• Title/Summary/Keyword: Equilibrium problem

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Prediction of Scour Depth Using Incorporation of Cluster Analysis into Artificial Neural Networks (인공신경망모형과 군집분석을 이용한 교각 세굴심 예측)

  • Lee, Chang-Hwan;Ahn, Jae-Hyun;Lee, Joo Heon;Kim, Tea-Woong
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.2B
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    • pp.111-120
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    • 2009
  • A local scour around a bridge pier is known as one of important factors of bridge collapse. Two approaches are usually used in estimating a scour depth in practice. One is to use empirical formulas, and the other is to use computational methods. But the use of empirical formulas is limited to predict a scour depth under similar conditions to which the formulas were derived. Computational methods are currently too expensive to be applied to practical engineering problems. This study presented the application of artificial neural networks (ANN) to the prediction of a scour depth around a bridge pier at an equilibrium state. This study also investigated various ANN algorithms for estimating a scour depth, such as Backpropagation Network, Radial Basis Function Network, and Generalized Regression Network. Preliminary study showed that ANN models resulted in very wide range of errors in predicting a scour depth. To solve this problem this study incorporated cluster analysis into ANN. The incorporation of cluster analysis provided better estimations of scour depth up to 42% compared with other approaches.

Dynamic Economic Load Dispatch Problem Applying Valve-Point Balance and Swap Optimization Method (밸브지점 균형과 교환 최적화 방법을 적용한 동적경제급전문제)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.16 no.1
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    • pp.253-262
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    • 2016
  • This paper proposes a balance-swap method for the dynamic economic load dispatch problem. Based on the premise that all generators shall be operated at valve-points, the proposed algorithm initially sets the maximum generation power at $P_i{\leftarrow}P_i^{max}$. As for generator i with $_{max}c_i$, which is the maximum operating cost $c_i=\frac{F(P_i)-F(P_{iv_k})}{(P_i-P_{iv_k})}$ produced when the generation power of each generator is reduced to the valve-point $v_k$, the algorithm reduces i's generation power down to $P_{iv_k}$, the valve-point operating cost. When ${\Sigma}P_i-P_d$ > 0, it reduces the generation power of a generator with $_{max}c_i$ of $c_i=F(P_i)-F(P_i-1)$ to $P_i{\leftarrow}P_i-1$ so as to restore the equilibrium ${\Sigma}P_i=P_d$. The algorithm subsequently optimizes by employing an adult-step method in which power in the range of $_{min}\{_{max}(P_i-P_i^{min}),\;_{max}(P_i^{max}-P_i)\}$>${\alpha}{\geq}10$ is reduced by 10; a baby step method in which power in the range of 10>${\alpha}{\geq}1$ is reduced by 1; and a swap method for $_{max}[F(P_i)-F(P_i-{\alpha})]$>$_{min}[F(P_j+{\alpha})-F(P_j)]$, $i{\neq}j$ of $P_i=P_i{\pm}{\alpha}$, in which power is swapped to $P_i=P_i-{\alpha}$, $P_j=P_j+{\alpha}$. It finally executes minute swap process for ${\alpha}=\text{0.1, 0.01, 0.001, 0.0001}$. When applied to various experimental cases of the dynamic economic load dispatch problems, the proposed algorithm has proved to maximize economic benefits by significantly reducing the optimal operating cost of the extant Heuristic algorithm.

