ECONOMIC RESEARCH CENTERDISCUSSION PAPER
E-Series

No.E14-10

Specificity and Economic Performanceby
Koji Yoneda
Tadashi Minagawa

December 2014

ECONOMIC RESEARCH CENTERGRADUATE SCHOOL OF ECONOMICSNAGOYA UNIVERSITY

Preliminary and Incomplete
Comments welcome

Specificity and Economic Performance∗
Koji Yoneda†and Tadashi Minagawa‡

AbstractLong-term business relationships with specific investments prevail extensively intransactions of intermediate goods, while economic theories have traditionally presumed market transactions. But relation-specific production is also known to have aweakness to economic shocks. This paper provides models of specific relations between
a manufacturer and its suppliers, examining how the degree of specificity affects theimpact of demand shocks on the ways of production, on the value of output, and thelike. The main findings we obtained are as follows. (i) Once the market conditions fall
below some critical level, specific relations break down rapidly. (ii) Facing a large drop
in demand, the percentage decrease in the value of output is greater in an industry
with higher specificity than lower specificity. (iii) Specific relations make output more
responsive to negative demand shocks.
JEL codes: D23, L14, L62, L64.
Keywords: relationship specificity, vertical relationships, global recession, Japanesemanufacturing.

1

Introduction

Long-term business relations with investments in specific assets prevail extensively in actual inter-firm transactions, while economic theories have traditionally presumed market
transactions.1 Especially in transactions of intermediate goods, specific relations are observed prominently (well-developed supply chains are found in many industries). Indeed,
it can be said that, except for final goods, few goods are sold and purchased through the∗
We are grateful for helpful comments to Sharif Mebed and the participants of the workshop “2011
Mathematical Economics” in Research Institute for Mathematical Sciences, and Kyoto Institute of Economic Research, Kyoto University.
†
Economic Research Center, Graduate School of Economics, Nagoya University.
‡
Department of Business Administration, Tokaigakuen University. Professor Emeritus of Nagoya University.
1
For example, Oliver Hart (1995) writes, “Economists have a very well-established theory of market
trading and are on the way to possessing a similarly well-developed theory of contractual transactions.
The economic analysis of institutions, however, is in a much more rudimentary state.”
But we can find insightful discussions on relation-specific investments in the modern economic analysis ofinstitutions, e.g., Benjamin Klein, Robert G. Crawford, and Armen A. Alchian (1978); Oliver E. Williamson(1985); Sanford J. Grossman and Oliver D. Hart (1986); Oliver Hart and John Moore (1990); Daron
Acemoglu, Pol Antràs, and Elhanan Helpman (2007); Nisvan Erkal (2007); and Charles I. Jones (2011).

1

100

95

90

85

80
France
Japan
US

75

Germany
UK

70

2008

2009

2010

2011

Figure I: Index of Industrial Production Compared by Country.
Source: Ministry of Economy, Trade and Industry (for Japan); Board of Governors of the Federal Reserve
System (for US); Eurostat (for France, Germany, and UK).

market. Similarly in transactions between employer and workers, long-term employment
for accumulating firm-specific skills is often observed.2
Why are specific relations highly developed in the transactions of many intermediate
goods? One reason is that production for specific customers enables firms to produce
more valuable goods more efficiently than production for general purpose. In this way, it
appears that specific transactions generate gains from specialization. However, in somestudies, firm-specific production is also known to have a weakness in regards to economic
shocks (Olivier Blanchard and Michael Kremer 1997; Ricardo J. Caballero and Mohamad
L. Hammour 1998).
It has been argued that specific production is prevalent in Japan, as observed in its
automobile (Banri Asanuma 1989; Jeffrey H. Dyer 1994) and electric machinery industry(Toshihiro Nishiguchi 1994). In the global recession that began in the United States in thelate 2000s, Japan experienced a larger decline in industrial production than other advanced
countries (Figure 1). Above all, the Chubu region,3 which is a center for machinery
manufacturing including automobiles, exhibited poor economic performance (Figure 2).
In addition, the industries that had exhibited higher profitability were more likely to havea larger decline in production. Those facts suggest that the weakness of specificity may
have played an important role in the large decline in Japanese industrial production.
Japan also had a serious recession in the late 1990s. This recession was triggered by
the domestic financial shock known as “the collapse of the asset price bubble.” A numberof economists have explicated the mechanisms that causes financial shocks to affect real2

Gary Becker (1964) is one of the most famous studies that analyzes relation-specific investments inhuman capital.
3
Chubu is the central region of the main island of Japan.

2

100
95
90
85
80
Hokkaido
Kanto
Kansai
Shikoku

75
70

Tohoku
Chubu
Chugoku
Kyushu

65
60

2008

2009

2010

2011

Figure II: Index of Industrial Production Compared by Region in Japan.
Source: Hokkaido Bureau of Economy, Trade and Industry; Tohoku Bureau of Economy, Trade and Industry; Kanto Bureau of Economy, Trade and Industry; Chubu Bureau of Economy, Trade and Industry; Kansai Bureau of Economy, Trade and Industry; Chugoku Bureau of Economy, Trade and Industry;
Shikoku Bureau of Economy, Trade and Industry; Kyushu Bureau of Economy, Trade and Industry.Source:
Hokkaido Bureau of Economy, Trade and Industry; Tohoku Bureau of Economy, Trade and Industry; Kanto
Bureau of Economy, Trade and Industry; Chubu Bureau of Economy, Trade and Industry; Kansai Bureau
of Economy, Trade and Industry; Chugoku Bureau of Economy, Trade and Industry; Shikoku Bureau of
Economy, Trade and Industry; Kyushu Bureau of Economy, Trade and Industry.

economies (e.g., Nobuhiro Kiyotaki and John Moore 1997; Ricardo J. Caballero, Takeo
Hoshi, and Anil K Kashyap 2008). The recession of the late 2000s was also triggered by afinancial shock. Nevertheless, it is notable here that the Japanese economy was depressed
to a greater extent than the U.S. economy despite the fact that it was the source of therecession. This also implies that higher specificity in Japanese manufacturing may havesomething to do with the larger decline in its output.
In this paper, focusing on specific relations between a manufacturer (an assembly firm)
and its suppliers (as observed in machinery manufacturing), we will show that in a major
recession, an industry with higher specificity experiences a larger decline in the value of
output. In our model, this arises from the replacement of customized intermediate goods
by standardized general-purpose goods. For example, a trend to standardize intermediate
goods can be found in the semiconductor market. The total sales of “logic” products,
which include customer specific products, decreased 11.3 percent in 2009 compared tothe previous year, whereas “MOS memory” products, most of which are standardized,
decreased only 3.3 percent.4
Our analysis compliments other explanations of the weakness of specificity to economic
4

The source is World Semiconductor Trade Statistics (WSTS), “News Release June 2010.” In the
product classification by WSTS, “logic” includes ASIC (Application Specific Integrated Circuits) such as
CSIC (Customer Specific Integrated Circuits). “MOS memory” consists of DRAM (Dynamic Random
Access Memory) devices, flash memory products, and the like.

