超額產能與聯合壟斷---以麵粉業為案例分析

行政院國家科學委員會專題研究計畫 成果報告

超額產能與聯合壟斷：以麵粉業為案例分析

中

華

民

國 92 年 9 月 15 日

2 摘要 國內麵粉業設備利用率長期維持在 50%以下，遠低於整體產業平均水準之 80%，為解釋以上現象，本研究嘗試建立一個二階段賽局，讓廠商在事前的投 資階段，決定產能；及在事後的營運階段，決定實際產出，此時，在事前階段 所決定之產能即成為一個內生性變數，並會影響到第二階段的市場競爭。本文 發現：在卡特爾的運作上，龐大的超額產能可作為卡特爾用以威脅成員不得秘 密增產的一種可信賴威脅，可以策略性的減少其他廠商產出。此外，並利用非 線性聯立方程式迴歸方法，對模型加以估計，結果顯示：麵粉業應存有利用超 額產能達成策略性壟斷之機制。 關鍵詞：超額產能、策略性聯合壟斷、可信賴的威脅

3 EXCESS CAPACITY AND COLLUSION: A CASE STUDY ON FLOUR INDUSTRY

Summar y

In Taiwan flour market, the capacity utilization rate of firms has maintained at 40%

for more than 20 years. This utilization rate is by far lower than the normal level of

80% and indicates a huge excess capacity at the industry level. Based on this fact, we

set up a two-stage game model and use the strategic effect of firm’s capital investment

on its rivals’ outputs to explain the nature of the excess capacity. Flour firms

simultaneously decide the fixed factor input (capital stock) in the first stage and then

choose the variable factor input so as to resolve quantity in the second stage. Thus,

capital is treated as an endogenous variable and is determined in the first stage that

affects market competition in the second stage. We find that a large capacity built in

period one can be used strategically to reduce other firms’ outputs in period two, since

it can deter firms from cheating under the agreement of tacit collusion. This leads to

an overinvestment in the first stage and causes the misallocation of resources. The

model is tested with panel data from Taiwan flour industry by using non-linear SURE.

The empirical evidences are consistent with the propositions of the model.

1 1. Introduction

Recent game theoretic contributions, such as Fundenberg and Tirole (1984), Bulow,

Geanakoplos and Klemperer (1985), and Roller and Sickles (2000) emphasize the

strategic effect of capacity. These models have a two-stage setup in common. In the first

stage, firms make capacity decision followed by a price-setting game in the second stage.

The stage one variable (capacity) is used to develop a strategic effect to influence other

firms’ stage two decision (price). Higher investment in stage one induces a softer action

by other firms in stage two.

Our study differentiates from the previous literature by introducing an expected effect

of firm’s first stage investment on its rivals’ outputs in the second stage. Thus, under the

specification of a collusive regime, we find that a large capacity built in period one can

be used strategically to reduce other firms’ output in period two, since it can deter firms

from cheating under the agreement of collusion. This leads to an overinvestment in the

first stage and causes the misallocation of resources. The model is used to explain the

huge excess capacity in Taiwan flour market.

In 2000, an antitrust case brought Taiwan Fair Trade Commission (TFTC, hereafter)

against the flour industry association, which were alleged to eliminate price competition

by collusive arrangements. The most interesting part of the case is that these flour firms

have maintained an extremely low level of capacity utilization rate, which is 40% at the

industry level, for more than 20 years.1 If 20 years is considered as long-run in terms of

economics, flour firms should have enough time to adjust their capacity. Thus, the

existence of excess capacity in such a long time is quite opposite to the theory. Faced

with such a contradiction, our model could be used to investigate the nature of the excess

capacity.

2

The model is tested with panel data from Taiwan flour industry by using non-linear

SURE. As to the panel data used for the empirical investigation are given in a report on

the TFTC (2001) inquiry into collusive behavior in Taiwan market for flour. The

empirical evidences are consistent with those proposed by the model. Oligopolists expect

that the long-term effects of their capacity investment may act to deter its competitors’

outputs. Besides, a certain amount of collusion exists in the second stage. The results are

robust to the sensitivity analysis and to correction for errors in variables.

2. A model of competition for the flour industr y

In this section, we set up a two-stage game model to deal with the competition issue in

flour market. The framework presented in this section has been inspired by Roller and

Sickles (2000) and Dixon (1986). In this model, flour firms simultaneously decide the

fixed factor input (capital stock) in the first stage and then choose the variable factor

input (such as wheat or labor) so as to resolve quantity in the second stage. Thus, capital

is treated as an endogenous variable and is determined in the first stage that affects both

the production cost and market competition in the second stage.