Dynamic Limit and Predatory Pricing Under Uncertainty (불확실성하(不確實性下)의 동태적(動態的) 진입제한(進入制限) 및 약탈가격(掠奪價格) 책정(策定))

  • Yoo, Yoon-ha
    • KDI Journal of Economic Policy
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    • v.13 no.1
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    • pp.151-166
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    • 1991
  • In this paper, a simple game-theoretic entry deterrence model is developed that integrates both limit pricing and predatory pricing. While there have been extensive studies which have dealt with predation and limit pricing separately, no study so far has analyzed these closely related practices in a unified framework. Treating each practice as if it were an independent phenomenon is, of course, an analytical necessity to abstract from complex realities. However, welfare analysis based on such a model may give misleading policy implications. By analyzing limit and predatory pricing within a single framework, this paper attempts to shed some light on the effects of interactions between these two frequently cited tactics of entry deterrence. Another distinctive feature of the paper is that limit and predatory pricing emerge, in equilibrium, as rational, profit maximizing strategies in the model. Until recently, the only conclusion from formal analyses of predatory pricing was that predation is unlikely to take place if every economic agent is assumed to be rational. This conclusion rests upon the argument that predation is costly; that is, it inflicts more losses upon the predator than upon the rival producer, and, therefore, is unlikely to succeed in driving out the rival, who understands that the price cutting, if it ever takes place, must be temporary. Recently several attempts have been made to overcome this modelling difficulty by Kreps and Wilson, Milgram and Roberts, Benoit, Fudenberg and Tirole, and Roberts. With the exception of Roberts, however, these studies, though successful in preserving the rationality of players, still share one serious weakness in that they resort to ad hoc, external constraints in order to generate profit maximizing predation. The present paper uses a highly stylized model of Cournot duopoly and derives the equilibrium predatory strategy without invoking external constraints except the assumption of asymmetrically distributed information. The underlying intuition behind the model can be summarized as follows. Imagine a firm that is considering entry into a monopolist's market but is uncertain about the incumbent firm's cost structure. If the monopolist has low cost, the rival would rather not enter because it would be difficult to compete with an efficient, low-cost firm. If the monopolist has high costs, however, the rival will definitely enter the market because it can make positive profits. In this situation, if the incumbent firm unwittingly produces its monopoly output, the entrant can infer the nature of the monopolist's cost by observing the monopolist's price. Knowing this, the high cost monopolist increases its output level up to what would have been produced by a low cost firm in an effort to conceal its cost condition. This constitutes limit pricing. The same logic applies when there is a rival competitor in the market. Producing a high cost duopoly output is self-revealing and thus to be avoided. Therefore, the firm chooses to produce the low cost duopoly output, consequently inflicting losses to the entrant or rival producer, thus acting in a predatory manner. The policy implications of the analysis are rather mixed. Contrary to the widely accepted hypothesis that predation is, at best, a negative sum game, and thus, a strategy that is unlikely to be played from the outset, this paper concludes that predation can be real occurence by showing that it can arise as an effective profit maximizing strategy. This conclusion alone may imply that the government can play a role in increasing the consumer welfare, say, by banning predation or limit pricing. However, the problem is that it is rather difficult to ascribe any welfare losses to these kinds of entry deterring practices. This difficulty arises from the fact that if the same practices have been adopted by a low cost firm, they could not be called entry-deterring. Moreover, the high cost incumbent in the model is doing exactly what the low cost firm would have done to keep the market to itself. All in all, this paper suggests that a government injunction of limit and predatory pricing should be applied with great care, evaluating each case on its own basis. Hasty generalization may work to the detriment, rather than the enhancement of consumer welfare.

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A Study on the Effect of Water Soluble Extractive upon Physical Properties of Wood (수용성(水溶性) 추출물(抽出物)이 목재(木材)의 물리적(物理的) 성질(性質)에 미치는 영향(影響))

