ](9)where p denotes the ratio of the intermediate goods price and final goods price (i.e., therelative price) and ω i the nominal wage rate in sector i divided by the final goods price (i.e.,
the real wage rate in sector i ).
We obtain the following proposition regarding the relative price and real wage rate.
Proposition 1. A rise in the mark-up rate in sector 1 increases the relative price and decreases
both sectors’ real wage rates. Moreover, a rise in the mark-up rate in sector 2 decreases therelative price and both sectors’ real wage rates. Furthermore, wage standardization increases
the relative price and real wage rate in sector 1 and decreases the real wage rate in sector 2.
Proof. See Appendix A, which is available on request.
Wage standardization, that is, a rise in θ , has contrary effects on the real wage rates in sector
1 and sector 2. A rise in the nominal wage rate in sector 1 with wage standardization increases
the final goods price by increasing the intermediate goods price. In sector 1, a rise in thenominal wage rate covers the rise in the final goods price and thus the real wage rate increases,
whereas in sector 2 a rise in the final goods price decreases the real wage rate.
We represent the profit share in each sector, m1 and m2 , as follows:

m1 =m2 = 1 −µ1 w1b1 X 1µ1 w1b1 X 1 + w1b1 X 1

ω 2 b2
1 − pa12

=

=

µ1
,
1 + µ1µ 2 b2 + µ 2 (1 + µ1 )a12 b1θ
.
(1 + µ 2 )b2 + µ 2 (1 + µ1 )a12 b1θ

(10)
(11)

Equation (10) shows that the profit share in sector 1 is positive and smaller than unity. In
6addition, since the numerator on the RHS is smaller than the denominator on the RHS ofequation (11), the profit share in sector 2 is also positive and smaller than unity.
We thus obtain the following proposition regarding the profit share.
Proposition 2. A rise in the mark-up rate in sector 1 increases both sectors’ profit shares.
Moreover, a rise in the mark-up rate in sector 2 increases the profit share in sector 2.
Furthermore, wage standardization increases the profit share in sector 2.
Proof. See Appendix B, which is available on request.
Because our model considers intermediate inputs, a change in the mark-up rate in sector 1
affects the profit shares in both sectors. In addition, since wage standardization decreases thereal wage rate in sector 2, it increases the profit share in sector 2.
2.3 Quantity system
Our model assumes that nominal investment normalized by the capital stocks in each sector isan increasing function of both the profit share and the rate of capacity utilization (Bhaduri andMarglin, 1990):

where g i

g1 ≡I1
= α 1 + β1 m1 + g 1u1 ,
K1

(12)

g2 ≡

I2
= α 2 + β 2 m2 + g 2 u 2 ,
K2

(13)

denotes the rate of capital accumulation, K i fixed capital stocks, andu i (≡ X i / K i ) the rate of capacity utilization.8 In addition, α i represents the firm’s animal
spirits, β i the coefficient of capital accumulation to the profit share, and g i the coefficientof capital accumulation to capacity utilization. α i , β i , and g i are assumed to be positive
constants. Contrary to previous two-sector models such as Dutt (1987, 1988), and Lavoie andRamírez-Gastón (1997), we emphasize that the demand regime is diverse and thus we do notconsider the negative impact of the rate of profit on capital accumulation, but rather consider
the effect of profitability on capital accumulation.
By dividing both sides of equation (4) by K 1 , we obtainD1 a12
=
u2 ,
K1
k
8

(14)

We assume that the ratio of the potential output to capital stocks is constant. Accordingly, the ratio of
output X to capital stocks K is a proxy variable of the capacity utilization rate.

7

where k (≡ K 1 / K 2 ) denotes the sectoral ratio of capital stocks.
Since excess demand (supply) leads to a rise (decline) in capacity utilization, the dynamics
of the rate of capacity utilization in sector 1 are

u1 = φ1

D1
a− u1 = φ1 12 u 2 − u1 ,
K1
k

(15)

where φi (> 0) denotes the adjustment speed of the intermediate goods market. Hereafter, thedot over the variable represents its time derivative.
Equation (6) is rewritten as 9C
= p (1 − m1 )ku1 + (1 − pa12 )(1 − m2 )u 2 ,
K2