We begin by specifying a quantity-setting game, where each flour firm produces a

homogeneous commodity and faces an inverse linear demand function of the form:2

) (

)

(

Q

a

b

q

Q

P

where P is the price and Q is the quantity demanded, and in equilibrium the market

quantity demanded equals the sum of the outputs of the individual firms. Let there be n

firms, each producing q such that _i

∑

is the industry output, and

i n i j j J q Q q Q =

∑

is the output of other firms in the same industry. Besides, the cost

structure can be specified as follows:

2

These assumptions could be justified by the technical structure of the industry we mentioned in section 2. For instance, the output of industry is generally homogeneous and the wholesale prices are generally uniform across firms. Therefore, the inverse demand function applies well.

3 i i i i i i SR i i i LR i q k C q m k r rk C ( , )= [ ( ) , ]+ (2)

where m is the variable factor input such as wheat and labor, _i LR i

C is the long-run cost

function, which amounts to short-run cost, SR i

C , added up by fixed cost r_ik_i. Note that,

given a capital stock (k_i =k_i0) and fixed capital price (r_i =r_i0), SR i

C is determined only

by q , which is function of _i m . We have i ( , )

0 0 i i i i i q m k r

q = as the short-run production

function. Thus, in the second stage, firms can only choose m to resolve _i q . However, _i

in the long-run (or the first stage), capital turns out to be variable and firms can change

their cost by purchasing k at a given price _i 0

i r .

Since the subgame perfect equilibrium is the solution concept, the game has to be

solved backwards. Firstly, we solve the second stage subgame in a conjectural variation

framework. We, then, turn to the first stage in which capital stock (or capacity) is

determined. Thus, in the second stage, each firm faces the following problem.

i i i i i i J i i i i it SR i it t i m m w r k m q Q r k m q P q C q Q P i − + = − = ) , ( ] ) , ( [ ) ( ) ( max 0 0 0 0 π (3)

Given a predetermined capital level (k ), in the short-run, production cost of firm i is ₀

determined only by the product quantity, which gives the total variable cost (w_im_i) at

factor pricew . We assume that _i w is exogenously determined. The first order condition _i

is given by, 0 ) 1 ( − = ∂ ∂ + + ∂ ∂ i i i i i i _{q w} m q b m q P θ (4) where i i m q ∂ ∂

is the marginal productivity of the variable input. Under the

conjectural-variation framework, the conjectural variation is

i J i q Q ∂ ∂ = θ . As stated earlier, J

Q is the output of other firms in the same industry. If we were interested in both the

existence and pattern of interdependence, it would be adequate to allow each firm to have

4

degree of freedom. Fortunately, we are only interested in the existence of oligopolistic

interdependence, it would be sufficient to evaluate the aggregate output response of the

other n 1− firms anticipated by firm i. Thus, by following Roller and Sickles (2000), and

Farrell and Shapiro (1990), we assume that θ_i =θ such that conjectural variation is the same across flour firms. In the special case of Cournot behavior, θ =0. Furthermore, under perfect competition θ =−1, and under collusive solution θ =n−1 , thus providing us with a basis for testing these hypotheses in the next section. We , then,

rewrite (4) as . ) 1 ( _i i i i _{b q} m q w P =− +θ ∂ ∂ − (5)

Since the price of variable factor is equal to its marginal revenue product, we

substitute i i i m q MR w ∂ ∂ ×

= into (5) and use the equilibrium condition of oligopoly market, which is MR=MC_i. After some manipulations, the first order condition (5) becomes

, ) 1 ( ε θ i i s P MC P− _{= +} (6) where Q q s i

i = is the market share of the individual firm,

Q P b − = ε is the price elasticity of demand. Equation (6) exhibits a oligopoly markup formula, which is

customarily used to measure the market power and is determined by market shares , _i

price elasticity ε and market conduct parameter θ . Econometrically, θ can be estimated as a free parameter and interpreted as “the average collusiveness of conduct”.

In the Cournot model, θ =0, the mark-up expression is reduced to

εi i s P MC P− ₌ . For

perfect collusion or monopoly, mark-up equals ε1, for perfect competition it is zero.