  • Shim, Chong-Supp
    • Journal of the Korean Wood Science and Technology
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    • v.10 no.3
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    • pp.13-44
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    • 1982
  • 1. Since long time ago, it has been talked about that soaking wood into water for a long time would be profitable for the decreasing of defects such as checking, cupping and bow due to the undue-shrinking and swelling. There are, however, no any actual data providing this fact definitly, although there are some guesses that water soluble extractives might effect on this problem. On the other hand, this is a few work which has been done about the effect of water soluble extractives upon the some physical properties of wood and that it might be related to the above mentioned problem. If man does account for that whether soaking wood into water for a long time would be profitable for the decreasing of defects due to the undue-shrinking and swelling in comparison with unsoaking wood or not, it may bring a great contribution on the reasonable uses of wood. To account for the effect of water soluble extractives upon physical properties of wood, this study has been made at the wood technology laboratory, School of Forestry, Yale university, under competent guidance of Dr. F. F. Wangaard, with the following three different species which had been provided at the same laboratory. 1. Pinus strobus 2. Quercus borealis 3. Hymenaea courbaril 2. The physical properties investigated in this study are as follows. a. Equilibrium moisture content at different relative humidity conditions. b. Shrinkage value from gre condition to different relative humidity conditions and oven dry condition. c. Swelling value from oven dry condition to different relative humidity conditions. d. Specific gravity 3. In order to investigate the effect of water soluble extractives upon physical properties of wood, the experiment has been carried out with two differently treated specimens, that is, one has been treated into water and the other into sugar solution, and with controlled specimens. 4. The quantity of water soluble extractives of each species and the group of chemical compounds in the extracted liquid from each species have shown in Table 36. Between species, there is some difference in quantity of extractives and group of chemical compounds. 5. In the case of equilibrium moisture contents at different relative humidity condition, (a) Except the desorption case at 80% R. H. C. (Relative Humidity Condition), there is a definite line between untreated specimens and treated specimens that is, untreated specimens hold water more than treated specimens at the same R.H.C. (b) The specimens treated into sugar solution have shown almost the same tendency in results compared with the untreated specimens. (c) Between species, there is no any definite relation in equilibrium moisture content each other, however E. M. C. in heartwood of pine is lesser than in sapwood. This might cause from the difference of wood anatomical structure. 6. In the case of shrinkage, (a) The shrinkage value of the treated specimen into water is more than that of the untreated specimens, except anyone case of heartwood of pine at 80% R. H. C. (b) The shrinkage value of treated specimens in the sugar solution is less than that of the others and has almost the same tendency to the untreated specimens. It would mean that the penetration of some sugar into the wood can decrease the shrinkage value of wood. (c) Between species, the shrinkage value of heartwood of pine is less than sapwood of the same, shrinkage value of oak is the largest, Hymenaea is lesser than oak and more than pine. (d) Directional difference of shrinkage value through all species can also see as other all kind of species previously tested. (e) There is a definite relation in between the difference of shrinkage value of treated and untreated specimens and amount of extractives, that is, increasing extractives gives increasing the difference of shrinkage value between treated and untreated specimens. 7. In the case of swelling, (a) The swelling value of treated specimens is greater than that of the untreated specimens through all cases. (b) In comparison with the tangential direction and radial direction, the swelling value of tangential direction is larger than that of radial direction in the same species. (c) Between species, the largest one in swelling values is oak and the smallest pine heartwood, there are also a tendency that species which shrink more swell also more and, on the contrary, species which shrink lesser swell also lesser than the others. 8. In the case of specific gravity, (a) The specific gravity of the treated specimens is larger than that of untreated specimens. This reversed value between treated and untreated specimens has been resulted from the volume of specimen of oven dry condition. (b) Between species, there are differences, that is, the specific gravity of Hymenaea is the largest one and the sapwood of pine is the smallest. 9. Through this investigation, it has been concluded that soaking wood into plain water before use without any special consideration may bring more hastful results than unsoaking for use of wood. However soaking wood into the some specially provided solutions such as salt water or inorganic matter may be dissolved in it, can be profitable for the decreasing shrinkage and swelling, checking, shaking and bow etc. if soaking wood into plain water might bring the decreasing defects, it might come from even shrinking and swelling through all dimension.