(16)

where 1 − pa12 > 0 .10 By using equations (12), (13), and (16), we rewrite equation (5) asD2= k (α 1 + β1 m1 + g 1u1 ) + α 2 + β 2 m2 + g 2 u 2 + p (1 − m1 )ku1 + (1 − pa12 )(1 − m2 )u 2 . (17)K2
As in the intermediate goods market, we assume that quantity adjustment works in the final
goods market; thus, the dynamics of the rate of capacity utilization in sector 2 areu 2 = φ2

D2
− u2
K2

. (18)= φ2 {[g 1 + p (1 − m1 )]ku1 + [g 2 + (1 − pa12 )(1 − m2 ) − 1]u2 + k (α1 + β1m1 ) + α 2 + β 2 m2 }Finally, taking the logarithmic derivative with respect to the time of the sectoral ratio of
capital stocks yields
k = ( g1 − g 2 )k = (g 1u1 − g 2u2 + α1 + β1m1 − α 2 − β 2 m2 )k .

(19)

This leads to a dynamical system composed of equations (15), (18), and (19) with endogenous
variables u1 , u 2 , and k .
3 Short-run dynamics
3.1 Stability analysis
Quantity adjustment in the goods market is practiced more rapidly than capital accumulation.
Accordingly, this section investigates only the dynamics of the rate of capacity utilization
while leaving capital stocks unchanged. We consider the case where the rates of capacity
9

From equation (10) and (11), we obtain the following equations.
ω1b1 = p(1 − m1 ) ,ω2b2 = (1 − pa12 )(1 − m2 ) .

Substituting these equations into equation (6) yields equation (16).
By using equation (7), we obtain10

1 − pa12 =(1 + µ1 )b2 + µ 2 (1 + µ1 )a12 b1θ
> 0.
(1 + µ 2 )[b2 + (1 + µ1 )a12 b1θ ]8utilization and the sectoral ratio of capital stocks simultaneously change in Appendix C, whichis available on request.
We define as the short-run equilibrium the situation where u1 = u 2 = 0 holds with constantk , that is, demand meets supply in both markets. In the short-run equilibrium, we obtain therate of capacity utilization as follows:

u1 =
u2 =

[α1 + β1m1 + (α 2 + β 2 m2 ) / k ]a12 ,pa12 m1 + (1 − pa12 )m2 − a12g 1 − g 2

k (α 1 + β1 m1 ) + α 2 + β 2 m2,
pa12 m1 + (1 − pa12 )m2 − a12 g 1 − g 2

(20)
(21)

where p , m1 , and m2 are given by equations (7), (10), and (11).
By using equations (15) and (18), we obtain the trace and determinant of Jacobian matrix

J:
traceJ = −φ1 − φ2 [1 − g 2 − (1 − pa12 )(1 − m2 )] ,(22)

det J = φ1φ2 [ pa12 m1 + (1 − pa12 )m2 − a12g 1 − g 2 ] .

(23)Here, we assume that g i is sufficiently small, which leads to traceJ < 0 and detJ > 0 .
The negative trace and positive determinant of the Jacobian matrix mean that the short-run
equilibrium is locally stable. Moreover, we find from equations (20) and (21) that the positive
determinant of the matrix is equivalent to a positive rate of capacity utilization.
3.2 Comparative static analysis in the short run
This subsection considers the effect of changes in the mark-up rate and wage standardizationon the short-run equilibrium rate of capacity utilization. By substituting u1 = 0 into equation(15), we obtain u1 = (a12 u 2 / k ) . This equation indicates that the rate of capacity utilization in
sector 1 is proportionate to that in sector 2 in the short run. Since the changes in the mark-up
rate and wage standardization shift both sectors’ rates of capacity utilization in the same
direction, this section considers only the rate of capacity utilization in sector 2.
Before starting the analysis, we introduce the following definition regarding the demand
regime.
Definition 1. When a rise in the mark-up rate in one sector increases (decreases) the short-run
equilibrium rates of capacity utilization in both sectors, the economy is called a profit-led(wage-led) demand regime.
The effect of a rise in the mark-up rate in sector 1 on the short-run equilibrium rate ofcapacity utilization in sector 2 is represented by
9

