The producer for the chip market Theory of _207

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The producer for the Theory of chip market

Abstract: This paper chip production activities for the special economic phenomenon, a mathematical model based on the classification of chip makers and dynamic adjustment of the production process, and profit maximization under the constraints of the problem and to consider further production of CPU and Chip Set combination mode. Theoretical point of view from the producers tried to give a preliminary analysis and interpretation.

Keywords: hierarchical control of production quality control cost production mix pricing model

Author: Zhou Xiaokang Shanghai University of Finance and Economics School of Economics, 00 (Base Class)

the information industry (IT) to provide what kind of products? In short, nothing more than the hardware (hardware), software (software) and services (service) [1]. In the late 1970s, early 1980s, the information industry prototype generation phase, IBM (International Business Machines Corporation) is the largest provider of hardware, the largest software provider and the largest service providers. Over time, the information industry began to evolve, hardware, software and services providers become increasingly specialized, and each formed a relatively independent of the market. [2] a variety of semiconductor integrated circuit chip is the main hardware products. We selected the most renowned and largest provider of semiconductor integrated circuit chip of Intel, as objects, expand the market for chip producers research.

one, Intel's grade production process
Intel produce a variety of semiconductor integrated circuit chips for personal computers (PC) of the two main product is the central processing unit (CPU) and chip set (Chip Set), the two are complements. Both have a complete product line, the former classification to the production, which does not take grade production. Intel 80486 processor in the production grade product was first introduced, followed by the production strategy to become the industry prevailing practices, including Intel main competitor AMD. What is the classification of production

? Companies directly in the production line for semi-finished stage in the CPU, using OC (over clock) and the heat stability test, successive separation of the low frequency from high-end products, the mainstream products and low-end products. The Pentium 3 (Pentium!!!) As an example: First of all frequencies in the 1GHz to accept the first round of testing, part of the CPU burned scrap, compliance of the CPU locked at 866MHz, packaged off the assembly line; not reached then stop the production line CPU in the 933MHz frequency to accept the second round of testing, standards of CPU locking in 800MHz, packaged off the assembly line, yet again downgraded the chip testing standards; and so on, until the lower limit of the test frequency, the last part of the CPU to catch the last train off the assembly line at last the rest out as unqualified. (Figure 1) clearly all the same production line is based on the same CPU core (die) of the different frequency chips. This mode of production known as grade production, the author called collinear flexible production (difference between the common line with the automobile manufacturing flexible production).

Figure 1: Classification production flow chart (fragment)

frequency identification (test frequency)

why the CPU to the decentralized production, and do not use Chip Set grade production? Just from the technical considerations, if n species with m kinds of CPU Chip Set, is bound to have m × n combinations, apparently increased the complexity of system production.

theoretical studies have shown a variable if by a large number of tiny, independent random factors, then the variable is usually a normal variable. Extremely complex structure of the chip to make it belong with the above situation. Therefore, we use the normal distribution in the mathematical model can simulate the visual classification of the production process.

1. normal

when μ = 0 and σ = 1 when the standard normal distribution.

2. the production of normal distribution based on hierarchical model (Figure 2)
to establish the actual speed of the chip frequency density function of independent variables,[link widoczny dla zalogowanych], plus several articles in the reference line perpendicular to the horizontal axis .

1) market acceptance of the boundary line on the left of the reference
agreed that any products are not accepted by the market, the enterprise quality control decisions and behavior can only occur in the actual production of the reference line on the right.

2) Quality Control Quality control of the border
overflow portion of the left boundary of substandard goods. Agreed to make the most optimal business decisions, this time to accept lower market combined with the quality control of the border, two reference lines coincide.

3) production technology, production technology, the boundary
overflow portion of the right side of the border scrap. Agreed the production reached the maximum production technology boundaries.

above three reference lines, the density function itself and the independent variables are axle enclosed area, that is, the production range. As the basis for our simulation of the dynamic adjustment process.

Second, the classification process of dynamic adjustment of production and technological progress

the dynamic adjustment process under
1) σ change (Figure 3)

μ changes (Figure 4)

σ and μ also changes (Fig. 5)
4) quality control of borders (market acceptance of the border) translation
Typically, quality control of the borders (market acceptance of the border) continue to improve: First of all, the unlimited capacity of information processing needs of the market to accept the boundary increase; then, companies were forced to take the initiative to adapt to the situation to improve quality control of the border.

exception: If the quality control of the border and market acceptance of such boundaries do not coincide agreed, then there is room for lowering the quality control of the border, this dynamic adjustment means that companies broaden the scope of business, its products began to penetrate the low-end .