3

shocks. Keiichiro Kobayashi (2000) explains that the delay in disposal of debt overhang,which makes it difficult to commit to specific relations, leads the economy to persistentstagnation. Caballero and Hammour (1998) show that a holdup problem arising from
specificity reduces the creation of new relations and thereby makes the cyclical responseof the economy elastic in recessions.
In contrast, we will describe that specificity increases the effect of negative demand
shocks through the following mechanism. Facing a large demand shock, assembly firms
shift from using specific intermediate goods to market-produced ones as a result of theirprofit maximization. Shifting to market-produced goods reduces the market value of the
final good. In consequence, the value of output is reduced not only by the demand shock
itself but also by the decreased product value due to the breakdown of specific relations.
Hence, where specific relations prevail more extensively, output is more responsive tonegative demand shocks.
Our analysis is based, to a large extent, on Blanchard and Kremer (1997). They focus
on an aspect of specific relations where firms have no alternative suppliers, showing the
weakness of specificity. In the early 1990s, the countries of the former Soviet Union had alarge decline in output. According to their analysis, high specificity where state firms had
only one supplier for each input played an important role in this large decrease. They provide sophisticated models to explain how specificity, together with either incompletenessof contracts or asymmetric information, causes a large decline in output. Different from
Blanchard and Kremer, our model examines how decreased demand affects the productionof private firms in market economies, whereas they show how the improvement in private
opportunities can lead to the collapse of production in the state sector. In this paper, we
do not consider the creation of new relations in recovery periods, because our concern here
is with the dissolution of pre-existing relations in recessions.
In Section II, we set up a basic model and draw the following insights: once the market
conditions fall below some critical level, specific relations break down rapidly; Facing alarge drop in demand, the percentage decrease in the value of output is smaller in anindustry with higher specificity than lower; specificity making output more responsive tonegative demand shocks.
Our basic model makes the assumption that if one or more inputs cannot be provided
by specific suppliers, the market value of the final goods falls to the lowest level. This
production technology is assumed in Blanchard and Kremer’s model. Blanchard and Kremer interpret this production technology as a kind of Leontief technology since all inputs
combine in a Leontief fashion. As an alternative way of modeling specificity of intermediate goods, for example, Jones (2011) uses a CES function. In Section III, weakening
the assumption, we consider another model in which the market value of the final goods
increases linearly with the fraction of inputs provided by specific suppliers. This second
model provides robustness to our findings by showing that specific relations exhibit thesame features as obtained in the basic model.
In Section IV, we provide empirical evidence that an industry with higher specificity
4

had a greater output decline in Japan during the late 2000s global recession. Finally,
Section V concludes this paper. An appendix follows.

2

Basic Model

2.1

Technology and Intermediate Goods Transactions

The model is as follows. An assembly firm needs n inputs in order to produce n unitsof a final good. Each input is provided by one supplier. In addition, specific relations
between an assembly firm and its suppliers increase the market value of the final goodby customizing the intermediate goods. Therefore, if all inputs are customized by specificsuppliers, the final goods are sold at the price (1 + θ)v. If one or more inputs cannot
be customized, the final good price falls to v. The parameter v is given by the market
conditions, and θ > 0 by available technologies.
Each input is produced at the cost c, distributed uniformly on [0, 1]. Draws are independent across suppliers (i.e., if we let ci denote c for the i th supplier or the i th input,
Cov(cj , ck ) = 0 for all j 6= k). The distribution of c is known, but the specific realizationof each c is private information to each supplier (i.e., there is information asymmetry
between the assembly firm and each supplier).
The assembly firm maximizes expected profit, and it announces a take-it-or-leave-it
price p to each supplier (given the symmetry built in the assumptions, the price is thesame for all suppliers). If p exceeds c for all suppliers, specific production takes placein the assembly firm. Otherwise, it cannot take place, because the suppliers with c > pcannot produce the customized goods.
When one or more suppliers cannot produce the customized goods, the final goods
are sold at the price of only v, regardless of whether the other inputs are customized.
For this reason, when some inputs cannot be customized, the assembly firm decides topurchase all inputs from the market and ends its relations with all suppliers. In otherwords, the assembly firm shifts from specific production to market production. In themarket for intermediate goods, the assembly firm purchases each input at the price equal
to the specific realization of c.
This model is assuming that the assembly firm announces a take-it-or-leave-it price p
to its suppliers. This assumption is made in Blanchard and Kremer’s model. In Japanese
automobile manufacturing, the take-it-or-leave-it assumption is applicable to relations
between a parts maker and its suppliers, most of which are small and medium-sized enterprises with little bargaining power.5 Indeed, in Japanese manufacturing, small and5

But in Japanese automobile manufacturing, many first-tier suppliers participate even in the productdevelopment (Asanuma 1989; Kim B. Clark and Takahiro Fujimoto 1991). This suggests that these
suppliers have some bargaining power against the assembly firms. Therefore, our assumption of a takeit-or-leave-it price may not successfully describe relations between an automobile manufacturer and its
first-tier suppliers. We also made the analysis assuming that the price of customized intermediate goods isdetermined by Nash bargaining between an assembly firm and its suppliers. The result was qualitatively
the same as in this paper.

5

medium-sized enterprises constitute more than 90 percent of all enterprises.6 These parts
makers and its suppliers have increased specificity of intermediate goods in their long-termbusiness relationships.

2.2

Assembly Firm’s Profit Maximization

In specific production, the assembly firm purchases n inputs at the price p and sells n unitsof the final good at the price (1 + θ)v, so its profit is n(1 + θ)v − np. In market production,
the assembly firm purchases n inputs from the market, in which the expected price of each
input is 1/2, and sells n units of the final good at the price v, so the expected profit isnv − n/2. Therefore, given the price p, the (unconditional) expected profit is given by³n´,
π = S[n(1 + θ)v − np] + (1 − S) nv −2

(1)

where S denotes the probability that specific production takes place.
The probability S depends on p. Given the price p, the probability that p exceeds c
for each supplier (and thereby it can produce the customized good) is given by Pr(c ≤p) = min(1, p). Hence, the probability that p exceeds c for all n suppliers and specificproduction takes place in the assembly firm can be written as
S = min(1, pn ).

(2)

Taking equation (2) into account, the assembly firm determines p to maximize equation(1). Note here that equation (2) may have different functional forms depending on whether
p exceeds one. Therefore, we have to examine each case separately.
Case 1. p > 1. Substituting S = 1 into equation (1), we get
π = n(1 + θ)v − np.

(3)

The expected profit π in equation (3) is a linear function of p with a slope of −n.
Case 2. p ≤ 1. Substituting S = pn into equation (1) we obtain·
π = n −p

n+1

¶
¸
µ
1
1
n
p +v−
.
+ θv +
2
2(4)

In equation (4), π is a polynomial function of p with degree (n + 1), which is concave with
6

In 2009, enterprises with 4 to 299 employees constituted 95.2 percent of all enterprises (excluding thosewith 3 employees or less) in Japanese motor vehicles, parts, and accessories industry. The source is the
Ministry of Economy, Trade and Industry “Census of Manufactures.”