∂u 2
σ1
=
,
∂µ1 [ pa12 m1 + (1 − pa12 )m2 − a12g 1 − g 2 ]2

(24)

where

σ1 =

∂m1
{kβ1 [(1 − pa12 )m2 − a12 g 1 − g 2 ] − pa12 (kα 1 + α 2 + β 2 m2 )}
∂µ1
+

+

∂m2
{β 2 ( pa12 m1 − a12 g 1 − g 2 ) − (1 − pa12 )[k (α 1 + β1 m1 ) + α 2 ]} .
∂µ1

(25)

+

+

∂p
a12 (m2 − m1 )[k (α 1 + β1 m1 ) + α 2 + β 2 m2 ]
) )
(
∂µ1
+

+

Equation (24) shows that σ 1 determines the sign of ∂u 2 / ∂µ1 . In turn, the sign of σ 1
depends on the following five effects. The first term on the RHS of equation (25) includes two
types of effects: via a rise in the profit share in sector 1, the effect of a rise in the mark-up rate
in sector 1 on investment in sector 111 and the negative effect of a rise in the mark-up rate insector 1 on the consumption of workers in sector 1. The second term also includes two types ofeffects: via a rise in the profit share in sector 2, the effect of a rise in the mark-up rate in sector
1 on investment in sector 2 and the negative effect of a rise in the mark-up rate in sector 1 onthe consumption of workers in sector 2. The third term represents the positive effect of a risein the mark-up rate in sector 1 on consumption via a rise in the relative price when m2 > m1
holds.12 Note here that supposing m 2 > m1 is realistic. By using equations (10) and (11), thisinequality is rewritten as ( µ1 − µ 2 )b2 < µ 2 (1 + µ1 )a12 b1θ . In reality, sector 1 is morecompetitive than sector 2, which implies that µ1 − µ 2 < 0 . Thus, we make the following
assumption.

Inequalities det J > 0 and (1 − pa12 )m2 − a12 g 1 − g 2 < 0 are compatible and thus the effect of arise in the mark-up rate in sector 1 on investment in sector 1 is not always positive. Similarly, the effectof a rise in the mark-up rate in sector 1 on investment in sector 2, the effect of a rise in the mark-up rate
in sector 2 on investment in sector 2, and the effect of wage standardization on investment in sector 2
are ambiguous. As a result, in contrast to the one-sector Kaleckian model (Blecker, 2002; Lavoie andStockhammer, 2013), even if β i is sufficiently large, a fall in the mark-up rate does not necessarily
increase the rate of capacity utilization in our model. For instance, when
(1 − pa12 )m2 − a12 g 1 − g 2 < 0 holds, a larger β1 tends to produce a wage-led demand regime.
12
A rise in the mark-up rate in sector 1 increases the intermediate goods price, which in turn increases
nominal income and accordingly raises workers’ consumption in sector 1. On the contrary, a rise in theintermediate goods price decreases value added and thus workers’ consumption in sector 2. Whenm2 > m1 holds, an increase in workers’ consumption in sector 1 compensates for the decrease inworkers’ consumption in sector 2. As a result, a rise in the mark-up rate in sector 1 positively affects therate of capacity utilization by increasing the relative price.
11

10Assumption 1. Sector 1 is more competitive than sector 2 and thus m2 > m1 holds.
According to the combination of these five effects, the effect of a rise in the mark-up rate insector 1 on capacity utilization can be positive or negative. If g i is sufficiently small, thenthe first and second terms on the RHS of equation (25) become positive, which implies that theeconomy exhibits a profit-led demand regime.
Next, the effect of a rise in the mark-up rate in sector 2 on the short-run equilibrium rate ofcapacity utilization in sector 2 is represented by

∂u 2
σ2
=
,
∂µ 2 [ pa12 m1 + (1 − pa12 )m2 − a12g 1 − g 2 ]2

(26)

where

σ2 =

∂m2
{β 2 ( pa12 m1 − a12 g 1 − g 2 ) − (1 − pa12 )[k (α 1 + β1 m1 ) + α 2 ]}
∂µ 2
+

∂p
+
a12 (m2 − m1 )[k (α 1 + β1 m1 ) + α 2 + β 2 m2 ]
) )
(
∂µ 2

.