Since _i i i i _{MR MC} m q w _{= =} ∂

∂ , by suing (4) and

P

a

b

q

Q

5 ) 2 ( ) , , ( θ θ + − − = = b bQ a MC MC Q r q i J i J i i . (7)

Note that the slope of the reaction function is

) 2 ( 1 θ + −

. Then, we turn to the first stage

of the game in which capital stock is determined. It is notable that the firm’s equilibrium

quantities defined by the second stage is the function of his own capital and rivals’

capital in the first stage. Thus, the equilibrium outcome of the second stage can be

represented by q_i*(k_i,k_J) and m_i*(k_i,k_J), where k is the capital of other firms. The _J

fact that the capital is committed before the firm makes its output decision implies that

the firm can use its investment decision strategically: the firm can influence its rivals’

outputs through its choice of capital stock.

Given the previous specification, the profit of firm i in the first stage is

. ) , ( ] ) , ( [ max * * * i i i i J i i J J i i i ki P q k k Q q k k rk wm − − + = π

Without loss of generality, we can omit the functional arguments “*” to keep notation

uncluttered. Thus, the corresponding first order condition for each firm is given by

, 0 ] ) 1 [( − = ∂ ∂ + ∂ ∂ + + ∂ ∂ i i i J i i i i _{q r} k Q k q b k q P θ

which could be rewritten as

]. ) 1 [( i J i i i i i i k Q k q s P r k q P ∂ ∂ + ∂ ∂ + = − ∂ ∂ θ ε (8) Here, i i k q ∂ ∂

is the marginal productivity of the capital, and

i J k Q ∂ ∂

is the strategic effect

of firm i’s capacity on its rivals’ outputs. We assume that i J k Q ∂ ∂

is constant and is the

same across the firms. In the subsequent empirical work, we try to estimate

i J k Q ∂ ∂ to

check if overinvestment is used to reduce the outputs of rivals or not. Thus,

i J k Q ∂ ∂ is

the strategic effect in this essay. This specification is different from the literature.

6

directly enter into its rival’s profit function, and k can only influence _i Q through its _J

effect on q . However, in our model, which allows the possibility of collusion, firm i_i

conjectures that k can influence its rival’s outputs directly. Thus, high level of excess _i

capacity could be used to punish deviators more harshly since the firms will easily

dump a large amount of products to the market. The accomplishment of cartel is

determined by the damage each firm can inflict on the others by producing up to the

capacity and dumping on the market. In this specification, large capacity is used as a

tool to punish the cheaters. Excess capacity is not from bad planning but is an

instrument to enforce the collusive agreement.

The economic significance of

i J k Q ∂ ∂

is evident if we bring the optimality conditions of

first stage and second stage together. The arrangement could be done by substituting (6)

into (8) and reducing (8) to

. 0 effect Strategic effect Direct = ∂ ∂ + ∂ ∂ − 43 42 1 4 43 4 42 1 ε i i J i i i i Ps k Q MC k q r (9)

According to Fudenberg and Tirole (1984) and Roller and Sickles (2000), (9) can be

decomposed into two effects. By changing k , firm i has a direct effect on its profit _i

( _i i i i MC k q r ∂ ∂

− ), which is the effect of firm i’s stage one investment on its cost. This effect

could not influence the output of firm j. On the other hand, the strategic effect (

εi i J Ps k Q ∂ ∂ )

results from the two-stage specification, which allows for the influence of firm i’s

investment in the first stage on the output of firm j in the second stage. Whenever i J k Q ∂ ∂

is zero, there is no strategic effect, and (9) reduces to _ik

i i i i i i MR MRP k q MC k q r = ∂ ∂ = ∂ ∂ =

which corresponds to one-stage, simultaneous move quantity game. However, if the

strategic effect dose exist and <0

∂ ∂ i J k Q

, then, the theoretical inferences seem to indicate

7

to reduce other firms’ output in period two.

Finally, in equation (9), <0 ∂ ∂ i J k Q means _i i i i MC k q r ∂ ∂

> , under the oligopoly equilibrium (MR=MC_i), which implies that capital price (r_i) is larger than its marginal revenue of product ( k

i

MRP ). Thus, a small marginal productivity of capital (

i i k q ∂ ∂ ) caused

by overinvestment in period one leads to an misallocation of resources in period two.3

3. Data, Empir ical Specification and Estimation

Data. Although there are 10 major firms in the industry, yet the TFTC data contains

only nine of them. The period that the data set covered is between 1994 and 1998. Thus,

we have 45 observations for the regression.