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Analysis of Orthotropic Body Under Partial-Uniform Shear Load (부분(部分) 등분포(等分布) 전단하중(剪斷荷重)을 받는 이방성(異方性) 구조체(構造體)의 해석(解析))

  • Chang, Suk Yoon
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.4 no.1
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    • pp.1-10
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    • 1984
  • This dissertation presents an exact solution for the shearing and normal stresses of an orthotropic plane body loaded by a pairtial-uniform shear load. The solution satisfies the equilibrium and compatibility equations concurrently. An Airy stress function is introduced to solve the problem related to an orthotropic half-infinite plane under a partial-uniform shear load. All the equations for orthotropy must be degenerated into the expressions for isotropy when orthotropic constants are replaced by isotropic ones. The author has evaluated all the equations of orthotropy and succeeded in obtaining exactly identical expressions to the equations of isotropy which were derived independently by means of L'hospital's rule. The analytical results of, isotropy ate compared with the simple results of other investigator. Since a concentrated shear load is a particular case of partial-uniform shear load, all the equations of partial-uniform shear load case are degenerated into the expressions for concentrated load case of isotropy and orthotropy. The formal solution is expressed in terms of closed form. The numerical results for orthotropy are evaluated for two kinds and two different orientations of the grain of wood. The type of wood considered are three-layered plywood and laminated delta wood. The distribution of normal and shearing stresses are shown in figures. It is noted that the distribution of stresses of orthctropic materials dependson the type of materials and orientations of the grain.

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Variation and Forecast of Rural Population in Korea: 1960-1985 (농촌인구(農村人口)의 변화(變化)와 예측(豫測))

  • Kwon, Yong Duk;Choi, Kyu Seob
    • Current Research on Agriculture and Life Sciences
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    • v.8
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    • pp.129-138
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    • 1990
  • This study investigated the relationship between the cutflow of rural population and agricultural policy by using time series method. For the analytical tools, decomposition time series methods and regression technique were employed in computing seasonal fluctuation and cyclical fluctuation of population migration. Also, this study predicted farmhouse, rural population till the 2000's by means of the mathematical methods. The analytical forms employed in forecasting farmhouse, rural population were Exponential curve, Gompertz curve and Transcendental form. The major findings of this study were identified as follows: 1) Rural population and farmhouse population began to decrease from 1965 and hastily went down since 1975. Rural population which accounted for 36.4 percent, 35.6 percent of national population respectively in 1960 diminished about two times: 17.5 percent, 17.1 percent respectively. 2) The rapid decreasing of the rural population was caused because of the outflow of rural people to the urban regions. Of course, that was also caused from the natural decreases but the main reason was heavily affected more the former than the latter. In the outflowing course shaped from rural to the urban regions, rural people concentrated on such metropolis as Seoul, Pusan, Keanggi. But these trends were diminishing slowly. On the other hand, compared with that of the 1970's the migration to Keanggi was still increasing in the 1980's. That is, people altered the way of migration from the migration to Seoul, Pusan to the migration to the out-skirts of Seoul. 3) The seasonal fluctuation index of population migration has gone down since the June which the request of agricultural labor force increases and has turned to be greatly wanted in the March as result of decomposition time series method. As result of cyclical analysis, the cyclical patterns of migration have greatly 7 cycle. 4) As result of forecasting the rural and farmhouse population, rural and farmhouse population in the 2000 will be about 9,655(thousand/people) and 4,429(thousand/people) respectively. Thus, it is important to analyze the probloms that rural and farmhouse population will decrease or increase by the degree. But fairly defining the agricultural into a industry that supply the food, this problem - how much our nation need the rural and farmhouse population - is greatly significant too. Therefore, the basic problems of the agricultural including the outflows of rural people are the earning differentials between rural and urban regions. And we should regard the problems of the gap of relative incomes between rural and urban regions as the main task of the agricultural policy and treat the agricultural policy in the viewpoint of developing economic equilibrium than efficiency by using actively the natural resources of the rural regions.