5) the boundary shift production technology and quality control of the border
(market acceptance of the border) were similar to the translation, in general, the border has continued to improve production techniques, so that the kernel does not modify the chip design under the premise , can produce higher frequency, more powerful chips.

special case: the 1999 Taiwan earthquake of local chip companies paralyzed the normal production, when production resumed after the pause, obviously not the optimal state, causing abnormally production technology boundaries shift inward. [3]

6) the dynamic adjustment process based on Moore's Law
Intel founder Gordon Moore in 1965 at Fairchild (Fairchild interpreter, another translation of Fair Chai Degong Division) established the first law of the semiconductor industry - , while the price of integrated circuits just reduced by half. Changes in the chip core, in fact, we can introduce a new density function curve, to complete the dynamic adjustment process based on Moore's Law, the operation can be both simple cf σ and μ change the dynamic of technological progress under the conditions of handling the challenges of the adjustment process methods.

7) Non-technical progress under the dynamic adjustment process
addition to the technical progress under the dynamic adjustment process, there are still non-technological progress under the dynamic adjustment process (it can not be through normal distribution model to directly reflect), typically exogenous type of expanded reproduction, that is not good by increasing the rate of chip production, but by adding new production lines to improve production. AMD recently the construction of Fab30 plant in Germany, Intel Ireland, the construction of Fab24 factory is one such business behavior.

to Craig Barrett from Andy Gelu Fu, Intel CEO have to take two By means of the successful use of the above, Intel under non-technological advances improving the dynamic adjustment process.

non-technical progress under the dynamic adjustment process, by the upstream product (silicon, transistors, etc.) supply and the supply prices, may be a positive benefit, there may be negative negative .

III, grade reference lines to maximize profits under the constraint of the problem
border in quality control and production technology division of the boundary distance between us and other n-1 条 grade reference lines (Fig. 6), sub- class labels of the products after the frequency of the abscissa by the classification decision guides, the lowest level of the chip frequency of the abscissa by the quality control of the border decision. Easy to find, identify the frequency and the actual frequency is not the same, familiar with PC hardware, readers from personal experience, is understandable. Therefore, reference line is not a rigid classification, grade production is also part of the controllable: agreement can serve as a low-frequency high-frequency chip chip sales, but not as high-frequency low-frequency chip chip sales may be partially integrated into the product to higher-level products. Popular have to say, is not allowed shoddy, but allow a good charge times. Since the formation of low and high frequency of n-level product series, each product corresponds to a price, then it also formed the n-level price series.

grade production, tiered pricing problem of profit maximization can be derived, which consists of two aspects, one is to maximize revenue, the other is to minimize costs.

exist in the chip market monopoly in the market for PC's CPU, Intel and AMD competing divide up the market share of almost all, Cyrix has been VIA (VIA Technologies) mergers, and VIA of the only a very small proportion of the volume. So we need to be considered in the analysis of monopoly price factors.

1. from the proceeds to consider

the monopolist's demand curve to the right under the slope, the only prices to increase sales, so that the total income and the relationship between price changes To determine the elasticity of demand: Ed> 1 时, TR and P reverse changes; Ed = 1 时, TR and P independent of changes; Ed AC, the companies were excessive profits π = PQ-TC or π = (P-AC) Q.
2) P = AC, the vendors were out of the normal offset of profits or income.
3) PAVC, may continue production; if the different levels of P production, tiered pricing, the manufacturer can implement a flexible decentralized operations, to avoid the risk of loss, to ensure that the case in the broader organization of production. It also provides a convenient market competition, product prices can have more space, or even loss of business to gain market share, loss of profits of products from other levels of compensation, on the whole still guarantees profitable.

a good rate of product costs directly linked, which means that quality control and cost control directly linked. Assumptions do not take grade production, the product will result in the procurement of a single one, then eventually the market acceptance of the boundary shift, the quality control of the border were forced to shift. Change in production technology and production capacity of the same boundary conditions, the product down the overall good rates, scrap and elimination products increases, the cost rise.

3. supplementary statement on the monopolistic competition

TL Sauty et al in 1970 proposed a combination of qualitative and quantitative, systematic, hierarchical analysis of the problem, called the level method (Analytic Hierarchy Process, referred to as AHP). This method is more complicated, more ambiguous easy way to make decisions, especially for those difficult to fully quantitative analysis of the problem.

