科技部補助專題研究計畫成果報告
期末報告
高科技廠商的最適生產結構調整: 以台灣的晶圓代工產業之生
產靈活性對公司表現指標之影響為例
計 畫 類 別 ： 個別型計畫 計 畫 編 號 ： MOST 103-2410-H-004-022-執 行 期 間 ： 103年08月01日至104年10月31日 執 行 單 位 ： 國立政治大學經濟學系 計 畫 主 持 人 ： 李文傑 共 同 主 持 人 ： 王信實 計畫參與人員： 此計畫無其他參與人員 報 告 附 件 ： 移地研究心得報告 處 理 方 式 ： 1.公開資訊：本計畫可公開查詢 2.「本研究」是否已有嚴重損及公共利益之發現：否 3.「本報告」是否建議提供政府單位施政參考：是，經濟部 中 華 民 國 105 年 02 月 01 日中 文 摘 要 ： 目前既有的文獻在探討高科技廠商的生產靈活性 (production flexibility)時，完全忽略了對廠商的個別生產績效指標，如生產 力，要素投入調整，不同生產技術調整運用的影響。縱使仍有為數 不少的經濟學或是商學研究雖已考慮生產靈活性對生產成本及廠商 競爭力的改善效果，然而由於一般理論模型設定皆失於簡略及未能 精確描述生產靈活性的理論涵義，以及個別公司之營運資料難以取 得。此二原因造成探討不同程度的廠商生產靈活性對廠商生產績效 指標的影響之研究仍付諸闕如。針對這個缺失，本研究計畫從新理 論模型的設定及建構個人廠商營運表現的資料庫著手改善，如 :(1)由一個明確定義的固定替代彈性 (CES)的理論模型以及可以自 由調整生產替代性技術的理論模型來具體描述生產靈活性的重要角 色(2)本計畫也對台灣晶圓代工產業，建構細步的營運表現的資料庫 。如此，採用模型校正(Parameter Calibration)刻化理論模型參數 以計算出公司層級的生產靈活性程度。運算結果顯示，晶圓代工的 兩家主要廠商其關鍵勝出條件為產品品質，及由技術累積形成的關 鍵技術力，以及生產彈性。台積電席捲市場的原因為其技術領先而 聯電能繼續生存的主要理由為其具有相當高的生產彈性。後續，並 可藉由擬真分析 (Counterfactual Analysis) 計算廠商的生產靈活 性改善是如何影響 (1) 生產要素配置 (2)生產技術調整的程度，並 以之做各項產業政策分析。 中 文 關 鍵 詞 ： 生產靈活性、生產技術調整、模型校正、晶圓代工產業
英 文 摘 要 ： What is the relationship between the production flexibility and the observed firm-level performance such as
productivities, development of production techniques and ease of adjustment in factor allocations within an high-technology sector? This question is left unexplored though a vast Business literature on manufacturing flexibility and production efficiency. This is because the concept of
production flexibility has not been formalized or
rigorously studied theoretically in the existing studies and the lack of disaggregated firm-level data of
operational details in the interested IT manufacturing sectors. To remedy these two problems, this proposal formalizes the concept of “production flexibility‘‘ using a constant elasticity of substitution (CES)
production function. This specification in turn allows us to calibrate industry and firm-level production function parameters, using an constructed data set of the foundry industry with giant duopolists producing over 70 percent of the world products. We found that the giant TSMC has
dominated the market by its reputed quality and accumulated techniques while UMS remains surviving in the market by its flexibility. This enables us to gain better insight toward understanding the duopolists‘s technology flexibility choice and their consequences for factor allocation and production efficiency. Such an endeavor also permits future
counterfactual policy experiments using a structural model consistent with the empirically observed industry
framework.
英 文 關 鍵 詞 ： Production Flexibility, Productivity, Adjustment Cost, Counterfactual Analysis, Semi-conductor Foundry Industry.
行政院國家科學委員會補助專題研究計畫
□期中進度報告
█期末報告
高科技廠商的最適生產結構調整:
以台灣的晶圓代工產業之生產靈活性對公司表現指標影響為例
計畫類別：█個別型計畫 □整合型計畫
計畫編號：NSC -103-2410-H-004 -022
執行期間：103 年 8 月 1 日至 104 年 10 月 31 日
執行機構及系所：國立政治大學經濟系
計畫主持人：李文傑
共同主持人：王信實
計畫參與人員：王平
本計畫除繳交成果報告外，另含下列出國報告，共 1 份：
■移地研究心得報告
□出席國際學術會議心得報告
□國際合作研究計畫國外研究報告
處理方式：除列管計畫及下列情形者外，得立即公開查詢
□涉及專利或其他智慧財產權，□一年□二年後可公開查詢
中 華 民 國 105 年 1 月 31 日
1
目 錄
摘要 ... II Abstract ... 錯誤! 尚未定義書籤。 一、 前言 ... 1 二、 研究方法 ... 5 2.1 理論模型 ... 6 2.2 延伸參數 ... 11 三、 資料與結果分析 ... 錯誤! 尚未定義書籤。 四、 結論 ... 錯誤! 尚未定義書籤。 六、 參考文獻 ... 錯誤! 尚未定義書籤。高科技廠商的最適生產結構調整: 以台灣的晶圓代工產
業之生產靈活性對公司表現指標之影響為例
摘要
目 前 既 有 的 文 獻 在 探 討 高 科 技 廠 商 的 生 產 靈 活 性 (production
flexibility)時，完全忽略了對廠商的個別生產績效指標，如生產力，要
素投入調整，不同生產技術調整運用的影響。縱使仍有為數不少的經濟學
或是商學研究雖已考慮生產靈活性對生產成本及廠商競爭力的改善效果，
然而由於一般理論模型設定皆失於簡略及未能精確描述生產靈活性的理論
涵義，以及個別公司之營運資料難以取得。此二原因造成探討不同程度的
廠商生產靈活性對廠商生產績效指標的影響之研究仍付諸闕如。針對這個
缺失，本研究計畫從新理論模型的設定及建構個人廠商營運表現的資料庫
著手改善，如:(1)由一個明確定義的固定替代彈性 (CES)的理論模型以及
可以自由調整生產替代性技術的理論模型來具體描述生產靈活性的重要角
色(2)本計畫也對台灣晶圓代工產業，建構細步的營運表現的資料庫。如此，
採用模型校正(Parameter Calibration)刻化理論模型參數以計算出公司層
級的生產靈活性程度。運算結果顯示，晶圓代工的兩家主要廠商其關鍵勝
出條件為產品品質，及由技術累積形成的關鍵技術力，以及生產彈性。台
積電席捲市場的原因為其技術領先而聯電能繼續生存的主要理由為其具有
相當高的生產彈性。後續，並可藉由擬真分析 (Counterfactual Analysis)
計算廠商的生產靈活性改善是如何影響 (1) 生產要素配置 (2)生產技術
調整的程度，並以之做各項產業政策分析。
關鍵詞: 生產靈活性、生產技術調整、模型校正、晶圓代工產業
Designing Manufacturability in an IT Industry : the Case of the
Semi-conductor Foundry Industry in Taiwan
Abstract
What is the relationship between the production flexibility and the observed firm-level performance such as produc-tivities, development of production techniques and ease of adjustment in factor allocations within an high-technology sector? This question is left unexplored though a vast Business literature on manufacturing flexibility and production efficiency. This is because the concept of production flexibility has not been formalized or rigorously studied theo-retically in the existing studies and the lack of disaggregated firm-level data of operational details in the interested IT manufacturing sectors. To remedy these two problems, this proposal formalizes the concept of ”production flexibility” using a constant elasticity of substitution (CES) production function. This specification in turn allows us to calibrate industry and firm-level production function parameters, using an constructed data set of the foundry industry with giant duopolists producing over 70 percent of the world products. We found that the giant TSMC has dominated the market by its reputed quality and accumulated techniques while UMS remains surviving in the market by its flexibili-ty. This enables us to gain better insight toward understanding the duopolists’s technology flexibility choice and their consequences for factor allocation and production efficiency. Such an endeavor also permits future counterfactual policy experiments using a structural model consistent with the empirically observed industry framework.
Keywords: Production Flexibility, Productivity, Adjustment Cost, Counterfactual Analysis, Semi-conductor Foundry Industry.
1 Introduction
