PLANNED OBSOLESCENCE AND THE QUALITY CHOICE OF DURABLE GOODS

Transcription

1 PANNED OBSOESCENCE AND TE UAITY COICE OF DURABE GOODS AN ABSTRACT SUBITTED ON TO TE DEPARTENT OF ECONOICS IN PARTIA FUFIENT OF TE REUIREENTS OF TE SCOO OF IBERA ARTS OF TUANE UNIVERSITY FOR TE DEGREE OF DOCTOR OF PIOSOPY BY XIA CEN APPROVED: STEFANO BARBIERI, Ph.D. Director DAVID AUEG, Ph.D. JONATAN PRITCETT, Ph.D.

2 Planned obsolescence refers to the situation where a comany has too high an incentie to create a new roduct that renders the old durable goods non-comatible or obsolete. Does this incentie ersist when the firm can choose what uality leel the new roduct has, instead of simly introducing a new roduct of a gien imroed uality? Assuming the outcome of innoation is uality increase in next eriods, this dissertation focuses on the effect of lanned obsolescence in relation to a monoolist s R&D inestment and uality choices. The monoolist is not choosing whether or not to introduce a new roduct, but rather how much uality the new roduct should hae, or in other words, how long the continuous R&D inestment should last. When a minor eolution i.e. lower uality imroement and a major reolution i.e. higher uality imroement of durable goods are mutually exclusie, for a certain range of R&D inestment cost, a monoolist is found to hae too low an incentie to introduce the major reolution. This situation is defined as lanned obsolescence of uality. The reason for such a behaior is time inconsistency, i.e. a monoolist s failure to commit to its original rofit-maximizing uality strategy once it enters the latter stage of the game. oweer if ealuated from a social lanner s ersectie, lanned obsolescence of uality, or the lack of commitment, turns out to be beneficial in alleiating the roblem of socially excessie uality at least artially. Once it can be erceied that the monoolist will not commit to its original otimal uality choice, a new discreancy would emerge between the monoolist and a social lanner. It is still beneficial for a social lanner to interene for certain ranges of R&D inestment cost. Under such circumstances, R&D

3 subsidies may be considered to induce the monoolist to moe out of the range of discreancy, roided that the gain in social welfare is larger than the cost of subsidy. This cost is smaller when the monoolist s marginal roduction cost is smaller.

4 PANNED OBSOESCENCE AND TE UAITY COICE OF DURABE GOODS A DISSERTATION SUBITTED ON TO TE DEPARTENT OF ECONOICS IN PARTIA FUFIENT OF TE REUIREENTS OF TE SCOO OF IBERA ARTS OF TUANE UNIVERSITY FOR TE DEGREE OF DOCTOR OF PIOSOPY BY XIA CEN APPROVED: STEFANO BARBIERI, Ph.D. Director DAVID AUEG, Ph.D. JONATAN PRITCETT, Ph.D. * I thank my committee members, es. Professor Daid alueg, deely for all the guidance and comments on this dissertation. All mistakes are mine and only mine. Citation from this dissertation is strictly limited.

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6 Table of Contents Introduction... Chaters Chater I. iterature Reiew... I. Classic Theories... I. Recent Deeloment... 5 I. Conclusion... Chater II. A Simle odel... 5 II. The odel Setu... 5 II. The Commitment Case... 4 II. The Non-Commitment Case... 9 II.4 The Role of Commitment... 8 II.5 Preliminary Conclusion Chater III. An Extended odel with Continuous uality Choice and Continuous and Decreasing Demand... 5 III. The odel Setu... 5 III. The Commitment Situation III. The Non-Commitment Situation III.4 Comarison between the Commitment and the Non-Commitment Situations III.5 Preliminary Conclusion... 8 Chater IV. Conclusion... 8 Aendices Aendix A. Price Structure of Path I and II Aendix B. Price Structure of Path III and IV... 9 Aendix C. Proof of emma Aendix D. Proof of emma Aendix E. Proof of emma Aendix F. Proof of <... ii

7 Aendix G. Aendix. Proof of Consumer Surlus Condition Comarison Plan D switching to Plan C... Proof of Consumer Surlus Condition Comarison Plan A switching to Plan C... 4 ist of References... 6 iii