6





Equation (4)Equation (4)Equation (3)Equation (3)

0

pM

p

1

0

1

pM

p

FIGURE I

Figure III: The Profit-maximizing
Price of the Intermediate Goods for the Cases pM < 1 and pM ≥ 1.
The Profit-maximizing Price of the Intermediate Goods for the Cases p  c and p  cMa maximum at7
p=p

M

n
≡
n+1

M

µ
¶
1
θv +
.
2

Figure 3 shows the expected profit π as the function of the price p for both intervals
together (note that pM > 0, since n, θ, v > 0). It is clear from the figure that π ismaximized at p = pM if pM < 1 and p = 1 otherwise. Therefore, the optimal price p∗ forthe assembly firm can be written as·np = min(1, p ) = min 1,
n+1
∗

M

µ
¶¸
1
θv +
.
2

(5)

In equation (5), the price is set at p∗ = 1 when
v≥

1
θ

µ

1 1
+
n 2

¶
(6)

holds.8
The price to maximize the expected profit is determined as shown above. However,the price does not always make a non-negative expected profit. The non-negative profit
condition (NNPC) for n > 2 is given by

v≥

7


1

 2 ,¡
1

1

θ n

 1
1+θ ,

¢
1

if θ ≤ 1 + n2

4
+ 2 , if 1 + n2 < θ ≤ 1 + n−2
4
if 1 + n−2< θ,

Taking the derivative of equation (4) with respect to p, we get
»
„
«
–
1
π 0 (p) = n −(n + 1)pn + n θv +pn−1 .
2

Solving π 0 (p) ≥ 0 and π 0 (p) < 0, we find that p ≤ pM ⇐⇒ π 0 (p) ≥ 0 and p > pM ⇐⇒ π 0 (p) < 0.
8
In equation (5), the price is set at p∗ = 1 if pM ≥ 1. Solving pM ≥ 1, we get equation (6).

7

1.2
1

 = 0.5
 = 0.35p*

0.8

 = 0.2

0.6
0.4
0.2
0
0

0.5

1

1.5

2

2.5

3

3.5

4

v

Figure IV: Behavior of Intermediate Goods Price for Different Values of θ.

and for n ≤ 2 by

(
v≥

1
2 ,¡
¢
1 1
1
θ n + 2 ,if θ ≤ 1 + n2
otherwise.

(see Appendix for details).

2.3Intermediate Goods Price and Demand Shocks

We can now turn to the effect of negative demand shocks on the price p∗ . Hereafter, we
think of decreased v as a decline in the revenue of an assembly firm, because the numberof units produced by the firm is fixed to n in our model for simplification.
Figure 4 compares the effects of decreased v on p∗ between different values of θ (given
the other parameter n = 5). This figure (and the following ones) plots only for the range
satisfying NNPC in each case (in this figure, NNPC holds for v ≥ 0.5 in all the threecases). In the figure, the price exhibits the following features.
First, as the value of θ is larger, the value of v that triggers the reduction of p∗ is lower(which is also obvious from equation (6)): where the gains from specialization are larger,
the assembly firm does not reduce the price until the market conditions worsen more
seriously. This is because the breakdown of specific production causes a greater decline
in the revenue of the firms with larger θ (and thus those firms are is more reluctant to
reduce the price).
Second, for p∗ < 1, the larger the value of θ, the steeper the slope: once the priceis reduced due to decreased demand, the price drops more rapidly where the gains from
specialization are larger. This may explain the observed fact in the Japanese economy
during the recession of the late 2000s. In our model, industries which had exhibited
higher profitability can be thought of as those with higher θ, and the value of shipments
8

1.2
1
n = 100p*

0.8

n = 10

0.6
0.4
0.2
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

v

Figure V: Behavior of Intermediate Goods Price for Different Values of n.

from suppliers (i.e., the revenue of suppliers) can be roughly thought of as the value of p∗ .9
In Japan, manufacturing industries with a higher ratio of operating profit to sales (greaterthan 3 percent) averaged a 24.8 percent decrease in the value of shipments for intermediate
goods from 2008 to 2009, whereas those with a lower ratio (less than 3 percent) averaged
a 16.2 percent decrease.10 This is consistent with the second feature in Figure 4. We findanother instance in the global semiconductor market.
Demand shocks are not the only cause of reductions in revenue for suppliers. Improved
product quality in emerging countries has made it harder for Japanese manufacturers tomaintain the competitiveness of their products, especially since the late 2000s. Our model
suggests that this decline in the competitiveness of products, which can be thought of as
decreased θ, reduces p∗ and thus the revenue of suppliers. In Figure 4, when v = 1.0, thevalue of p∗ is nearly equal to 0.83 for θ = 0.5, to 0.71 for θ = 0.35, and to 0.58 for θ = 0.2.
As shown in this figure, the lower the value of θ, the lower the value of p∗ even if v does
not decrease.
Figure 5 compares the effects of decreased v on p∗ between different values of n (given
the other parameter θ = 0.5). From the figure, we can see the following. Firstly, as the
9

In this model, the number of units produced by each supplier is fixed to one. Thus, the value of
shipments per supplier (in expectation) is given by
„
«
1
1
1
,
Sp∗ + (1 − S) = + min[1, (p∗ )n ] p∗ −222
where we assume that, if specific production breaks down, the suppliers shift to producing marketed goods.
The above equation shows that the value of shipments increases with p∗ for p∗ > n/(2n + 2).
10
Operating profit and sales are for fiscal year 2007, and the source is the Ministry of Finance Japan, “Financial Statements Statistics of Corporations by Industry.” The value of shipments for intermediate goods(producer goods) is obtained from the Ministry of Economy, Trade and Industry, “Indices of Industrial
Production,” the base year of which is 2005.

9

1.2
1
0.8
S

 = 0.5
0.6

 = 0.35

0.4

 = 0.2

0.2
0
0

0.5

1

1.5

2

2.5

3

3.5

4

v

Figure VI: Probability that Specific Production Will Take Place for Different Values of θ.

value of n is larger, the value of v that triggers the reduction of p∗ is lower (which isalso obvious from equation (6)): where the production process of the final goods is more
complex, the assembly firm does not reduce the price until the market conditions worsen
more seriously. This is for the following reason. The larger the value of n, the lower the
probability that specific production takes place if all the other parameters are held fixed.
Hence, reductions in p∗ are more likely to cause a breakdown of specific production where
n is larger. Therefore, the firm with larger n is more likely to keep p∗ at one to avoid
revenue reduction due to the breakdown of specific production.
Secondly, for p∗ < 1, the larger the value of n, the greater the decline in p∗ as v
decreases: once the price is reduced due to decreased demand, the price decreases more
rapidly in firms with a more complex production process.

2.4

Probability that Specific Production Will Take Place

We now turn to how negative demand shocks reduce the probability that specific production will take place. Substituting p = p∗ into equation (2), we get,11
½ ·
µ
¶¸ ¾
n
1 n
S = min 1,
θv +
.
n+1
2

(7)

In equation (7), the probability S is equal to one if p∗ = 1 (when equation (6) holds).
Figure 6 compares the effects of decreased v on S between different values of θ (given
11

Substituting p = p∗ and equation (5) into equation (2) yields
 »„«–ffn ffn
1
S = min 1, min 1,
θv +
.
n+1
2

Rearranging, we get the equation (7).