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Limit Pricing by Noncooperative Oligopolists (과점산업(寡占産業)에서의 진입제한가격(進入制限價格))

  • Nam, Il-chong
    • KDI Journal of Economic Policy
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    • v.12 no.1
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    • pp.127-148
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    • 1990
  • A Milgrom-Roberts style signalling model of limit pricing is developed to analyze the possibility and the scope of limit pricing in general, noncooperative oligopolies. The model contains multiple incumbent firms facing a potential entrant and assumes an information asymmetry between incombents and the potential entrant about the market demand. There are two periods in the model. In period 1, n incumbent firms simultaneously and noncooperatively choose quantities. At the end of period 1, the potential entrant observes the market price and makes an entry decision. In period 2, depending on the entry decision of the entrant, n' or (n+1) firms choose quantities again before the game terminates. Since the choice of incumbent firms in period 1 depends on their information about demand, the market price in period 1 conveys information about the market demand. Thus, there is a systematic link between the market price and the profitability of entry. Using Bayes-Nash equilibrium as the solution concept, we find that there exist some demand conditions under which incumbent firms will limit price. In symmetric equilibria, incumbent firms each produce an output that is greater than the Cournot output and induce a price that is below the Cournot price. In doing so, each incumbent firm refrains from maximizing short-run profit and supplies a public good that is entry deterrence. The reason that entry is deterred by such a reduced price is that it conveys information about the demand of the industry that is unfavorable to the entrant. This establishes the possibility of limit pricing by noncooperative oligopolists in a setting that is fully rational, and also generalizes the result of Milgrom and Roberts to general oligopolies, confirming Bain's intuition. Limit pricing by incumbents explained above can be interpreted as a form of credible collusion in which each firm voluntarily deviates from myopic optimization in order to deter entry using their superior information. This type of implicit collusion differs from Folk-theorem type collusions in many ways and suggests that a collusion can be a credible one even in finite games as long as there is information asymmetry. Another important result is that as the number of incumbent firms approaches infinity, or as the industry approaches a competitive one, the probability that limit pricing occurs converges to zero and the probability of entry converges to that under complete information. This limit result confirms the intuition that as the number of agents sharing the same private information increases, the value of the private information decreases, and the probability that the information gets revealed increases. This limit result also supports the conventional belief that there is no entry problem in a competitive market. Considering the fact that limit pricing is generally believed to occur at an early stage of an industry and the fact that many industries in Korea are oligopolies in their infant stages, the theoretical results of this paper suggest that we should pay attention to the possibility of implicit collusion by incumbent firms aimed at deterring new entry using superior information. The long-term loss to the Korean economy from limit pricing can be very large if the industry in question is a part of the world market and the domestic potential entrant whose entry is deterred could .have developed into a competitor in the world market. In this case, the long-term loss to the Korean economy should include the lost opportunity in the world market in addition to the domestic long-run welfare loss.

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Analysis of Orthotropic Body under Ultimate Moment Load (극한(極限)모멘트 하중(荷重)을 받는 이방성(異方性) 구조체(構造體)의 해석(解析))

  • Chang, Suk Yoon
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.5 no.3
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    • pp.95-105
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    • 1985
  • This dissertation presents an exact solution for the normal and shearing stresses of an orthotropic plane body loaded by a moment load. The solution satisfies the conditions of equilibrium compatibility equations concurrently and is governing for the body being in the elasto-plastic state. An Airy stress function is introduced to solve the problem related to an orthotropic half-infinite plane under a moment load. All the equations for orthotropy must be degenerated into the expressions for isotropy when orthotropic constants are replaced by isotropic ones. The author has evaluated all the equations of orthotropy and succeeded in obtaining exactly identical expressions to the equations of isotropy which were derived independently by of L'hosptials rule. The analytical results of isotropy are compared with the simple results of other investigator. Since moment Load under the elastic state and plastic state only is a particular case of moment load under the elasto-plastic state. All the equations of elasto-plastic state case are degenerated into the expressions for the each case. The formal solution is expressed in terms of closed form. The orthotropic constants are evaluated for two kinds and two different orientations of the grain of wood and two kinds of structures. The numerical results for orthotropy are evaluated for one kind and two different orientations of three-layered ply wood. The distribution of normal and shearing stresses are shown in figures. It is noted that the distribution of stresses of orthotropic materials depends on the type of materials and orientations of the grain and stiffening.