The discussion regrading production flexibility as well as the producing factor al-location always fascinates economists. The economists would like to ease the gap between the long believed neoclassical production technology assuming constant re-turns to scale technology and the production process that governs the real profitable model in the production side. In this vein the firm would have to deal with some lim-ited access to the key production techniques or limlim-ited usage of producing factors in the short-term adjustment production batch. In this research project I; thus, describe the role of techniques substitution in an industry characterized by labor adjustment costs (such as labor hoarding): For example, the skill intensive IT industry where firms can adjust their Human Capital (labor in the follow-up setting in the model formulation) in the short-run only if they incur some adjustment costs. The research
efforts are exerted to show that the ability to adjust production techniques (towards labor intensive production) mitigates labor adjustment costs and further to investigate whether the flexibility of production determines the ease of technique substitution.1 Specifically, we try to revisit the big-push development issues in the semiconductor foundry industry and apply a well-devised theoretic model to calibrate the crucial factors in the name of production flexibility to back out the embeded rationales that shape the leading Semiconductor Foundry Industry in Taiwan.2
This paper begins by briefly reviewing the economics as well as the business e-conomics literatures in the discussion of how the levels of production flexibilities affects the firm-level performance in the manufacturing sectors. On the one hand, the theroretic and empirical economic literatures elaborates on the importance of pro-duction flexibilities. First, the notion of flexibility in the operations of the firm seems to have been first introduced into the economics literature by George Stigler ( JPE, 1939). He defined flexibility as those attributes of a production technology which accommodate greater output variation. Following Stigler’s definition on flexibility, Marschak and Nelson ( Metroeconomica, 1962) take more specific view in the fol-lowing three viewpoints: (1) The size of the choice set: a more flexible initial action preserves more choices for actions in the following periods. (2) Marginal cost: a more flexible plant requires less additional cost to move toward the next position (essentially the Stigler view). (3) Marginal expected profit: a more flexible plan-t generaplan-tes more profiplan-ts or smaller losses in moving plan-to a new posiplan-tion. Jones and Ostroy (RES, 1984), for example, following Marschak and Nelsons ideas of flexibil-ity. They defined flexibility as “a property of initial positions. It refers to the cost, or possibility, of moving to various second period positions.” Industrial economists also view the flexibility as means to counter the uncertainty existing in the market. Burton Klein (1984) states a dynamically efficient firm is one which generates new ideas and is quick to respond to new ideas, wherever they happen to originate, so that
1Although there is a vast Business literature on manufacturing flexibility and production efficiency. Nonetheless, the concept of production
flexibility has not been formalized or rigorously studied theoretically.
2The foundry industry originates itself by the the separation of the production side from a whole vertically integrated semiconductor company.
In other words, a semiconductor fabrication plant operation (foundry) is splitted from an integrated circuit design operation, into separate companies or business units. The separate foundry firms use cutting-edge production facilities or techniques to do the contracting manufacturing for the brand name semiconducotr designing companies.
it can take advantage of these new ideas before its competitors do. By organizing the firm and providing internal incentives in such a way as to be able to react quickly to new impulses, no matter what their particular content, it is possible to reduce the cost of a negative impact and to increase the probability of a positive result for the firm. In this vein, Vives (IJIO, 1986) has analyzed the choice of flexible production technology in a game-theoretic approach and found that if the technology is inflexi-ble, capacity is a good precommitment variable; on the other hand, if the technology is flexible, precommitment to a particular capacity is not a good strategy. Vives has also shown that where firms have the same precision of information, an increase in uncertainty leads them to seek a more flexible position. Other than the theoretic viewpoints, Mills and Schumann ( AER, 1985) formulated and tested the hypothe-sis that a competitive equilibrium with demand fluctuations can have diverse firms with varying cost structures coexisting: ”Small firms are able to compete successful-ly with large, more staticefficient producers by absorbing a disproportionate share of industrywide output fluctuations. This is possible because small firms use production technologies that are more flexible than those chosen by large firms. Large firms . . . (have) lower minimum average costs, due largely to scale economies, while small competitors have an offsetting advantage in their superior responsiveness to cycli-cal or random swings in demand. (Mills and Schumann, p. 766).” However, all the above mentioned literatures share one common research caveat by lacking in the full specification of production flexibility in the producer side. The best work horse idea is to take the ad hoc assumption by adding a reduced form model to apply a vague idea of production flexibility to the ambiguous production efficiency measurement mentioned in the current existing literatures.