10

1.2
1
n = 100S

0.8

n = 10

0.6
0.4
0.2
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

v

Figure VII: Probability that Specific Production Will Take Place for Different Values of n.

the other parameter n = 5). The features shown in the figure are as follows.First, as thevalue of θ is larger, the value of v that triggers the decline in S is lower (which is also obvious
from equation (6)): where the gains from specialization are larger, specific production isless likely to break down when the market conditions are worsening. Second, for S < 1,
the larger the value of θ, the greater the decline in S as v decreases: once S falls below
one, specific production breaks down more rapidly where the gains from specialization arelarger.
Figure 7 compares the effects of decreased v on S between different values of n (given
the other parameter θ = 0.5). This figure firstly shows that the larger the value of n, thelower the value of v that triggers the decline in S (which is also obvious from equation(6)): where the production process is more complex, specific production is less likely to
break down when the market conditions are worsening. Secondly, for S < 1, the larger
the value of n, the greater the decline in S as v decreases: once S falls below one, specificproduction breaks down more rapidly where the production process is more complex.

2.5

Specific Relations vs. Market Transactions

Turning to the expected output (or revenue) of an assembly firm. Let YS denote theexpected output of the final good produced by specific relations. Specific production
takes place with probability S. If it takes place, the assembly firm generates revenue ofn(1 + θ)v. Thus, we can get
YS = Sn(1 + θ)v.

(8)

For market production, let YM denote the expected output of the final good produced bymarket transactions. The assembly firm decides to purchase all inputs from the market

11

35

Expected Output

30
25
20

Specific Produciton

15
10
5

Market Produciton

0
0

0.5

1

1.5

2

2.5

3

3.5

4

v

Figure VIII: Expected Output of Specific and Market Production for θ = 0.5.

with probability (1 − S). If it purchases inputs from the market, it generates revenue ofnv. Hence, YM is given by
YM = (1 − S)nv.

(9)

Although YS and YM are the probabilistic expected values of the output in a typical firm,
these can be also thought of as the approximations of total output in one industry. Suppose
now that an industry consists of an infinite number of identical assembly firms, where therealizations of c are independent across all the firms,12 and normalize the number of thefirms to one. Then, by the law of large numbers, we can think of YS and YM as theapproximate outputs of the entire industry.13
Figure 8 compares the effects of decreased v on YS and on YM between different valuesof θ (given the other parameter n = 5). In the figures, the outputs exhibit the following
features.First, for v above some critical level (i.e., for v that satisfies equation (6)), YS
decreases linearly with v. For v below it, YS turns convex, and YM appears. Second, as
the value of θ is larger, the value of v at which YS turns convex is lower. Third, once YS
turns convex in each case, it decreases more sharply where θ is larger. This is because thebreakdown of specific production causes a larger decline in the product value of the final
good where θ is larger.
Figure 9 compares the effects of decreased v on YS and on YM between different valuesof n (given the other parameter θ = 0.5). From the figures, we can firstly see that as the12

In other words, it is assumed that, in specific production, no intermediate goods are supplied to morethan one assembly firm.
13
Some readers may think that an industry consisting of identical assembly firms has only two extreme
states: whether specific production takes place in all the firms or not. Indeed, all the assembly firms in
the industry have the same value of p∗ . However, given p∗ , it is uncertain whether c exceeds p∗ (where weassume that p∗ < 1), because c is the random variable. In consequence, specific production will take placein some assembly firms and not in the others, even if all the identical firms make the same decisions.

12

30

Expected Output

25
20

Specific Produciton

15
10Market Produciton

5
0
0

0.5

1

1.5

2

2.5

3

3.5

4

v

Figure VIII (Continued): Expected Output of Specific and Market Production for θ = 0.2.

25
Specific Production

Expected Output

20
15
10
Market Production
5
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

v

Figure IX: Expected Output of Specific and Market Production for n = 10.

13

250
Specific Production

Expected Output

200
150
100

Market Production

50
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

v

Figure IX (Continued): Expected Output of Specific and Market Production for n = 100.

value of n is larger, the value of v at which YS turns convex is lower. Secondly, once YS
turns convex in each case, it decreases more sharply where n is larger. This is because
retaining specific production is more difficult (more expensive) where n is larger.

2.6

Total Output in an Industry

We are now ready to define the total output of one industry. If we continue to supposethat an industry consists of an infinite number of assembly firms and to normalize thenumber of the firms to one, the total output of an industry is given by
W = YS + YM .

(10)

Figure 10 compares the relative declines in total output W between different valuesof θ (given the other parameter n = 5). In this figure, the output W in each case isnormalized to 1 at v = 3.5, which is the minimum value of v that satisfies S = 1 in bothcases where θ = 0.5 and where θ = 0.2. The features exhibited in the figure are as follows.
In a mild recession (when v is between 3.5 and nearly 1.12 in the case of this figure), thelarge-θ case (i.e., the case where the gains from specialization are larger) exhibits a smaller
decline in output compared to the small-θ case.
By contrast, in an extremely deep recession (when v is below about 1.12), the small-θ
case has a smaller decline in output compared to the large-θ case. This is consistent withthe fact that Japan, where specific production has been highly developed, had a larger
decline in industrial production than other advanced countries.
Figure 11 compares the relative declines in total output W between different valuesof n (given the other parameter θ = 0.5). In this figure, the output W in each case isnormalized to 1 at v = 1.2 (since both cases take S = 1 for v ≥ 1.2). The figure shows14W (normalized to 1 at v = 3.5)

1.2
1
0.8
0.6

 = 0.5

 = 0.2

0.4
0.2
0
0

0.5

1

1.5

2

2.5

3

3.5

4

v

Figure X: Relative Output (Normalized to 1 at v = 3.5) for Different Values of θ.
In the figure, both cases are at the same level for v ≥ 3.5. The case θ = 0.2 has a turning point at v = 3.5,
being at a lower level than the case θ = 0.5 for v between 3.5 and nearly 1.12. The case θ = 0.5 has aturning point at v = 1.4, being at a lower level than the case θ = 0.2 for v below about 1.12.

W (normalized to 1 at v = 1.2)

1.4
1.2
1

n = 100
n = 10

0.8
0.6
0.4
0.2
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

v

Figure XI: Relative Output (Normalized to 1 at v = 1.2) for Different Values of n.
In the figure, both cases are at the same level for v ≥ 1.2. The case n = 10 has a turning point at v = 1.2,
being at a lower level than the case n = 100 for v between 1.2 and nearly 1. The case n = 100 has aturning point at v = 1.02, being at a lower level than the case n = 10 for v below about 1.

15

that in a mild recession (when v is between 1.2 and nearly 1 in this figure), the large-ncase (i.e., the case with a more complex production process) exhibits a smaller decline in
output compared to the small-n case. By contrast, in an extremely deep recession (whenv is below about 1), the small-n case has a smaller decline in output compared to thelarge-n case.