(27)

+

−

The first term on the RHS of equation (27) includes two types of effects: via a rise in the profit
share in sector 2, the effect of a rise in the mark-up rate in sector 2 on investment in sector 2
and the negative effect of a rise in the mark-up rate in sector 2 on the consumption of workers
in sector 2. The second term indicates the negative effect of a rise in the mark-up rate in sector
2 on consumption via a fall in the relative price.13 According to the combination of these threeeffects, a rise in the mark-up rate in sector 2 positively or negatively affects capacity utilization.
If g i is sufficiently small, then the first term on the RHS of equation (27) becomes positive
and a profit-led demand regime appears.
The effect of wage standardization on the short-run equilibrium rate of capacity utilizationin sector 2 is represented by

σ3
∂u 2
=
,
∂θ [ pa12 m1 + (1 − pa12 )m2 − a12g 1 − g 2 ]2

(28)

where

13

A rise in the mark-up rate in sector 2 increases the final goods price, which in turn decreases the real
wage rate and accordingly reduces workers’ consumption in sector 1. On the contrary, a rise in the final
goods price increases value added and thus raises workers’ consumption in sector 2. When m 2 > m1
holds, the decrease in workers’ consumption in sector 1 exceeds the increase in workers’ consumption
in sector 2. As a result, a rise in the mark-up rate in sector 2 negatively affects the rate of capacity
utilization by decreasing the relative price.

11

σ3 =

∂m2
{β 2 ( pa12 m1 − a12 g 1 − g 2 ) − (1 − pa12 )[k (α 1 + β1 m1 ) + α 2 ]}
∂θ
+

∂p
+
a12 (m2 − m1 )[k (α 1 + β1 m1 ) + α 2 + β 2 m2 ]
) )
(
∂θ
+

.

(29)

+

The first term on the RHS of equation (29) includes two types of effects: via a rise in the profit
share in sector 2, the effect of wage standardization on investment in sector 2 and the negative
effect of wage standardization on the consumption of workers in sector 2. The second term
indicates the positive effect of wage standardization on consumption via a rise in the relative
price.14 If g i is sufficiently small, then the first term on the RHS of equation (29) becomes
positive, which in turn increases the rate of capacity utilization when wage standardization
occurs.
The diverse conditions under which these two types of demand regimes appear are
summarized in Table 2. Changes in the mark-up rates in both the intermediate goods sector
and the final goods sector can produce a profit-led demand regime as well as a wage-led
demand regime.
(Table 2 here)
3.3 Summary
Let us now return to the problem of who should take responsibility for the cost reduction
owing to price competition. In our model, there are four ways in which to reduce the final
goods price: falls in the mark-up rate and the nominal wage rate in sector 1 and falls in themark-up rate and the nominal wage rate in sector 2. Among these, a fall in the nominal wage
rate in sector 2 does not affect the rate of capacity utilization. This is because a fall in thenominal wage rate in sector 2 decreases the final goods price, which remains both sectors’ real
wage rates unchanged, and a fall in nominal wage rate in sector 2 decreases both the nominal
wage rate in sector 1 and that in sector 2 to the same degree, which keeps the relative priceconstant.15 Thus, a cost reduction, which changes the rate of capacity utilization, can occur in
14

Similar to a rise in the mark-up rate in sector 1, wage standardization, that is, a rise in the nominal
wage rate in sector 1, increases the intermediate goods price. According to the mechanism explained infootnote 12, wage standardization positively affects the rate of capacity utilization by increasing therelative price.
15
Because a fall in w does not always lead to a fall in p2 to the same degree, the real wage rate
can increase or decrease. For instance, when the decrease in w exceeds that in p2 , the real wage rate

decreases, which means that either µ1 or µ 2 increases. As a result, costs can reduce through falls inµ1 , µ 2 , and θ .