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A Study on Decision of Cut Rock Slope Angle Applied Shear Strength of Continuum Rock Mass Induced from Hoek-Brown Failure Criterion (Hoek-Brown 파괴기준에서 유도된 연속체암반의 전단강도를 적용한 깎기 암반사면 경사 결정 연구)

  • Kim, Hyungmin;Lee, Byokkyu;Woo, Jaegyung;Hur, Ik;Lee, Junki;Lee, Sugon
    • Journal of the Korean GEO-environmental Society
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    • v.20 no.5
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    • pp.13-21
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    • 2019
  • There are many cuts or natural rock slopes that remain stable for a long time in the natural environment with steep slopes ($65^{\circ}$ to $85^{\circ}$). In terms of design practice, the rock mass consisting of similar rock condition and geological structures is defined as a good continuum rock slope, and during the process of decision making angle of this rock slope, it will be important to establish the geotechnical properties estimating method of the continuum rock on the process of stability analysis in the early stages of design and construction. In this study, the stability analysis of a good continuum rock slope that can be designed as a steep slope proposed a practical method of estimating the shear strength by induced from the Hoek-Brown failure criterion, and in addition, the design applicability was evaluated through the stability analysis of steep rock slope. The existing method of estimating the shear strength was inadequate for practical use in the design, as the equivalent M-C shear strength corresponding to the H-B envelope changes sensitively, even with small variations in confining stress. To compensate for this problem, it was proposed to estimate equivalent M-C shear strength by iso-angle division method. To verify the design applicability of the iso-angle division method, the results of the safety factor and the displacement according to the change in angle of the cut slope constructed at the existing working design site were reviewed. The safety factor is FS=16~59 on the 1:0.5 slope, FS=12~52 on the 1:0.3 slope, most of which show a 10~12 percent reduction. Displacement is 0.126 to 0.975 mm on the 1:0.5 slope, 0.152 to 1.158 mm on the 1:0.3 slope, and represents an increase of 10 to 15%. This is a slightly change in normal proportion and is in good condition in terms of stability. In terms practical the working design, it was confirmed that applying the shear strength estimated by Iso-angle division method derived from the H-B failure criterion as a universal shear strength for a good continuum rock mass slope was also able to produce stable and economic results. The procedure for stability analysis using LEM (Limit Equilibrium Analysis Method) and FEM (Finite Element Analysis Method) will also be practical in the rock slope where is not distributed fault. The study was conducted by selecting the slope of study area as a good rock condition, establishing a verification for which it can be applied universal to a various rock conditions will be a research subject later on.

A Study on Interactions of Competitive Promotions Between the New and Used Cars (신차와 중고차간 프로모션의 상호작용에 대한 연구)