2.7

Output Elasticity

Caballero and Hammour (1998) show that specificity, together with incompleteness ofcontracts, makes economies more responsive to shocks under weak market conditions. Is
this finding exhibited in our model? We will also compare the elasticities of total output
with respect to negative demand shocks between the specific-production sector and themarket-oriented one.14 The specific-production sector consists of assembly firms whichchoose between specific and market production in a way to maximize their profits. The
market-oriented sector refers to a sector in which specific production does not take placeat all (i.e., S is held fixed to zero) for some institutional reason.
The elasticity of total output with respect to negative demand shocks can be defined
as
e=

∆W/W
.
∆v/v

We now let eS and eM denote respectively the elasticities in the specific-production sector
and in the market-oriented one. The value of eM is constant at one. This is because,in the market-oriented sector, the output W is always equal to nv, so the change in W
caused by a one-percent change in v is constant at one percent. For deriving the elasticity
eS , see Appendix.
Figure 12 compares the output elasticities between different values of θ (given the otherparameter n = 5). Note here that the figure never indicates the responses to increased
demand but only to decreased demand, since this model does not consider the creation of
new relations in recovery periods. This figure shows that when the market conditions fall
below some critical level in each case (i.e., for v < 1.4 in the case θ = 0.5, and for v < 3.5 inthe case θ = 0.2), the specific-production sectors are more responsive to negative demand
shocks than the market-oriented sector. In short, specificity can increase the impact ofnegative demand shocks. This is because, in the sector where specific relations are used,
the output is reduced by not only the demand shock itself but also the decreased productvalue due to the breakdown of specific production.
On the other hand, under extremely weak market conditions (i.e., for v < 1.4), thelarge-θ case (i.e., the case where the gains from specialization are larger) is more responsive
to negative demand shocks than the small-θ case. This is because the breakdown of specific
14Specificity is characterized by a joint surplus from an economic relationship in Blanchard and Kremer(1997) and by irreversible investment in Caballero and Hammour (1998). Our modeling follows the former
approach. Therefore, we compare the output elasticities between cases where the surplus from specificity
is available and where it is not. By contrast, Caballero and Hammour make a comparison between cases
where irreversible investment causes holdup and where it does not.

16

2.2

Elasticity of Output

2
1.8

 = 0.5

1.6
1.4

 = 0.2

1.2
1
0.8
0

0.5

1

1.5

2

2.5

3

3.5

4

v

Figure XII: Output Elasticity with Respect to Negative Shocks for Different Values of θ.

production causes a larger decline in the product value where θ is larger.
The results we obtained above are consistent with Caballero and Hammour’s finding thatspecificity, together with incomplete contracts, makes recessions excessively sharp.
Figure 13 compares the elasticities between different values of n (given the other parameter θ = 0.5). The figure shows again that, when the market conditions fall below
some critical level in each case (i.e., for v below about 1.2 in the case n = 10, and for v
below about 1.02 in the case n = 100), the specific-production sectors are more responsive
to negative shocks than the market-oriented sector. By contrast, roughly speaking, under
extremely weak market conditions (i.e., for v between about 1.02 and about 0.95), thelarge-n case (i.e., the case with a more complex production process) is more responsive tonegative shocks than the small-n case.

3

Another Production Technology: Robustness of Findings

In our basic model, we make the extreme assumption that, if one or more of the customized
intermediate goods are not available, the market value of the final goods falls to the lowest
level. But even if this extreme assumption is weakened, we arrive at the same results
as shown in the basic model. This section provides a second model with the weakerassumption that the market value of the final goods increases linearly as the fraction ofcustomized intermediate goods increases.

3.1

Technology and Intermediate Goods Transactions

An assembly firm needs n intermediate goods in order to produce n units of a final good,which is the same as the basic model. But the final goods in this second model are sold

17

20
18
Elasticity of Output

16
14
12
10

n = 100

8
6
4

n = 10

2
0
0

0.2

0.4

0.6

0.8

1

1.2

1.4

v

Figure XIII: Output Elasticity with Respect to Negative Shocks for Different Values of n.





1+

1+

1

1

0

1

s

0

In Section II

1s

In Section III

Figure XIV: Fraction of Customized Inputs and Market Value of Final Goods.
FIGURE XII

at the price of αv, and the parameter α is defined asα(s) = 1 + θs, θ > 0,(11)where s denotes the fraction of customized inputs to all n inputs. That is, the price ofthe final good is equal to v if none of the inputs are customized by specific suppliers. If
all inputs are customized, increasing linearly with s, the price goes to (1 + θ)v (see also
Figure 14).
This section continues the previous discussion on transactions of intermediate goods:
the assembly firm announces a take-it-or-leave-it price p to each supplier; each input isproduced at the cost c, distributed uniformly on [0, 1]; the suppliers with c > p cannot
produce the customized intermediate goods.

18

In the previous section, if one or more suppliers cannot produce customized goods,
the assembly firm decides to purchase all inputs from the market. This is because, when
one or more inputs cannot be customized, the market value of the final goods falls to thelowest level regardless of whether the other inputs are customized. But in this section,even if some inputs cannot be customized, the other customized inputs still contribute to
the market value of the final goods, given the assumption that the value of the final goods
increase linearly with the fraction of customized inputs. Therefore, in this model, theassembly firm uses marketed intermediate goods only for the inputs that specific supplierscannot provide (i.e., the assembly firm can combine customized and marketed intermediate
goods in order to produce the final goods).

3.2

Assembly Firm’s Profit Maximization

The assembly firm sells n units of the final good at the price αv. Hence, from equation(11), its expected revenue is nαv = n(1 + θs)v. On the other hand, it purchases sn inputs
at the price p, and (1 − s)n inputs from the market in which the expected prices of inputs
are equal to 1/2. Therefore, given the price p, the expected profit of the assembly firm isgiven byhni
π = n(1 + θs)v − snp + (1 − s) .
2

(12)

We now turn to the fraction s. Given the price p, the probability that p exceeds c
for each supplier is given by Pr(c ≤ p) = min(1, p). Therefore, the expected fraction ofcustomized inputs to all n inputs is equal to15
s = min(1, p).

(13)

Equation (13) may have different functional forms depending on whether p exceeds one.
Thus, we have to examine each case separately.
Case 1. p > 1. Substituting s = 1 into equation (12), we obtain
π = n(1 + θ)v − np.

(14)

The expected profit π in equation (14) is a linear function of p with a slope of −n.
Case 2. p ≤ 1. Substituting s = p into equation (12), we get
·

¶
¸
µ
1
1
p+v−
.
π = n −p + θv +
2
2
2

15

(15)

Let di be a binary variable taking the value of 1 if the i th input is customized and 0 otherwise. The
fraction of customized inputs with respect to total number of inputs can be written as (d1 + d2 + ... + dn )/n.
Thus, the expected fraction of customized inputs is given by E[(d1 + d2 + ... + dn )/n] = [E(d1 ) + E(d2 ) +... + E(dn )]/n. Substituting E(di ) = min(1, p), we can get [n · min(1, p)]/n = min(1, p).

19

In equation (15), π is a quadratic function of p, which is maximized at16
θv 1
+ .
2
4

p = pM ≡We have now obtained the expected profit π as the function of the price p for the casesp > 1 and p ≤ 1. Drawing the functions for both cases together, we obtain a graphicalrepresentation similar to Figure 3. Therefore, the price to maximize the expected profit
is p = pM if pM < 1 and p = 1 otherwise. That is, the optimal price p∗ can be written asµ¶θv 1
p = min(1, p ) = min 1,
+
,
2
4
∗

M

(16)

where the price is set at p∗ = 1 when
v≥

3
2θ

(17)

holds.17 In addition, NNPC is given byv≥−θ − 4 + 2

p2θ(1 + θ) + 4,
2θ2(see Appendix for details).