On the other hand, there has been a vast literature “manufacturing flexibility and production efficiency”. The literature highlights “insurance” and “strategic compet-itiveness” roles of manufacturing flexibility. To the end of insurance role, including Fine and Freund (1990, Management Science), Fine (1993, Handbook in OR and MS) and Netessine et al. (2002, OR), many have argued that managers see flexibil-ity as an adaptive response when hedging against uncertain environments (factor or
technology related uncertainty as well as product uncertainty). With respect to the competitiveness role, as pointed out for example by Roller and Tombak (1990, Jour-nal of Industrial Economics) and (1993, Management Science), high manufacturing flexibility of a particular firm can induce higher competitive pressure for its rivals, and increase profit margins for the relatively more flexible firm. Concerning both views: Firms might “bank flexibility”, that is holding flexibility in reserve to meet future needs. In this sense flexibility is an investment which creates future options for a company. Gerwin (1993, Management Science) provides empirical evidence in line with these theoretical arguments: As the author shows, for example Minneso-ta Manufacturers Survey reports that as market unpredicMinneso-tability and competitiveness increases, flexibility of the production processes go up.
Concerning the effects of factor and technology flexibility on efficiency the fol-lowing theoretical and empirical observations are important for our work: In an em-pirical study, Upton (1995, Harvard Business Review) documents for the U.S. paper-manufacturing industry, where products are quite comparable across manufacturers that there is substantial cross-sectional heterogeneity in production flexibility. Inter-estingly, the paper finds that newer and bigger processes are typically better able to perform quick changeovers than older and smaller machines. As another empirical evidence, Adler et al. (1999, Organization Science) studies the effect of organization-al flexibility on efficiency. By providing detailed micro-level evidence from Toyotas NUMMI plant in California, authors document that companys policy changes that have led to increases in its labor input flexibility stimulated production efficiency at the beginning of 1990s, and gained the company a large competitive advantage over its big rivals Ford, Chrysler and GM. Theoretically, Slack (1988, Computer-Integrated Manufacturing Systems) proposes a hypothetical business model where a manufacturing firm determines the appropriateness of various level of manufactur-ing flexibility by analyzmanufactur-ing how flexibility contributes to the competitive advantage of the firm, and how flexibility guides the selection of various productive resources, such as the production technology. Goyal and Netessine (2007, Management Sci-ence) study the causality of structure of competition on firms technology flexibility
choice using a game-theoretic framework. Formally, the authors show that the cost premium which a duopolist is willing to accept, when investing in a flexible technol-ogy, is higher than the premium which a monopolist is willing to accept, if the rival duopolist is investing in a rigid production technology.
This paper is related with both Economic and Business Economics literature by the following two dimensions. Theoretically, this paper contributes by formalizing the concept of “production flexibility” using a constant elasticity of substitution (CES) production function in the theoretic set-up. Numerically, this theoretical specification in turn allows us to calibrate industry and firm-level production function parameters and run counterfactual policy experiments using a structural model consistent with the empirically observed industry framework. In the end, our theoretic model when using the intended hand-collected firm-level dataset in the Semiconductor Foundry industry would reflect the true interaction intertwined among production flexibility, factor allocations and production efficiency in the firm level.
The large Taiwan Semiconductor Manufacturing Company (TSMC) dominates the market by its premium quality and accumulated production techniques while UMC stay survived in the market by its production flexibility to keep its cost pegging the level of TSMC.
The rest of the paper is structured as follows. Section 2 introduces the data and describes the characteristics of educational networks between venture capitalists and start-up entrepreneurs. Section 3 discusses the hypotheses to be tested and show the descriptive statistics of all the used variables. Section 5 presents the empirical analysis and the main findings. Section 6 concludes.
2 The Methodology
This paper is devoted to investigate the causal relationship intertwined among pro-duction flexibility, productivity and factor allocation. In this end, the past literatures in both economics and business economics did not specify clearly the formalized definition of profuction flexibility. This paper; thus, have to suggest a clear and valid theoretic definition of production flexibility that would facilitate our parameter
cli-bration by applying the firm-level foundry firms data. In the last step we can have a policy implication on the IT developmental miracles in the Taiwanese foundry in-dustry.
Thus in the first stage of the research, I would suggest a theoretic framework methodologically to capture the effects of production flexibility on the productivities and factor allocation. The concept of “production flexibility” can be best descibed by using a constant elasticity of substitution (CES) production function in the theo-retic set-up since this theotheo-retical specification in turn would numerically allow us to calibrate industry and firm-level production function parameters. The counterfactual policy experiments using the structural model consistent with the empirically ob-served industry framework can also be possible to point out the policy implications accordingly. In the end, our theoretic model when using the intended hand-collected firm-level dataset in the Semiconductor Foundry industry would reflect the true in-teraction intertwined among production flexibility, factor allocations and production efficiency in the firm level.
2.1 Methods: The Theoretic Model
Here in this section, a benchmark theoretic framework without any factor adoption frictions (labor adjustment cost in terms of the labor hoarding ) is proposed. A gen-eralized version with the prospective factor adoption frictions will follow later.
To reflect the importance of production flexibility in the output production in semi-conductor manufacturing industry, we assume that firms within a narrowly-defined industry produce by using the procured labor and capital in the form of CES aggre-gator introduced by Solow (1956). Specifically, suppose the production function of a firm takes the following functional form:
Y = [λ(aKK)ρ+ (1 − λ)(aLL)ρ]
1 ρ
Firm decides on K and L (namely, production factors), and aK and aL (production
At first, we study firm’s optimization problem without labor and technique adjust-ment costs. Then, we will introduce technique adjustadjust-ment and labor adjustadjust-ment costs and study the implications of labor hoarding on optimum technique substitution.