12the following ways: a fall in the mark-up rate in sector 1 (a fall in µ1 ), a fall in the nominal
wage rate in sector 1 (a fall in θ ), and a fall in the mark-up rate in sector 2 (a fall in µ 2 ). In
the following, we consider which of these three parameters should be reduced to positively
affect the rate of capacity utilization.
To begin with, we compare the effects of a fall in µ 2 with a fall in θ . We find fromequations (27) and (29) that the first terms on the RHS of both equations always show thesame sign. For instance, when the first term on the RHS of equation (27) becomes positive, thefirst term on the RHS of equation (29) becomes positive. By contrast, the second term on the
RHS of equation (27) is negative, whereas the second term on the RHS of equation (29) is
positive. Therefore, compared with a fall in the nominal wage rate in sector 1, a fall in themark-up rate in sector 2 is likely to increase the rate of capacity utilization in the short run.
Next, we compare the effects of a fall in µ1 with a fall in µ 2 . Since this comparison ismore difficult, we additionally assume that g i is sufficiently small. The second term on the
RHS of equation (25) shows the same sign as the first term on the RHS of equation (27).
Moreover, the third term on the RHS of equation (25) is positive, whereas the second term on
the RHS of equation (27) is negative. Furthermore, when g i is sufficiently small, we obtain(1 − pa12 )m2 − a12 g 1 − g 2 > 0 , which makes the first term on the RHS of equation (25) positive.
Thus, compared with a fall in the mark-up rate in sector 2, a fall in the mark-up rate in sector 1
is likely to decrease the rate of capacity utilization in the short run.
Finally, we compare the effects of a fall in µ1 with a fall in θ . Here, we assume that g i
is sufficiently large. The second term on the RHS of equation (25) shows the same sign as thefirst term on the RHS of equation (29). Moreover, both the third term on the RHS of equation(25) and the second term on the RHS of equation (29) are positive. Furthermore, if g i issufficiently large, we obtain (1 − pa12 )m2 − a12 g 1 − g 2 < 0 , which makes the first term on the
RHS of equation (25) negative. This means that, in sector 1, compared with a fall in thenominal wage rate, a fall in the mark-up rate is likely to increase the short-run equilibrium rateof capacity utilization.
We summarize the above arguments as follows.
Proposition 3. In the short-run equilibrium, if g i is sufficiently small, a fall in the mark-up
rate in sector 2 comparatively increases the rate of capacity utilization. By contrast, if g i issufficiently large, a fall in the mark-up rate in either sector is likely to increase the rate ofcapacity utilization compared with cutting the nominal wage rate in sector 1.
Consider the situation where anyone could be a victim of an income reduction to reduce the13final goods price. From Proposition 3, we find that firms in the final goods sector should takeresponsibility for the cost reduction by cutting their mark-up rate when g i is sufficiently
small. On the contrary, when g i is sufficiently large, firms in either sector should takeresponsibility for the cost reduction and not shift their burden to the workers in theintermediate goods sector.
4 Long-run dynamics
4.1 Stability analysis
This section considers the long-run dynamics of the sectoral ratio of capital stocks. By
substituting equations (20) and (21) into equations (12) and (13), we obtain each sector’s rateof capital accumulation in the short run:

g1 = α1 + β1m1 + g 1
g 2 = α 2 + β 2 m2 + g 2[α1 + β1m1 + (α 2 + β 2 m2 ) / k ]a12 ,pa12 m1 + (1 − pa12 )m2 − a12g 1 − g 2

k (α1 + β1m1 ) + α 2 + β 2 m2.
pa12 m1 + (1 − pa12 )m2 − a12g 1 − g 2

(30)
(31)

We obtain the long-run dynamical equation by substituting equations (30) and (31) into
equation (19). We define as the long-run equilibrium the situation where k = 0 holds. In thelong-run equilibrium, we find from equation (19) that a BGP, that is, g1 = g 2 , appears.
Moreover, dg1 / dk < 0 and dg 2 / dk > 0 from equations (30) and (31), and accordingly thefollowing equation holds:
dk dg1 dg 2
=
−
< 0.
dk
dk
dk

(32)

Equation (32) shows that the long-run equilibrium is locally stable.
Equations (30) and (31) are depicted in Figure 1, in which the vertical axis indicates the rateof capital accumulation and the horizontal axis indicates the sectoral ratio of capital stocks. At
the intersection point, e , between the two curves, we obtain the long-run rate of capital
accumulation, that is, the rate of capital accumulation on the BGP, and the long-run sectoral
ratio of capital stocks. By using this figure, we investigate the effect of changes in the mark-up
rate and wage standardization on the long-run rate of capital accumulation and rate of capacity
utilization.
4.2 Comparative static analysis
The long-run dynamics of the rate of capital accumulation are more difficult to investigate
than the short-run dynamics of the rate of capacity utilization. In this section, to consider the
more plausible case, we assume that g i is sufficiently small. Under this condition, as Table 2
14