3.3

The Price and the Fraction of Customized Inputs

In the basic model, either specific or market production takes place. But in this section,
the assembly firm can combine customized and marketed intermediate goods in order toproduce the final goods. Thus, we will here consider the effects of demand shocks on thefraction of customized inputs, instead of on the probability that specific production takes
place.
Substituting p = p∗ into equation (13), we get the expected fraction of customized
inputs,18

¶
µ
θv 1
+
.
s = min 1,
2
4

(18)

The right-hand side of equation (18) is identical to that of equation (16), so we deal
16

Taking the derivative of the above equation with respect to p, we get„«1
π 0 (p) = n −2p + θv +.
2

Solving π 0 (p) = 0, we obtain the equation in the body text.
17
In equation (16), the price is set at p∗ = 1 if pM ≥ 1. Solving pM ≥ 1 with respect to v, we getequation (17).
18
Substituting p = p∗ and equation (16) into equation (13) yields
»
„
«–
θv
1
s = min 1, min 1,+.
2
4
Rearranging, we get equation (18).

20

1.2
1

 = 1.0

p*, s

0.8

 = 0.5

0.6
 = 0.2

0.4
0.2
0
0

0.5

1

1.5

2

2.5

3

3.5

v

Figure XV: The Price and the Fraction of Customized Inputs for a Linear Production Technology.

with both the price and the fraction of customized intermediate goods at the same time.
Figure 15 compares the effects of decreased v on p∗ or on s between different values ofθ. This figure (and the following ones) plots only for the range satisfying NNPC (in thisfigure, NNPC holds for v above about 0.328 in the case θ = 1.0, about 0.381 in the case
θ = 0.5, and about 0.415 in the case θ = 0.2). From the figure, we can see the samefeatures as shown in the basic model: the larger the value of θ, the lower the value of v
that triggers a decline in the price p∗ (or the fraction s); the larger the value of θ, thegreater the decline in p∗ (or s) as v decreases.
In the previous section, we compared different values of n. However, in this section,
the parameter n does not affect the price p∗ nor the fraction s. For this reason, here andhereafter, we make no comparison between different values of n. Moreover, we cannot
here examine how decreased demand affects the expected output of specific production
and that of market production. This is the result of the assumption that in this section,
an assembly firm can combine customized and marketed inputs to produce the final goods,
whereas in the previous section, only one, specific or market production takes place.

3.4

Total Output in an Industry

Like in the previous section, we suppose there is an industry consisting of an infinite
number of assembly firms, and normalize the number of the firms to one. Then we canthink of the expected output of an assembly firm as the total output in an industry. A
typical assembly firm sells n final goods at the price αv. Thus, from equation (11), thetotal output of the industry is given by
W = nα(s)v = n(1 + θs)v.

21

(19)

W (normalized to 1 at v = 3.0)

1.2
1
0.8
 = 1.0

0.6

 = 0.5
0.4
0.2
0
0

0.5

1

1.5

2

2.5

3

3.5

v

Figure XVI: Relative Output (Normalized to 1 at v = 3.0) for a Linear Production Technology.
Both cases are at the same level for v ≥ 3.0. The case θ = 0.5 has a turning point at v = 3.0, being at
a lower level than the case θ = 1.0 for 0.75 < v < 3.0. The case θ = 1.0 has a turning point at v = 1.5,
being at a lower level than the case θ = 0.5 for v < 0.75.

Figure 16 compares the relative declines in total output W between different values ofθ (given the other parameter n = 1). In this figure, the output W is normalized to 1 at
v = 3.0 (since both cases take s = 1 for v ≥ 3.0). The figure exhibits the same features
as shown in the basic model: in a mild recession (i.e., for 0.75 < v < 3.0 in the case ofthis figure), the large-θ case has a small relative decline in output compared to the small-θ
case; in an extremely deep recession (i.e., for v < 0.75), the small-θ case has an advantage.

3.5

Output Elasticity

Turning to the elasticities of the total output with respect to negative demand shocks, we
compare those between the specific-production sector and the market-oriented one.
First, we derive the total output in the specific-production sector in order to obtainits output elasticity eS . Substituting equation (18) into equation (19) yields19·¸
θ2 2 1
W = n · min (1 + θ)v, v + (θ + 4)v .
2
4

(20)

If equation (17) holds (i.e., when s = 1), equation (20) becomes a linear function of v,
so eS = 1 (because the change in W caused by a one-percent change in v is constant atone). If equation (17) does not hold (i.e., when s < 1), substituting equation (20) and its
19

Substituting equation (18) into equation (19) yields
»
„
«–
θv
1
W = n 1 + θ · min 1,
+
v.
2
4

Rearranging that, we get equation (20).

22derivative with respect to v into eS = (∆W/W )/(∆v/v), we get20
eS = 1 +2θ2 v.
2θ2 v + θ + 4(21)Thus, the elasticity in the specific-production sector can be finally written as
(
eS =

1,
1+

2θ2 v
2θ2 v+θ+4

3
if v ≥ 2θ, otherwise.

Secondly, we turn to the elasticity in the market-oriented sector. In this sector, atypical assembly firm always sells n final goods at the price v. Thus, the total output canbe expressed as W = nv. Hence, it is clear that eM = 1.
We are now ready to compare the elasticities between the specific-production andthe market-oriented sector. The second term in equation (21) is always positive, sinceθ, v > 0. Thus, it is clear that eS > eM if equation (17) does not hold. On the other hand,
if equation (17) holds, eS and eM are equal to one. That is, as well as in the previous
section, the specific-production sector is more responsive to negative demand shocks thanthe market-oriented sector when the market conditions fall below some critical level.
In addition, Figure 17 compares the elasticities between different values of θ. From
the figure, we can see the same features as in the basic model: as θ is larger, output
is more responsive to negative demand shocks under extremely weak market conditions(when v < 1.5 in the case of this figure).

4

Evidence on Output Decline from Japanese Manufacturing Industry

One implication we got in the previous section is that an industry with higher specificity
has a greater output decline during a major recession. In this section, we provide empiricalevidence that the output decline is larger in an industry with a higher percentage of thesubcontracting cost in the sales cost. For manufacturers, we can equate the sales cost withthe production cost, so the percentage of subcontracting cost in sales cost can be thoughtof as the proportion of customized inputs in all inputs.
We use data on the sales of 56 Japanese manufacturing industries21 in the fiscal year
2007 and 2009, and construct the growth rate of output for each industry. The output
growth from fiscal year 2007 to 2009 can capture the output decline during the 2008
global recession. The data come from the Basic Survey of Japanese Business Structure
20

Rewrite eS as eS = ∆W/∆v · v/W . Substituting equation (20) and ∆W/∆v = n[θ2 v + (θ + 4)/4] yieldseS =4θ2 v + θ + 4.
2θ2 v + θ + 4

Rearranging that, we get equation (21).
21
The data source classifies printing industry into manufacturing, but we exclude printing industry fromour data set.