2.2 Cost Minimization
The optimization program is devised to be a 2-stage process. In the first stage the firm decides on the optimalK − L(as in the standard neoclassical cost minimization problem), and then in the second stage the aK − aL decision is made.3
2.2.1 Factor Allocation: K-L Choice
This is the standard Neo-classical cost minimization problem:
min
K,L wL + rK (1)
s.t. Y = [λ(aKK)ρ+ (1 − λ)(aLL)ρ]
1
ρ (2)
Denote the lagrange multiplier with respect to constraint (2) with µ1. Note that
solving for µ1 will provide the marginal cost of producing one extra unit of output.
FOCs with respect to K and Lare as the following:
K : r = µ1λaρKKρ−1[(aKK)ρ+ (aLL)ρ] 1−ρ ρ ⇒ K = µ 1 1−ρ 1 r −1 1−ρλ 1 1−ρa ρ 1−ρ K Y (3) L : w = µ1(1 − λ)aρLLρ−1[(aKK)ρ+ (aLL)ρ] 1−ρ ρ ⇒ L = µ 1 1−ρ 1 w −1 1−ρ(1 − λ) 1 1−ρa ρ 1−ρ L Y (4)
Putting (3) and (4) together we can solve for the optimum K/Lratio:
K L = w r 1−ρ1 λ 1 − λ 1−ρ1 aK aL 1−ρρ . (5)
PluggingK andL from (3) and (4) into (2) gives:
Y = " r aK ρ−1ρ λ1−ρ1 µ ρ 1−ρ 1 + w aL ρ−1ρ (1 − λ)1−ρ1 µ ρ 1−ρ 1 #1ρ Y
3The novel feature of this research is that the dual approach is utilized to solve for the optimal production factor adoption and the production
Solving forµ1 gives the unit cost of production: µ1 = c(r, w; aK, aL, ρ) = " r aK ρ−1ρ λ1−ρ1 + w aL ρ−1ρ (1 − λ)1−ρ1 #ρ−1ρ (6) The total cost of producingY units:
C(Y ) = c(r, w; aK, aL, ρ)Y C(Y ) = " r aK ρ−1ρ λ1−ρ1 + w aL ρ−1ρ (1 − λ)1−ρ1 #ρ−1ρ Y. (7)
Having determined the unit cost of production we can move on to determine the optimumaK − aL Choice.
2. Production Technique Choice: aK-aL
Our next objective is to find the optimum aK and aL that minimize the unit cost of
production derived at (6):
min aK,aL
c(r, w; aK, aL, ρ)
s.t. H(aK, aL) = z,
wherez is the scale of knowledge, andH(aK, aL)summarize the combinations of aK − aL pairs that attain a certain level ofz. For now, we don’t assume adjustment
costs in techniques (an adjustmentφ()function will be introduced later on). We will put adjustment costs later on to see how things change when we deviate from this benchmark model. We assume that H(aK, aL) = aαKa1−αL . So the second stage cost
minimization problem can be stated as the following:
min aK,aL " r aK ρ−1ρ λ1−ρ1 + w aL ρ−1ρ (1 − λ)1−ρ1 #ρ−1ρ (8) s.t. aαKa1−αL = z (9)
aK and aL: aK : r ρ ρ−1λ 1 1−ρa− ρ ρ−1−1 K " r aK ρ−1ρ λ1−ρ1 + w aL ρ−1ρ (1 − λ)1−ρ1 #ρ−1ρ −1 = µ2αaα−1K a1−αL (10) aL : w ρ ρ−1(1 − λ) 1 1−ρa− ρ ρ−1−1 L " r aK ρ−1ρ λ1−ρ1 + w aL ρ−1ρ (1 − λ)1−ρ1 #ρ−1ρ −1 = µ2(1 − α)aαKa −α L (11) Putting (10) and (11) together we can solve for the optimumaK/aL ratio:
aK aL = r w 1 − λ λ 1ρ 1 − α α ρ−1ρ . (12)
Plugging (12) in (5) solves for the optimum K/Lratio:
K L = w r α 1 − α λ 1 − λ. (13)
To solve for the scale ofaK andaL as a function of z,w/r, αand ρ, we plug (12)
in (9), and solve: aK = z r w 1−α α 1 − α (1−α)(1−ρρ ) 1 − λ λ (1−α)(1ρ) , (14) aL = z r w −α α 1 − α −α(1−ρρ ) 1 − λ λ −α(ρ1) . (15)
aK andaL in (6) provides the unit cost of production in terms ofz,w, r,α andρ:
c(w, r; z, α, ρ) = 1 zr αw1−α λα(1 − λ)1−α− 1 ρ " α 1 − α 1−α + 1 − α α α# ρ−1 ρ (16) Putting related terms together:
c(w, r; z, α, ρ) = 1 z r α λ α −1ρ!α w 1 − α 1 − λ 1 − α −1ρ!1−α (17) When K and L are perfect complements (ρ → −∞) unit cost of production converges to: c(w, r; z, α, ρ) = 1 z r α α w 1 − α 1−α , (18)
when K and L are perfect substitutes (ρ → 1) unit cost of production converges to: c(w, r; z, α, ρ) = 1 z r λ α w 1 − λ 1−α . (19)
2.3 Optimum Level of Production Flexibility
Studying comparative statistics at marginal cost function (17) provides important insights:
1. As a standard result, the level of technology z monotonically decreases the marginal cost of production. So if firms had a choice of technology level z, they would choose the highest possible one because this would minimize the unit cost of production and hence maximize profits.
2. Another standard result is related torandw: As the input prices rise the marginal cost of production rises monotonically.