  • Chang, Kwangpil
    • Asia Marketing Journal
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    • v.14 no.1
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    • pp.83-98
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    • 2012
  • In a market where new and used cars are competing with each other, we would run the risk of obtaining biased estimates of cross elasticity between them if we focus on only new cars or on only used cars. Unfortunately, most of previous studies on the automobile industry have focused on only new car models without taking into account the effect of used cars' pricing policy on new cars' market shares and vice versa, resulting in inadequate prediction of reactive pricing in response to competitors' rebate or price discount. However, there are some exceptions. Purohit (1992) and Sullivan (1990) looked into both new and used car markets at the same time to examine the effect of new car model launching on the used car prices. But their studies have some limitations in that they employed the average used car prices reported in NADA Used Car Guide instead of actual transaction prices. Some of the conflicting results may be due to this problem in the data. Park (1998) recognized this problem and used the actual prices in his study. His work is notable in that he investigated the qualitative effect of new car model launching on the pricing policy of the used car in terms of reinforcement of brand equity. The current work also used the actual price like Park (1998) but the quantitative aspect of competitive price promotion between new and used cars of the same model was explored. In this study, I develop a model that assumes that the cross elasticity between new and used cars of the same model is higher than those amongst new cars and used cars of the different model. Specifically, I apply the nested logit model that assumes the car model choice at the first stage and the choice between new and used cars at the second stage. This proposed model is compared to the IIA (Independence of Irrelevant Alternatives) model that assumes that there is no decision hierarchy but that new and used cars of the different model are all substitutable at the first stage. The data for this study are drawn from Power Information Network (PIN), an affiliate of J.D. Power and Associates. PIN collects sales transaction data from a sample of dealerships in the major metropolitan areas in the U.S. These are retail transactions, i.e., sales or leases to final consumers, excluding fleet sales and including both new car and used car sales. Each observation in the PIN database contains the transaction date, the manufacturer, model year, make, model, trim and other car information, the transaction price, consumer rebates, the interest rate, term, amount financed (when the vehicle is financed or leased), etc. I used data for the compact cars sold during the period January 2009- June 2009. The new and used cars of the top nine selling models are included in the study: Mazda 3, Honda Civic, Chevrolet Cobalt, Toyota Corolla, Hyundai Elantra, Ford Focus, Volkswagen Jetta, Nissan Sentra, and Kia Spectra. These models in the study accounted for 87% of category unit sales. Empirical application of the nested logit model showed that the proposed model outperformed the IIA (Independence of Irrelevant Alternatives) model in both calibration and holdout samples. The other comparison model that assumes choice between new and used cars at the first stage and car model choice at the second stage turned out to be mis-specfied since the dissimilarity parameter (i.e., inclusive or categroy value parameter) was estimated to be greater than 1. Post hoc analysis based on estimated parameters was conducted employing the modified Lanczo's iterative method. This method is intuitively appealing. For example, suppose a new car offers a certain amount of rebate and gains market share at first. In response to this rebate, a used car of the same model keeps decreasing price until it regains the lost market share to maintain the status quo. The new car settle down to a lowered market share due to the used car's reaction. The method enables us to find the amount of price discount to main the status quo and equilibrium market shares of the new and used cars. In the first simulation, I used Jetta as a focal brand to see how its new and used cars set prices, rebates or APR interactively assuming that reactive cars respond to price promotion to maintain the status quo. The simulation results showed that the IIA model underestimates cross elasticities, resulting in suggesting less aggressive used car price discount in response to new cars' rebate than the proposed nested logit model. In the second simulation, I used Elantra to reconfirm the result for Jetta and came to the same conclusion. In the third simulation, I had Corolla offer $1,000 rebate to see what could be the best response for Elantra's new and used cars. Interestingly, Elantra's used car could maintain the status quo by offering lower price discount ($160) than the new car ($205). In the future research, we might want to explore the plausibility of the alternative nested logit model. For example, the NUB model that assumes choice between new and used cars at the first stage and brand choice at the second stage could be a possibility even though it was rejected in the current study because of mis-specification (A dissimilarity parameter turned out to be higher than 1). The NUB model may have been rejected due to true mis-specification or data structure transmitted from a typical car dealership. In a typical car dealership, both new and used cars of the same model are displayed. Because of this fact, the BNU model that assumes brand choice at the first stage and choice between new and used cars at the second stage may have been favored in the current study since customers first choose a dealership (brand) then choose between new and used cars given this market environment. However, suppose there are dealerships that carry both new and used cars of various models, then the NUB model might fit the data as well as the BNU model. Which model is a better description of the data is an empirical question. In addition, it would be interesting to test a probabilistic mixture model of the BNU and NUB on a new data set.

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