23

1.4

Elasticity of Output

1.35

 = 1.0

1.3
1.25

 = 0.5

1.2
1.15
1.1

 = 0.2

1.05
1
0.95
0

0.5

1

1.5

2

2.5

3

3.5

v

Figure XVII: Output Elasticity with Respect to Negative Shocks for a Linear Production Technology.

and Activities by the Ministry of Economy, Trade and Industry.
We regress the output growth on the percentage of subcontracting cost in the sales
cost and three additional control variables.
For the percentage of the subcontracting cost in the sales cost, we take data for the
fiscal year 2007 from the Basic Survey of Japanese Business Structure and Activities,
which is the same as the source of the output growth. Table 1 shows the percentage ofthe subcontracting cost for each industry. In this table, 56 industries are aggregated into
23 categories. Seeing the ranking, the percentage of the subcontracting cost seems to be agood measure of the customization of inputs. For example, production machinery has thehighest percentage of subcontracting cost, and petroleum and coal has the lowest. Overall
the percentage of subcontracting cost tends to be higher if the produced goods are more
complex.
Durability, the first additional variable, is a dummy that is equal to one if the industry produces durable goods, and zero otherwise. Blanchard and Kremer (1997) also use
this dummy in their regression of output growth. An output decline during recessions istypically larger in durable goods industries than non-durable goods industries.
Next two variables, input price growth and output price growth, come from InputOutput Price Index of the Manufacturing Industry by Sector (IOPI) released by the Bankof Japan.22 Input (output) price growth is the growth rate of the input (output) priceindex for each industry from fiscal years 2007 to 2009. The effects of these two variables
are ambiguous. For example, output price growth is expected to have a positive effect on
the output growth if the price elasticity of demand is sufficiently lower than one.
22

IOPI classifies manufacturing industries into 16 sectors and reports the input price index for eachsector. Therefore, the industries which belong to the same sector in IOPI have the same value for input
and output price growth.

24

Table I: Percentage of Subcontracting Cost in Sales Cost
Industry

Percentage

Petroleum and Coal

0.82

Beverages, Tobacco and Feed

2.95

Non-Ferrous Metals

3.72

Chemical

4.04

Food

4.26

Pulp and Paper

4.85

Lumber and Wood Products, Except Furniture

5.12

Miscellaneous Manufacturing Industries

8.42

Rubber

8.56

Iron and Steel

8.87

Leather Tanning, Leather Products and Fur Skins

8.93

Plastic

8.99

Furniture and Fixtures

9.05

Electrical Machinery, Equipment and Supplies

9.53

Ceramic, Stone and Clay

10.51

Electronic parts, Devices and Electronic Circuits

12.22

Textile Mill

13.49

Transportation Equipment

14.79

Fabricated Metal

14.99

Information and Communication Electronics Equipment

17.84

General-Purpose Machinery

20.47

Business Oriented Machinery

21.37

Production Machinery

21.73

Sources: see text.

25

Table II: Summary Statistics
Mean

Std Dev

Minimum

Output growth-0.1820.243-0.740Maximum
0.526

Percentage of subcontracting cost

9.991

5.898

0.770

23.750

Output price growth-0.0300.070-0.1970.071

Input price growth-0.0550.073-0.3100.023

Durability

0.554

0.502

0.000

1.000

Sources: see text.

Table 2 shows summary statistics for output growth, the percentage of subcontracting
cost, and three additional variables.
The regression results are reported in Table 3. Column 1 shows the result of the simple
regression model which has only one explanatory variable, the percentage of subcontracting
cost. The estimated coefficient is negative and significant at the 1 percent level. Columns
2 to 8 report the results of the regressions including the additional control variables.
Especially durability are highly correlated with the percentage of subcontracting cost(the correlation coefficient between two variables is 0.547), but the negative effect of thepercentage of subcontracting cost is still significant at 5 percent level in all the regressions.
Summarizing the results in the table, a one percent increase in the percentage of thesubcontracting cost leads to a 1.5 to 1.9 percent decrease in output.

26

27
0.125

0.119

0.128

0.112

0.746
(0.992)0.502(0.461)(0.958)(0.006)-0.019***(0.091)-0.266(0.006)-0.018***(0.077)

(4)
0.038

0.370

(0.005)(0.005)(3)0.025(0.447)-0.016***-0.015***(0.064)(0.060)(2)-0.010(1)-0.028

(5)

(6)

0.109

0.103

-0.009(0.072)(0.071)(0.456)0.362(0.006)-0.016**(0.065)-0.009-0.017(0.006)-0.015**(0.061)-0.026*, **, *** indicate significance at 10, 5 and 1%, respectively.

Dependent variable is Output growth. Sample size is 56. Standard errors are reported in parenthesis.

Adjusted R-squared

Durability

Input price growth

Output price growth

Percentage of subcontracting cost

Constant

Table III: Regression Results
(7)

0.111

(0.071)-0.011(0.467)0.497(0.007)-0.017**(0.078)

0.026

(8)

0.095

(0.073)-0.015(1.008)0.769(0.981)-0.300(0.007)-0.018**(0.092)0.041

5Conclusions

In this paper, we tried to explain how specificity affects the response of production tonegative demand shocks. In Section II, we set up our basic model of specific relations
between an assembly firm and its suppliers, showing that those specific relations exhibit
the following features.
First, specific production in which the gains from specialization are larger does notbreak down until the market conditions become even more critical. But highly specificproduction dissolves more rapidly once the market conditions fall below some critical level(these features are shown in Figure 6).
Second, in an extremely deep recession, highly specific production has a larger percentage decline in the value of output, but it has a smaller percentage decline in a mild
recession (from Figure 10). In short, specificity of production is advantageous in favorable
market conditions, whereas it is disadvantageous in depressions. This is consistent with
the Japanese experience of the late 2000s recession. The industries which had exhibited
higher profitability (i.e., industries with higher specificity)23 were more likely to have alarger decline in production.
Third, under extremely weak market conditions, the value of output is more responsive
to negative demand shocks in an industry with higher specificity than that with lower
specificity (from Figure 12). This is because the decline in product value due to thebreakdown of specific production is larger in an industry with higher specificity.
Our basic model assumes that, if one or more intermediate goods cannot be customized,
the market value of the final goods falls to the lowest level. In Section III, weakening thisassumption, we also consider another model with the assumption that the market valueof the final goods increases linearly with the fraction of customized intermediate goods.
This analysis produces the same results as in Section II, indicating the robustness of ourfindings.
In the late 2000s global recession, Japanese economy had a larger decline in industrial
production compared to other advanced countries. The results of our analysis suggestthat highly specific production in Japan may have played an important role in this poor
economic performance. Although Japanese economy in the late 2000s did not have a
sharp increase in bankruptcies, we can observe a trend to move from specific inputs tostandardized or semi-standardized ones as seen in semiconductor market.
Our theoretical model can be also applied to a number of other discussions. It can
explain the impact of the decline in product competitiveness due to improved product23

From our model, we can derive that an industry with higher specificity has higher profitability infavorable market conditions (when specific production surely takes place). Substituting p = p∗ = 1 into
equation (3) gives π = n(1+θ)v−n. In addition, from equation (8) to (10) and S = 1, we get W = n(1+θ)v.
Thus, the ratio of profits to output in an industry is given byn(1 + θ)v − n
1
π
=
=1−
.
W
n(1 + θ)v
(1 + θ)v
The profit ratio in the above equation increases with θ, since v > 0.

28

quality in emerging countries, as mentioned in Section II. It can be applied to the analysis
on the impacts of foreign currency depreciation, since we can think of decreased v as the
reduction in the revenue of manufacturers from their export goods due to foreign currency
depreciation. This is the same for increased competition from globalization. A decreasein v can be thought of as the revenue reduction caused by increased competition.
The weakness of higher specificity is an issue that many economists are interested in.
Recent literature on “product modularity” (e.g., Carliss Y. Baldwin and Kim B. Clark
2000; Masahiko Aoki 2001; Takahiro Fujimoto and Jewheon Oh 2004) are, in some ways,
studies that attempt to seek a way to overcome the weakness of highly specific production.
The creation of new specific relations is beyond the scope of this paper, while we
investigated how decreased demand affects pre-existing relations. In future work, there isa need to take into account how improved demand creates new relations.