Just to compare the effects ofρon cost of productioncin this current specification (with λshares in CES) against that of from the previous section (withoutλ shares in CES), we produce the following math step which is comparable to (17):
c(w, r; z, α, ρ) = 1 zr α w1−α λ α (1 − λ)1−α−1 | {z } Ω1 1 ρ α α (1 − α)1−α | {z } Ω2 1−ρ ρ (20)
The first term inside the square brackets (Ω1) is greater than 1 whereas the second
term (Ω2) is smaller than 1. Therefore, with λ shares in CES specification we no
longer have the weird limiting case that implies as ρ → 0, c() → 0.
However, one can easily see that the impact of more flexibility on marginal cost of production depends onλ andα. Specifically, if
λα(1 − λ)1−α > αα(1 − α)1−α (21)
2.4 Optimum scale of production
Optimum scale of production can be computed for various demand specifications. For the simplest case of linear demand:
Yd = b1P + b2,
where Yd is quantity demanded and P as the price of output, firm’s optimization problem is: max Y Y Y − b2 b1 − c(w, r; z, α, ρ)Y.
The optimum scale of production can be derived as:
Y∗ = b1c(w, r; z, α, ρ) + b2
2
Note that as for case 1 described above: Firm 1, who has 0 < ρ1 < ρ2 compared
to another Firm 2, operates at a larger scale of production due to its cost advantage associated in being closer to the unit elasticity of input substitution. For case 2 the opposite result is true.
We can derive clear results for the case of monopolistic competition, Cournot and Bertrand as well.
The results so far show that:
1. Production flexibility is important for the cost of production and hence explain-ing price, scale differences across firms.
2. The effects of flexibility on firm performance is not trivial. It all depends how firms’ production flexibility compares to unit-elastic production function.
2.5 Generalized Model with Technique and Labor Adjustment Costs
Suppose firms face (linear) labor adjustment costs when they deviate from a pre-set
¯
dynamic analysis, L¯ will be the level of capital utilized in the previous period. So, firm’s cost minimization problem now looks as the following:
min
K,L wL + rK +η|L − ¯L| (22)
s.t. Y = [λ(aKK)ρ+ (1 − λ)(aLL)ρ]
1
ρ (23)
Denote the lagrange multiplier with respect to constraint (23) with µ1. Note that
solving for µ1 will again provides us the unit cost of producing one extra unit of
output. FOCs with respect to K andL are as the following:
K : r = µ1λa ρ KK ρ−1[(a KK)ρ+ (aLL)ρ] 1−ρ ρ ⇒ K = µ 1 1−ρ 1 r −1 1−ρλ 1 1−ρa ρ 1−ρ K Y (24) L : w +η = µ1(1 − λ)aρLLρ−1[(aKK)ρ + (aLL)ρ] 1−ρ ρ ⇒ L = µ 1 1−ρ 1 w −1 1−ρ(1 − λ) 1 1−ρa ρ 1−ρ L Y (25)
Putting (24) and (25) together we can solve for the optimum K/Lratio:
K L = w +η r 1−ρ1 λ 1 − λ 1−ρ1 aK aL 1−ρρ . (26)
PluggingK andL from (24) and (25) into (23) gives:
Y = " r aK ρ−1ρ λ1−ρ1 µ ρ 1−ρ 1 + w +η aL ρ−1ρ (1 − λ)1−ρ1 µ ρ 1−ρ 1 #1ρ Y
Solving forµ1 gives the unit cost of production:
µ1 = c(r, w; aK, aL, ρ) = " r aK ρ−1ρ λ1−ρ1 + w +η aL ρ−1ρ (1 − λ)1−ρ1 #ρ−1ρ (27) The total cost of producingY units:
C(Y ) = c(r, w; aK, aL, ρ)Y C(Y ) = " r aK ρ−1ρ λ1−ρ1 + w +η aL ρ−1ρ (1 − λ)1−ρ1 #ρ−1ρ Y. (28)
aK− aLChoice with Technique and Labor Adjustment Costs
As we did at section 2-4, we will proceed with factor adoption frictions in terms of technique adjustment and the labor adjustment costs. Our objective is to find the optimum aK and aL that minimize the marginal cost of production with technique
and labor adjustment costs:
min aK,aL
c(η, r, w; aK, aL, ρ) +φ(aK, aL)c(η, r, w; aK, aL, ρ) (29)
s.t. H(aK, aL) = z, (30)
Denote the Lagrange multiplier associated with the hyperbola byµ2. FOCs with
respect toaK and aL are:
aK: (1 + φK)(r) ρ ρ−1λ1−ρ1 a− ρ ρ−1−1 K " r aK ρ ρ−1 λ1−ρ1 + w +η aL ρ ρ−1 (1 − λ)1−ρ1 #ρ−1ρ −1 = µ2αaα−1K a 1−α L (31) aL: (1 + φL)(w +η) ρ ρ−1(1 − λ)1−ρ1 a− ρ ρ−1−1 L " r aK ρ−1ρ λ 1 1−ρ+ w +η aL ρ−1ρ (1 − λ) 1 1−ρ #ρ−1ρ −1 = µ2(1 − α)aαKa −α L (32)
Putting (31) and (32) together we can solve for the optimumaK/aL ratio:
aK aL = r w +η 1 − λ λ 1ρ 1 − α α ρ−1ρ 1 + φK 1 + φL ρ−1ρ . (33)
Plugging (33) in (26) solves for the optimumK/Lratio:
K L = w +η r α 1 − α λ 1 − λ 1 + φL 1 + φK . (34) I define again: Φ ≡ 1 + φL 1 + φK (35) To solve for the scale ofaK andaL as a function of z,w/r, αand ρ, we plug (33)
in (30) and use (35): aK = z r w +η 1−α α 1 − α (1−α)(1−ρρ ) 1 − λ λ (1−α)(1ρ) Φ(1−α)(1−ρρ ),(36) aL = z r w +η −α α 1 − α −α(1−ρρ ) 1 − λ λ −α(1ρ) Φ−α(1−ρρ ). (37)
Unit cost of production is then provided by: c(Φ, η) = 1 zr α(w +η)1−α λα(1 − λ)1−α− 1 ρ " αΦ 1 − α 1−α + 1 − α αΦ α# ρ−1 ρ (38) Putting related terms together:
c(Φ, η) = 1 z r α λ α −ρ1!α w +η 1 − α 1 − λ 1 − α −1ρ!1−α Φα(1−ρρ ) [1 + α (Φ − 1)] ρ−1 ρ = 1 z r α λ α −ρ1!α w +η 1 − α 1 − λ 1 − α −1ρ!1−α Φα 1 + α (Φ − 1) 1−ρρ (39) Remarks.