[8] studied the use of AHP method the nature of monopolistic competition, monopolistic competition that the market equilibrium price is the quality comparison matrix of the principal eigenvectors, and on the basis of maximum profit for producers of the conditions. [8] also pointed out the advantages of participating firms in monopolistic competition the equilibrium price level is relatively low up to maximize profits, he said the price competition in a relatively good position, there is strong competition. And it is often the initiator of a price war, he cut the price to the lowest level, but just realize its profit maximization. The mathematical deduction and the real chip market in line, reflecting the characteristics of the chip market producers, at this stage is to have this monopoly Intel producers a competitive advantage.

The model is a single-product firms monopolistic competition model, we expanded into multi-product firms monopolistic competition model of monopolistic competition that is involved in the vendor market is a product output beam, rather than a a single product. Expand the quality of the comparison matrix, through the block to distinguish between its own products and relationships with other vendors products; take k-sub-sub-type to characterize the relationship between the market and the market as a whole. This product corresponds to the product bundle pricing to determine the benchmark price, quality comparison matrix that is the main feature vectors.

assignment functions as long as the establishment (in reference line of the abscissa position classification variables, and other performance factors as the reference variable), we can pair a set of chips ratio for a given quality factor, in order to build quality comparison matrix . Meanwhile, the aforementioned normal distribution model can output vector is given by integration. From a psychological point of view

, grading will be beyond many people's ability to judge, not only increasing the difficulty of making judgments, but also may easily provide false information. Sauty et al experimentally compared under a variety of different scales to judge the correctness people, test results show that the 1-9 scale is ideal. Therefore, production of the series should not be too hierarchical, otherwise no significant difference between the assignment, the demand side can not distinguish between different products, through market will price convergence.

IV, CPU and Chip Set
combination mode of production we now consider the CPU and Chip Set for joint production.

not produced by Chip Set classification inevitably have to face the production of non-optimal state. Chip Set technically easier to produce than the CPU, in theory, can produce more equal material into the Chip Set, but the production of non-optimal state to offset this advantage. There, CPU's high returns that companies are more likely to produce it. (Figure Cool

construct an original point of non-linear concave production possibility frontier and linear yield curve, etc., to describe the production of selected models. Assume that the demand for CPU and Chip Set is 1:1, and profit maximization will lead to the supply gap Chip Set, Chip Set in turn do not support, CPU's excess supply of some of the producers, there will be no return.

In extreme cases, if the production possibility frontier is linear, business or even give up the production Chip Set. (Figure 9)

Chip Set this on the production must be compensated, compensation is the licensing and transfer of production. Third-party companies to pay royalties to Intel's patents for technology licensing, technology, or both enter into a patent cross-license agreement, of course, is a patented technology licensing time effect. Have a technical basis, the third-party companies can design compatible with the production of similar products, make up the supply gap Chip Set. Intel on several occasions at different times with the VIA (VIA), SiS (SiS), ALi (ALi) [4] and other companies to cross-license patented technology to enable them to produce enough volume to meet Chip Set launch of the new Intel CPU, but also expanded its technical reserves. Therefore, it is actually a joint product of intellectual property transactions under question. [5]

Recently, the U.S. Supreme Court's Festo automation machinery components sued Shoketsu patent infringement case made its ruling to cancel patents in the produced little change the basic functions of patent protection and the same products. The United States are common law countries, the use of case law, this ruling far-reaching, shaking the entire IT industry, need to be given adequate attention. [6]

V. CONCLUSIONS
First, although technological progress has always been throughout the chip manufacturing process, but the performance of the short term is not simply declining to make price the only factor. The short term, chip manufacturers can rely only on production optimization corresponding adjustment of output, thereby directly affect the market equilibrium price, in order to develop new products much lower than the costs, gain competitive advantage.

Second, the chip market clearing price and product quality, production-related characteristics and classification. The total production capacity in the case known, with the production model and empirical data classification can be directly derived the theoretical yield of each product. By assigning the function and quality of the comparison matrix, the beam can be indirectly derived products, the benchmark price, as well as individual product pricing, quality is the main feature vector comparison matrix, which is the market clearing price.

Finally, the chip manufacturer's proprietary trading may not be in accordance with the value of the patent itself, trying to make up for gaps in the supply of a product can also be a motivation factor of the patent deal. In other words, two or even cross-licensing patents, is a combination of the value of their patented technology to optimize and make the production of these two different properties.

In summary, the author of the initial chip makers to give the basic operations of the economics. Derived not only from the theoretical production quality control and grading of the direct impact on product pricing, and intellectual property rights will be extended to areas of the chip manufacturers to analyze patent licensing and transfer of production behavior. From the development of national high-tech industry perspective, we can draw useful lessons, namely, by the comparative advantages of production companies in exchange for absolute advantage of advanced technology to achieve rapid jump development. Taiwan's successful model worth learning from.