shows, falls in the mark-up rate in both sectors and cutting the nominal wage rate in sector 1(wage non-standardization) are likely to decrease both sectors’ short-run equilibrium rates ofcapacity utilization. In other words, a profit-led demand regime is likely to appear. Moreover,as Proposition 2 shows, a fall in the mark-up rate in sector 1 decreases both sectors’ profit
shares and accordingly decreases both sectors’ short-run rates of capital accumulation.
Furthermore, a fall in the mark-up rate in sector 2 and cutting the nominal wage rate in sector
1 decrease the profit share in sector 2 and thus decrease both sectors’ short-run rates of capital
accumulation.
Figure 1 shows the case where in the profit-led demand regime a fall in the mark-up rate ineither sector or cutting the nominal wage rate in sector 1 shifts both sectors’ short-run
equilibrium rates of capital accumulation downwards. In this figure, the rates of capital
accumulation, which shifted after the mark-up rate rise, are represented by the dashed line andthe long-run equilibrium moves from eu to e′ . Thus, in the profit-led demand regime, a fallin the mark-up rate in either sector or cutting the nominal wage rate in sector 1 always
decreases the long-run equilibrium rate of capital accumulation. In addition, the long-run
sectoral ratio of capital stocks depends on the movement of the short-run rate of capital
accumulation. In Figure 1, since the rate of capital accumulation in sector 1 decreases morethan that in sector 2, the sectoral ratio of capital stocks decreases. Equations (20) and (21)show that a fall in the sectoral ratio of capital stocks has a positive effect on the long-run rateof capacity utilization in sector 1 and a negative effect on that in sector 2. Thus, even if theeconomy exhibits a profit-led demand regime in the short run, a fall in the mark-up rate orwage non-standardization may increase only the long-run equilibrium rate of capacity
utilization in sector 1.
Even if g i(Figure 1 here)is small, a profit-led regime does not necessarily appear. We find from

Proposition 3 that a fall in the mark-up rate in sector 2 tends to increase the short-run
equilibrium rates of capacity utilization in both sectors rather than cutting the mark-up rate andnominal wage rate in sector 1 when g i is small. In other words, as for the change in themark-up rate in sector 2, the economy is likely to exhibit a wage-led demand regime. 16 In
such a wage-led demand regime with a fall in the mark-up rate in sector 2, the short-run rate ofcapital accumulation changes in two ways. The first pattern is that in both sectors the short-run
rates of capital accumulation increase with the rising short-run rates of capacity utilization.
The second pattern is that only the short-run rate of capital accumulation in sector 2 decreases
because of the falling profit share in sector 2.
16

We show such a case by using numerical simulations in Appendix C, which is available on request.

15

We consider the first pattern in Figure 2. Because a fall in the mark-up rate in sector 2 shifts
both sectors’ rates of capital accumulation upwards, which are represented by the dashed line,
a long-run equilibrium shifts from e to e′ and accordingly the long-run equilibrium rate ofcapital accumulation increases.
(Figure 2 here)
Next, we consider the second pattern in Figure 2. Since a rise in the mark-up rate in sector 2
increases capital accumulation in sector 1, which is represented by the dashed line, but
decreases that in sector 2, which is represented by the dotted line, an equilibrium shifts frome to e′′ and accordingly the long-run equilibrium sectoral ratio of capital stocks increases.
In this situation, is the new equilibrium rate of capital accumulation larger than the old one?
Equation (30) shows that the larger α 2 + β 2 m2 , the more quickly g1 decreases withincreasing k . Similarly, equation (31) shows that the larger α 1 + β1 m1 , the more quickly g 2
increases with increasing k . Accordingly, if the animal spirits in sector 1 (sector 2) aresufficiently large (small), the rate of capital accumulation in sector 2 (sector 1), which was
temporally reduced (raised) by a mark-up rate rise in sector 2, rapidly increases (slackly
decreases). According to the combination of such motions in g1 and g 2 , the new
equilibrium e′′ holds and thus the rate of capital accumulation on the BGP increases. Such a
movement is intuitively explained as follows. A fall in the mark-up rate in sector 2 increases
the short-run equilibrium rate of capital accumulation in sector 1, while it decreases theshort-run equilibrium rate of capital accumulation in sector 2, which implies that capital stocks
accumulate in sector 1 rather than in sector 2. Then, if the animal spirits in sector 1 are larger
than those in sector 2, capital stocks accumulate in the sector where being eager to invest
prevails and accordingly macroeconomic capital accumulation rises.
Finally, in the second pattern, a rise in the long-run sectoral ratio of capital stocks negatively
affects the long-run rate of capacity utilization in sector 1 and positively affects the long-run
rate of capacity utilization. Even if the economy exhibits a wage-led demand regime in the
short run, a fall in the mark-up rate, especially in sector 2, may decrease only the long-run
equilibrium rate of capacity utilization in sector 1. Thus, the short-run results are less reliablein the long run.
5 Conclusion
Even under modern capitalism where oligopolistic firms have dominated the market, pricecompetition in both domestic and international markets does not easily disappear. In this study,
we constructed a Kaleckian model with an intermediate goods sector and a final goods sector
and considered the problem of who should take responsibility for the cost reduction owing to16