Labor Adjustment Costs, Technique Adjustment Costs and Flexibility.
1. The unit cost of production with labor and technique adjustment costs isc(Φ, η). 2. The only term that contains the labor-adjustment cost parameter atc(Φ, η) func-tion from (39) is the first term in brackets. η creates a wedge above the neoclassi-cal unit cost of production (cfrom equation 17) . η has a monotone distortionary effect. The higherη the larger is the distortion.
3. As we can see from c(Φ, η)the only term that contains η does not directly inter-act with the flexibility parameterρ.
⇒This means unlike what we have seen in the previous section with technique adjustment costs (c(Φ)), a change in flexibility ρ does not dampen the distor-tionary effects of labor-adjustment costs on unit cost of production (relative to
c).
* Result. Flexibility dampens the distortionary effects of adjustment costs only when adjustment friction is related to techniques. When adjustment friction is only related to labor (or capital), which means aK andaL can be
freely adjusted, then flexibility does not have an influence on relative wedges created above the unit cost of production.
The figure 1 below draws the unit cost function c(Φ, η) as a function of Φ and shows an increase inη shifts the unit cost function. The figure 2 drawsη and Φ com-binations that keep the unit cost constant (iso-cost): Ability to substitute techniques vs. ability to adjust labor.
) ; (Φη c c(Φ;ηh) c(Φ;ηl) 1
Figure 1. The Effect of a rise in η on unit cost of production
η ( ; ) 1 Φη c ) ; ( 2 Φη c 1
Figure 2. Isocost Functions with c1(Φ;η)>c2(Φ;η)
Φ
3 Data and Results 3.1 Data
We compute the average α and average ρ for two Taiwanese foundry firms (UMC and TSMC), by assuming λ = 12 (Later we will test the robustness of the numeri-cal results when variatingλ ∈ [0.45, 0.55]). We use the Taiwanese borrowing rate announced by the Bank of Taiwan as our interst rate in the computation. There we can compute the average r = 4.29% (assuming including the depreciation) as well as have all the quarterly data (for 2000Q1-2013Q2) of Y,K,L,c, andw.45
3.2 Calibration in the Benchmarked Model
At calibrating the model parameters we will exploit the following equations:
K L = w r α 1 − α λ 1 − λ (40) aK aL = r w 1 − λ λ 1ρ 1 − α α ρ−1ρ (41) Y = [λ(aKK)ρ + (1 − λ)(aLL)ρ] 1 ρ (42) z = aαKa1−αL (43) c(w, r; z, α, ρ) = 1 z r α λ α −ρ1!α w 1 − α 1 − λ 1 − α −1ρ!1−α (44) Since we knowK,L,w,r, c, andY we can follow the following algorithm:
Step 1: Using sector-level data from the Taiwanese foundry industry we will have a “guess” forλ by probably adopting the industrial average output share of labor: This will provide us 5 equations with 5 unknowns.
4Y is derived from the quarterly net sales data of each of foundry firm. K is the quarterly stock of fixed capital net of depreciation. L is derived
by using the annual data of hired employees. We also have the ship-out quantities of the wafers which are recomputed into the 8 inch equivalent wafers and then we divide the netsales by the 8 inch ship-out quantities to get the unit price. The unit cost is derived by the multilication of the unit price and the operating cost percentage which can be computed by subtracting the operating margins from one. Finally the wage can be computed by dividing the total labor compensation by the hired employee numbers.
5The K, Y, c, w data are backed out from the quarterly media annoucement of the operational financial information of the foundry firms. The
Step 2: Using equation 40 back-outα. Step 3: Using equation 41 write aK
aL(ρ).
Step 4: Draw out the labor input L and aL from the CRS production function
(42). Then, put aK
aL(ρ)into (42). Now, we know aL(ρ).
Step 5: PutaL(ρ)and aaKL(ρ)into 43 and derivez(ρ).
Step 6: Putz(ρ)in 44, and solve forρ.
Step 7: Solve for all model parameters, and derive the firm-level TFP from 42. (Note: Sectoral parametersρandαwill be common to all firms, therefore knowl-edge z will derive idiosyncratic TFP differences across the Taiwanese foundry producers in step 7.)
Step 8: Provide a test for the model by comparing the z we derived from the model against thez from the patent count data.
Sinceρ is in the exponent the system will be highly non-linear. Sinceρ is in the exponent the system will be highly non-linear.
Using equation (60) we back out αi, i ∈ {U M C, T SM C} as explained above:
The average firm-level αi, i ∈ {U M C, T SM C}specifically can be computed by
Ki Li = wi ri αi 1 − αi λ 1 − λ, i ∈ {U M C, T SM C}
The benchmark case is λ = 12
αU M C = 0.6081
αT SM C = 0.6184
Forλ = 12, the equation (69) reduces to:
wiLi ciYi = 1 − αi αi αi [αi(1 − αi)] 1 ρi, i ∈ {U M C, T SM C} (45)
Now using the following average data observations we back-out the flexibility parameter for each firm:
cY wL U M C = 6.28 cY wL T SM C = 6.70 cU M C = 31157 cT SM C = 28121
The equation (70) can be further simplified to
ρi = log[αi(1 − αi)] log ciYi wiLi + αilog( 1−αi αi ) , i ∈ {U M C, T SM C} (46)
Plugging the associated data into equation (71) yields the firm-level elasticity of sub-stitutionρas follows:
ρU N C = 0.9131
ρT SN C = 0.9000
We thus proceed the computation of the firm-level knowledge zi based on the
equation (67) and the firm-level T F Pi based on the definitions of the neoclassical
total factor productivities (TFP) as follows:
T F Pi = Yi [λ(Ki)ρi + (1 − λ)(Li)ρi] 1 ρi , i ∈ {U M C, T SM C} (47)
The firm-level zi andT F Pi is computed and reported in the following section.