Empirical Specification. Econometrically, we should proceed the above model by

estimating demand function and two optimality conditions (6) and (9) from supply side

simultaneously. This approach needs to specify a linear demand function such as

cZ bQ a

P= − + , in which P is the flour price, Q is the industry output, and Z is a

set of some exogenous variables, so that we could estimate the elasticity of demand ε . However, the span of data covers only 5 years such that pertinent demand elasticity

cannot be estimated. We have to select a plausible parametric value for demand elasticity

to implement the nonlinear regression analysis. Thus, we use 1.0 as the demand elasticity

in the baseline specification. Furthermore, in order to make the model persuasive, a

sensitivity analysis will be performed to check the robustness of the empirical result.

Since the model has to be imbedded within a stochastic framework for empirical

implementation, we assume that both equations (6) and (9) are stochastic due to errors in

optimization where e1_i and e2i are error terms. We now apply these two optimality

conditions, obtained from previous theoretical framework to test the market behavior of

3 _{This results is consistent with the findings of Eaton and Grossman (1984), Yarrow (1985), Dixon (1986),}

and Roller and Sickles (2000). These models exhibit the asymmetry between k and m that leads to a non-optimal capital-labor ratio. Although production is efficient in the short-run, the strategic use of capital makes firms are not on their long-run cost functions.

8

flour industry in Taiwan. First, rewrite (6) as

i i i _e s MC P 1 ) 1 ( 1 + + − = ε θ (10)

Second, after some manipulations, (9) could be written as

P r k Q P MC k Q k q s i i J i i J i i i ε ε ∂ ∂ − ∂ ∂∂ ∂ = 1

Then, we differentiate reaction function (7) with respect to k to get _i

θ + − = ∂ ∂∂ ∂ 2 1 i J i i k Q k q , and let J i i J Q k k Q ∂ ∂ =

γ as the elasticity to measure the impact of individual firm’s investment on its rivals’ output. We have

i J i i i i e PQ k r P MC s 2 1 ) 2 ( 1 _{− +} + − = ε γ ε θ . (11)

Empirical Results. Using these two functional forms we estimate the system of two

equations (10) and (11) by non-linear SURE. We also correct the covariance matrix for

conditional heteroscedasticity and serial correlation. Note that the coefficients we

estimate are θ and γ .

Table 1 Empirical Results for Two-Stage Game (ε =1)

Coefficient Estimates Standard Deviation

θ 7.70* 0.06

γ _−0.29*

0.02

Notes: The estimates of γ is converted into elasticity. Number of observations = 45. ∗ denotes that the estimates is significant at the level of 1%.

In Table 1, the main result is that the baseline specification (ε =1.0) generates the expected sign of θ and γ . For the measurement of market power (θ ), there is

9

sufficient evidence to suggest that flour firms monopolize the market through collusion.

The estimated θ is 7.70 which is significantly different form 0 (Cournot model) and 1

− (perfect competition model). Since there are nine flour firms in the sample, the result of θ =7.7 is approximated to n−1=8 under collusive regime. This implies that firms do work out some forms of concerted actions to monopolize the market. Thus, our

empirical evidences support the decision made by the TFTC.

For the effect of strategic investment, which determines whether two-stage setup can

be reduced to single-stage model, the result exhibits a negative and significant

29 . 0

− =

γ . The fact that the capital stock is determined before the firm makes its output decision implies that the firm can use its investment decision strategically. For the

individual firm, it conjectures that 1% increase in capital investment could reduce the

outputs of its rivals by 0.29%. This encourages the firm to increase its capacity beyond

the optimal level.

4. Conclusion

In this essay, a two-stage game model is set up to deal with the strategic effect of

firm’s capital investment on its rivals’ outputs. The model is tested with panel data from

Taiwan flour industry. The empirical evidences show that oligopolists expect that the

long-term effects of their capacity investment may act to deter its competitors’ outputs.

This leads to the overinvestment in the first stage and causes the misallocation of

1 References

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2

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Differentiated Products, Journal of Industrial Economics, 33, 515-530. Evaluation

In this essay, a two-stage game model is set up to deal with the strategic effect of

firm’s capital investment on its rivals’ outputs. We also use a legal case to study the

concrete arrangements for the cartel to carry out the collusion. The empirical

evidences show that oligopolists expect that the long-term effects of their capacity

investment may act to deter its competitors’ outputs. The results might allow this

paper to be published in the academic journal. We also expect that this study is helpful