price competition to maintain effective demand and economic growth. Our results are
summarized as follows.
First, in the short run where capital does not accumulate, if the coefficient of the rate ofcapacity utilization in the investment function is sufficiently small, a fall in the mark-up rate in
the final goods sector tends to increase the short-run rate of capacity utilization. This finding
implies that firms in the final goods sector should bear the pain of price competition by cutting
their mark-up rates. On the contrary, if the coefficient of the rate of capacity utilization in theinvestment function is sufficiently large, either firms in the intermediate goods sector or thosein the final goods sector should take responsibility for reducing costs.
Second, compared with cutting the mark-up rate in either sector, a fall in the nominal wage
rate in the intermediate goods sector is likely to reduce the short-run rate of capacity utilization.
In this sense, workers in the intermediate goods sector should not bear the pain of pricecompetition. On the contrary, wage standardization, that is, raising the nominal wage rate of
the intermediate goods sector to the level of the final goods sector, positively affects the rate ofcapacity utilization. Wage standardization, however, requires consensus between workers in
the intermediate goods sector and workers of the final goods sector because it raises the real
wage rate in the former, but decreases that in the latter.
Finally, in the long run where capital accumulates, owing to the short-run effects, a fall inthe mark-up rate in the final goods sector is likely to increase the rate of capital accumulationon the BGP when the coefficient of the rate of capacity utilization in the investment function is
sufficiently small. Thus, to promote economic growth, firms in the final goods sector should
be targeted for the cost reduction. Moreover, in the long run, a change in the sectoral ratio of
capital stocks, which is caused by a change in the mark-up rate or wage standardization,
moves each sector’s rate of capacity utilization in the opposite direction. This phenomenon
indicates that determining distributive policy by taking into account only one sector may be
unsuitable for another sector’s performance.
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Figures and Tables

Eq. (31)

Eq. (30)

Figure 1: The long-run equilibrium under the profit-led demand regime

Eq. (31)

Eq. (30)

Figure 2: The long-run equilibrium under the wage-led demand regime

20

Intermediate demandIntermediate

Final demand

Total output

Sector 1

Sector 2

Consumption

Investment

Sector 10

p1 a12 X 200

p1 X 1

Sector 2

0

0

p2C

p2 (I1 + I 2 )p2 X 2

Wages

w1b1 X 1

w 2 b2 X 2Profitsµ1 w1b1 X 1µ 2 ( p1 a12 + w2 b2 ) X 2

p1 X 1

p2 X 2

input

Value added

Total output

Table 1: Hypothetical two-sector transaction table21Impact on capacity

Demand regime

Conditions

Profit-led

g 1 and g 2 are small

utilization
Rises in u1 and u 2
A rise in µ1

Positive effect of the relative price is likely to raise u1 and u 2
Falls in u1 and u 2

Wage-led

g 1 and g 2 are large

Rises in u1 and u 2Profit-led

g 1 and g 2 are small

Falls in u1 and u 2

Wage-led

g 1 and g 2 are large

A rise in µ 2
Negative effect of the relative price is likely to reduce u1 and u 2

g 1 and g 2 are small

Rises in u1 and u 2
A rise in θ

Positive effect of the relative price is likely to raise u1 and u 2

g 1 and g 2 are large

Falls in u1 and u 2

Table 2: Demand regime in the short-run equilibrium

22