4 Conclusion
Collecting and supplementing data on Taiwanese Foundry Industry and modelling the foundry business competition with a CES framework, We found that the giant TSMC has dominated the market by its reputed quality and accumulated techniques while UMS remains surviving in the market by its flexibility. We also discuss the relation between Labor Adjustment Costs, Technique Adjustment Costs and Flexi-bility. Flexibility dampens the distortionary effects of adjustment costs only when adjustment friction is related to techniques. When adjustment friction is only related to labor (or capital), which means aK and aL can be freely adjusted, then flexibility
does not have an influence on relative wedges created above the unit cost of produc-tion.
References
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[4] Grewin, D., “Manufacturing exibility: a strategic perspective, Management Sci-ence, 39:4 (1993), 395-410.
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1
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出國類別：研究)
「赴美國聖路易華盛頓大學
執行 103 年國科會補助專題計畫：」
心得報告書
服務機關：國立政治大學經濟系 職稱：助理教授 姓名：李文傑 出國地區：美國密蘇里州聖路易市 出國期間：104 年 4 月 12 日 至 104 年 4 月 27 日 報告日期：104 年 4 月 30 日出國成果報告書（格式）
計畫編號 執行單位 政大經濟系 出國人員 助理教授李文傑 出國日期 104 年 4 月 12 日至 104 年 4 月 27 日， 共 16 日 出國地點 美國密蘇里州聖路易市 出國經費 新台幣 10 萬元 報告內容摘要(請以 200 字～300 字說明) 在國科會計畫以及王平院士的支持下，本研究團隊得以委派經濟系李文 傑助理教授得以至聖路易華盛頓大學的動態經濟研究中心與王平院士 共同針對國科會計畫「高科技廠商的最適生產結構調整: 以台灣的晶圓 代工產業之生產靈活性對公司表現指標影響為例」，發展計劃中所需的 理論模型，並且進一步推導相關的參數動差估計式，此次研究成果豐 碩，已完成理論模型設定並分析。根據理論模型縮減式之分析討論以及 實際資料的運算結果，我們歸納出以下結論，晶圓代工的兩家主要廠商 其關鍵勝出條件為產品品質，及由技術累積形成的關鍵技術力，以及生 產彈性。台積電席捲市場的原因為其技術領先而聯電能繼續生存的主要 理由為其具有相當高的生產彈性。 。3
目 錄
壹、 前言………4
貳、 研究過程………4
參、 本次出國目的………5
肆、 本次出國研究之理論模型的重要結論………6
伍、 心得與建議………7
壹、 前言:
本年度國科會計畫「高科技廠商的最適生產結構調整: 以台灣的 晶圓代工產業之生產靈活性對公司表現指標影響為例」，須以一精密 理論模型支持主要推論，由於研究時程設定相當緊迫，因此研究團 隊指派經濟系助理教授李文傑前往美國聖路易華盛頓大學動態經濟 研究中心，與王平院士針對研究議題: 對於不同廠商的生產彈性對 於組織層級競爭力的影響，密集討論並設定一精密的理論模型以供 後續政策分析建議及評估做一確實推估，在與王平院士的 16 天密切 互動中，完成核心理論模型的推導，得出了晶圓代工的兩家主要廠 商其關鍵勝出條件為產品品質，及由技術累積形成的關鍵技術力， 以及生產彈性。台積電席捲市場的原因為其技術領先而聯電能繼續 生存的主要理由為其具有相當高的生產彈性，出國學者帶回的寶貴 研究成果將供研究團隊後續之參數估計及供政策推論之用。除此之 外，出國學者也得以將此一寶貴研究成果，廣泛徵詢聖路易華盛頓 大學的著名學者，以確實改進本理論模型的可能缺失，在這 4 周的 緊密研究形成中，相信對此一計畫的品質及未來發表方向都有了更 進一步的掌握，以下則針對與王平院士完成的研究成果做詳細說明。
貳、 研究過程:
美國聖路易華盛頓大學的動態經濟研究中心為聖路易地區內 動態經濟學領域的最高層級學術交流及研討中心，其成立主旨在 於鼓勵方法及發展對於人力資本，區域經濟，國際經濟，經濟體 內重要人力資本累積等各類美國及世界重要經濟體面對的當前重 要經濟議題之關注及進一步提出解決方法之高階研究場所，因此 本次國科會計畫研究團隊因計畫「高科技廠商的最適生產結構調5 整: 以台灣的晶圓代工產業之生產靈活性對公司表現指標影響為 例」，與動態經濟研究中心之研究主旨切合，故透過計畫主持人李 文傑與計畫協同研究人員王平院士的申請，經半個多月的行政申 請作業程序後，由動態經濟研究中心的秘書 Carissa 發給研究成員 經濟系助理教授李文傑邀請函，即期動身前往美國密蘇里州聖路 易市。 總計本次在美國動態經濟研究中心主要在與王平院士處理關 於廠商生產彈性的 1. 各項文獻整理以及分析 2. 設定及發展生產 彈性測度的理論模型 3.推導理論模型的縮減式 4. 發展模型參數 校正方法 (Calibration) 5.提出目前現階段的結論及建議等。總歸來 說，除了出國學者義務必須完全參與的與王平院士的討論及工作 之外，仍盡力貢獻所學及研究知識與國際學者積極交流，了解最 新發展經濟學中關於資源錯置領域的明日之星研究，並在出國人 研究生產彈性問題以及資源錯置衡量上讓與會的各國同領域研究 者了解國科會計畫目前研究進展，使其他學者了解此際計畫的研 究資料，獨有的模型設定，以及模型運算的結果，相信在同行加 持下，研究成果會更加豐富。