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[3] Asanuma, Banri. 1989. “Manufacturer-Supplier Relationships in Japan and theConcept of Relation-Specific Skill.” Journal of the Japanese and International
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Appendix
Deriving Non-negative Profit Condition in Section II
We here derive NNPC in Section II. At the beginning, we consider the following threecases. If p∗ = 1 (i.e., if equation (6) holds), specific production surely takes place (Case1). On the other hand, if p∗ < 1 (i.e., if equation (6) does not hold), it may take place(Case 2) or not (Case 3).
Case 1. If p∗ = 1, specific production surely takes place (i.e., S = 1), and thereby the
expected profit of the assembly firm is equal to n(1 + θ)v − n. Thus, NNPC in this caseis given by
v≥

1
.
1+θ
30

(22)

v



v 1 11
 n 2

 : Equation (6)v12: Equation (24)

v 1
1

: Equation (22)



0

1 2
n

1 4
n2

Figure A I: Non-negative Profit Condition in Section II.

Case 2. If p∗ < 1 and specific production takes place, NNPC is given by n(1+θ)v−np ≥0. Substituting p = p∗ and equation (5) into it yieldsv≥

1.
2 + 2(1 + θ)/n(23)

Case 3. If p∗ < 1 and specific production does not take place, the expected profit
becomes nv − nc. Hence, NNPC in this case is given by
1
v≥ ,
2

(24)

since the expectation of c is equal to 1/2.
We have now obtained NNPC in all three cases. Comparing NNPC between in Case2 and in Case 3, we can see that equation (A2) is satisfied whenever equation (A3) holds(since, from n, θ > 0, it follows that the right-hand side of equation (A3) is always greaterthan that of equation (A2)). Therefore, a sufficient condition for non-negative profit ifp∗ < 1 is given simply by equation (A3).
Taking all three cases into account, NNPC in Section II is given by equation (A1) if
equation (6) holds and by equation (A3) otherwise. Figure A1 plots the right-hand sidesof equation (6), (A1), and (A3) on the vertical axis against θ on the horizontal axis (notethat, if n ≤ 2, there is no intersection between equation (6) and (A1) for θ > 0). From
the figure, it is clear that NNPC for n > 2 can be written as

v≥


1

 2 ,¡
1

1

θ n

 1
1+θ ,

¢
1

if θ ≤ 1 + n2

4
+ 2 , if 1 + n2 < θ ≤ 1 + n−2
4
if 1 + n−2
< θ,

31

and for n ≤ 2 as

(

1
2 ,¡
¢
1 1
1
θ n + 2 ,v≥

if θ ≤ 1 + n2
otherwise.

The figure also provides important insights. For 1 + 2/n ≤ θ < 1 + 4/(n − 2), NNPCis given by equation (6) itself. For θ ≥ 1 + 4/(n − 2), NNPC is broken when equation (6)is still satisfied. That is, for θ ≥ 1 + 2/n, specific production surely takes place (i.e., S is
kept at 1) whenever NNPC holds.

Deriving Output Elasticity in Section II
This subsection derives the output elasticity with respect to negative demand shocks inthe specific production sector in Section II.
If equation (6) holds, specific production takes place in all assembly firms (i.e., S = 1).
Hence, the total output in the industry is equal to W = n(1 + θ)v (where the number offirms in the industry is normalized to one). Therefore, it is obvious that eS = 1 if equation(6) holds.
On the other hand, if equation (6) does not hold, then S = pn . Substituting p = p∗and equation (5) into S = pn yields
µ
S=

¶n µ
¶
1 n
θv +
.
2

n
n+1

This can be rewritten as
µ
S=

n
n+1

¶n

Pn

"

i=0

µ ¶i #
1
Pn+1−i,1+i θn−i v n−i,2where Pj,k denotes the (j, k) entry of the symmetric Pascal matrix defined as
1 1 1 ···

1 2 3 · · ·P=
1 3 6 · · · .
.. .. .. . .
.
. . .
Substituting S and equation (8) and (9) into equation (10), we getµ
W = nv +

n
n+1

¶n

Pn

i=0

"

µ ¶i #
1
Pn+1−i,1+i θn−i v n+1−inθ.
2Substituting the above equation and its derivative with respect to v into eS = ∆W/∆v ·v/W yields
P
1 + [n/(n + 1)]n ni=0 [(n + 1 − i)Pn+1−i,1+i θn−i v n−i (1/2)i ]θ
PeS =.
1 + [n/(n + 1)]n ni=0 [Pn+1−i,1+i θn−i v n−i (1/2)i ]θ

32

Rearranging that, we obtainP[n/(n + 1)]n ni=0 [(n − i)Pn+1−i,1+i θn−i v n−i (1/2)i ]θ
P.
eS = 1 +
1 + [n/(n + 1)]n ni=0 [Pn+1−i,1+i θn−i v n−i (1/2)i ]θ

(25)

The second term in equation (A4) is always positive, since n, θ, v > 0. Hence, it is clearthat eS > eM if equation (6) does not hold.
The elasticity in the specific-production sector can be finally written as

 1,
eS =

 1+

if v ≥ 1θ

[n/(n+1)]n

¡1

1
n + 2

¢

Pn
n−i v n−i (1/2)i ]θ
n+1−i,1+i θ
i=0
P[(n−i)P, otherwise.
nnn−i n−ii

1+[n/(n+1)]i=0 [Pn+1−i,1+i θv(1/2) ]θDeriving Non-negative Profit Condition in Section III
In this subsection, we derive NNPC in Section III. At the beginning, we consider the twocases that equation (17) holds (i.e., p∗ = 1) and that it does not (i.e., p∗ < 1).
Case 1. p∗ = 1. Substituting p = p∗ = 1 into equation (14) yields the expected profit
π = n(1 + θ)v − n. Thus, NNPC for this case is given by
v≥

1
.
1+θ

(26)

However, equation (A5) is satisfied whenever equation (17) holds (the right-hand side ofequation (17) is always greater than that of equation (A5), since θ > 0). That is, theexpected profit is always non-negative if equation (17) holds.
Case 2. p∗ = p∗M . Substituting p = p∗ and equation (16) into equation (15) gives the
expected profit. Hence, NNPC for this case can be written as
" µ
#
¶
¶µ
¶
µ
θv 1 2
1
θv 1
1
n −
+
+ θv +
+
+v−
≥ 0.
2
4
2
2
4
2
Rearranging that gives
4θ2 v 2 + (4θ + 16)v − 7 ≥ 0.
Solving the above inequality with respect to v, we get24v≥−θ − 4 + 2

p2θ(1 + θ) + 4.
2θ2

This is NNPC in Section III in the body text.

24

The solutions for the above inequality also containsp−θ − 4 − 2 2θ(1 + θ) + 4
v≤
.
2θ2

However, this inequality is never satisfied, since, from θ > 0, it follows that the right-hand side of theinequality is always negative.

33