參、 本次出國研究目的:
在研究計畫發想之初，計畫主持人李文傑即針對目前各研究 文獻作衣全面性回顧及整理，了解到晚近發展之探討廠商生產彈 性差異的經濟模型，為了反映不同生產彈性對企業全要素生產力 (TFP)差異的影響，既存文獻有兩種不同的處理形式，如前所述(1) 商學領域中的生產彈性個案研究(2)經濟學中的生產彈性的定義 的研究，此為近期異質性生產者(Heterogeneous Producers)的一般均衡模型研究著力及側重方向，然而不同模型側重點並不能精 確符合台灣晶圓代工的產業特性，因此由模型所得的政策並不能 給予台灣此類的新興工業國訂定研發及產業發展的政策依據，例 如探討生產彈性的早期文獻 Stigler (1939) 所提及的產業內廠 商間的生產彈性差異致使廠商觀摩差異是一例，其發現了以下生 產彈性與廠商競爭力的重要關係: (i)生產彈性與生產成本為一負 向的指數關係，其稱之為廠商的可行的最適生產規模調整，每一 次成功的生產規模調整將導致廠商可用高一個層級的規模生產較 低成本的產品(ii) 生產彈性與產品品質之間的抵換關係，生產彈 性之高低並不意味著廠商產品品質的走向，過去的商學文獻通過 運用個別廠商的表現個案來推測此兩者關係並不必然存在。 基於既存文獻分別有兩種不同的型式處理生產彈性對於廠商競 爭力的影響，最終，本一年期計畫的執行兼顧由於生產彈性的討 論以及各項企業表現指標的衡量，對台灣晶圓代工產業的個別生 產者選取的規模與社會最適規模差異的影響，而我們完成了台灣 晶圓代工產業的產業結構及生產彈性差異對產業的生產效率差別 的分析，而所建構的台灣晶圓代工的廠商層級資料庫可以供做後 續關於東亞新興工業國家產業轉型或是產業生產力比較之使用， 本研究結果實際證明晶圓代工的兩家主要廠商其關鍵勝出條件為 產品品質，及由技術累積形成的關鍵技術力，以及生產彈性。台 積電席捲市場的原因為其技術領先而聯電能繼續生存的主要理由 為其具有相當高的生產彈性，並充分探究不同的生產彈性在不同 的產業結構上，對廠商 TFP 的影響。
肆、 此次出國研究之重要結論
一. 實證結果7 晶圓代工的兩家主要廠商其關鍵勝出條件為產品品質，及由技術 累積形成的關鍵技術力，以及生產彈性。台積電席捲市場的原因為其 技術領先而聯電能繼續生存的主要理由為其具有相當高的生產彈性。 後續，並可藉由擬真分析 (Counterfactual Analysis) 計算廠商的生產靈 活性改善是如何影響 (1) 生產要素配置 (2)生產技術調整的程度，並 以之做各項產業政策分析。
伍、 心得與建議
本次出國研究，發展以及推倒出的模型的強項在於我們將可
以實際計算產業內廠商之生產彈性以及各項生產力衡量指標
的差異性間的關係，並討論政策當局可否藉著調整產業結構
以矯正廠商的資源錯置程度並藉此提升產業的生產效率，結
果發現晶圓代工的兩家主要廠商其關鍵勝出條件為產品品
質，及由技術累積形成的關鍵技術力，以及生產彈性。台積
電席捲市場的原因為其技術領先而聯電能繼續生存的主要理
由為其具有相當高的生產彈性。
科技部補助計畫衍生研發成果推廣資料表
日期:2016/02/01 科技部補助計畫 計畫名稱: 高科技廠商的最適生產結構調整: 以台灣的晶圓代工產業之生產靈活性對公 司表現指標之影響為例 計畫主持人: 李文傑 計畫編號: 103-2410-H-004-022- 學門領域: 經濟發展、技術變動與成長 無研發成果推廣資料103年度專題研究計畫研究成果彙整表
計畫主持人：李文傑 計畫編號： 103-2410-H-004-022-計畫名稱：高科技廠商的最適生產結構調整: 以台灣的晶圓代工產業之生產靈活性對公司表現指標之 影響為例 成果項目 量化 單位 備註（質化說明 ：如數個計畫共 同成果、成果列 為該期刊之封面 故事...等） 實際已達成 數（被接受 或已發表） 預期總達成 數（含實際 已達成數） 本計畫實 際貢獻百 分比 國內 論文著作 期刊論文 0 0 100% 篇 研究報告/技術報告 0 0 100% 研討會論文 1 1 100% 於2014年台灣經 濟學年會發表 專書 0 0 100% 章/本 專利 申請中件數 0 0 100% 件 已獲得件數 0 0 100% 技術移轉 件數 0 0 100% 件 權利金 0 0 100% 千元 參與計畫人力 （本國籍） 碩士生 0 0 100% 人次 博士生 0 0 100% 博士後研究員 0 0 100% 專任助理 0 0 100% 國外 論文著作 期刊論文 1 1 100% 篇 獲得國際期刊遴 選收錄 研究報告/技術報告 0 0 100% 研討會論文 1 1 100% 獲得2015年之公 共經濟年會發表 機會 專書 0 0 100% 章/本 專利 申請中件數 0 0 100% 件 已獲得件數 0 0 100% 技術移轉 件數 0 0 100% 件 權利金 0 0 100% 千元 參與計畫人力 （外國籍） 碩士生 3 3 100% 人次 博士生 1 1 100% 博士後研究員 0 0 100% 專任助理 0 0 100% 其他成果 （無法以量化表達之 成果如辦理學術活動 、獲得獎項、重要國 訓練重要產業分析人力，發展之模型以及生產彈性衡量方法可供後續的政策分 析及擬真分析之用際合作、研究成果國 際影響力及其他協助 產業技術發展之具體 效益事項等，請以文 字敘述填列。） 成果項目 量化 名稱或內容性質簡述 科 教 處 計 畫 加 填 項 目 測驗工具(含質性與量性) 0 課程/模組 0 電腦及網路系統或工具 0 教材 0 舉辦之活動/競賽 0 研討會/工作坊 0 電子報、網站 0 計畫成果推廣之參與（閱聽）人數 0