8 Introduction The first generation of ersonal comuters PCs consisted of little more than kits for electronics hobbyists. Since that moment eolutions in the PC industry hae neer stoed. Take Ale comuters for examle. When Ale I came as a kit in 976, users had to add keyboard, case and ower suly themseles. Ale deeloed acintosh in 984, Fat ac in the same year and ac Plus in 986. The successful iac roided a reolutionary colorful illustration to the PC industry in 998. By the new ipod and ibook had finally heled the comany return to rofit. The first ipad released in was a comlete game changer. Together with iphones, it fundamentally altered the direction of the entire comuter industry for the future. While all these eolutions and reolutions haened, what consumers obsered is a trend of continuous decrease of PC rices and shortening of roduct lies. Such a situation is what economists call lanned obsolescence, because when a new ersion of the durable good comes on market, the older one becomes obsolete. Planned obsolescence is sometimes also referred to as creatie destruction in business literature, which imlies why it is lanned. Another term releant to lanned obsolescence is ostoned obsolescence, which means the urosely-delayed introduction of a new roduct or an imroed ersion of the old roduct. The most familiar examle of ostoned obsolescence exists in the ublishing industry, where the ublishing of the arry Potter series had been seculated to be ostoned to kee the book rice high for extra rofits. Another examle

9 is the debate in the automobile industry about whether the industry should continue inesting heaily on imroing the traditional gas-fueled ehicles or should it change course drastically for alternatie-owered new concet cars. Some eole beliee that there is actually ostoned obsolescence in the automobile industry to continuously exloit oil rofit. This dissertation studies the toic of lanned obsolescence of durable goods with resect to uality choices. Chater I describes the state of the literature and briefly summarizes the main outcomes and contributions. Chater II constructs a two-eriod simle model built uon Waldman 996 and extends the uality choice of a monoolist roducer from binary selections i.e. ositie uality ugrade or no ugrade to discrete, low, medium and high uality ugrade choices. Chater III introduces continuous uality choices and continuous consumer demand as well as a more comrehensie discussion of social welfare imlications. Chater IV summarizes the findings and concludes the dissertation. Further research ossibilities e.g. lanned obsolescence and cometition are also discussed in this chater.

10 Chater I. iterature Reiew Planned obsolescence in economics refers to the roduction of durable goods with short life sans. Waldman categorizes the durable goods theory into three classic categories in which two closely relate to the toic of lanned obsolescence: otimal durability and time inconsistency. I. Classic Theories I.. Otimal Durability Swan 97, 97 considers the monoolist market of durable goods. e claims that no distortion to durability is generated, since the monoolist will roduce the serice streams at minimum cost, i.e. the monoolist chooses the same durability as a cometitie industry would choose. Numerous studies were conducted afterwards inestigating the robustness of Swan s conclusions. One may relax many assumtions of these studies e.g. discount rates, maintenance decisions, etc. without affecting Swan s result. oweer a critical assumtion for this conclusion is erfect substitutability between new and used units. Waldman considers this assumtion as unrealistic for most durable roducts and states that a more realistic assumtion that catures imerfect

11 4 substitutability between new and used units will generate significantly different conclusions. A different yet related study by alueg and Solow 99 focusing on the monooly roduction of durable exhaustible resources also addresses the issue of otimal durability. The study considers a dynamically consistent lan which roides no incentie for the monoolist to deiate from its otimal decision at eery date. Both a discrete-time model with a strictly finite initial stock of resources and a continuous-time model with an increasing roduction cost function are exlored. Similar results are generated from the two models: the monooly structure generally leads to oerconseration. In the language of lanned obsolescence, this is euialent to too much durability, or ostoned obsolescence. I.. Time Inconsistency Coase 97 and Bulow 98 argue that the durable goods sold in the future affect the future alue of units sold today, and, in the absence of the ability to commit, the monoolist does not internalize this externality. As a result of this time inconsistency issue, there is a socially wasteful short life. This is the cost imosed on consumers by the monoolist when roducing durable goods, because the monoolist can always transfer the increases in cost to rices. Bulow shows that the monoolist can aoid this roblem by leasing as oosed to selling because by owning the used units at the beginning of the second eriod, the monoolist internalizes how its second-eriod actions affect the alue of those units. This dissertation focuses on the study of time inconsistency in relation to

12 5 the theory of lanned obsolescence, therefore the following literature reiew will rimarily coer this line of research. I. Recent Deeloment I.. Durability and uality Choice In Bulow 986, a durability factor is built exlicitly into a comany s cost function and deending on the underlying market structure, it could be either lower or higher than the rofit maximization leel. In a monooly market, howeer, this durability is found to be always too low. In other words, a monoolist would always urosely reduce the life of its durable goods to a leel below its rofit otimization osition. This outcome can be socially inefficient deending on the alues of the arameters selected. Bulow also oints out that instead of a comany s exlicit choice of durability, lanned obsolescence exists more likely in the form of a new roduct that dries the old ones obsolete. Waldman 99 adots this form of lanned obsolescence in which the monoolist roduces an imroed new roduct that suersedes the older one under full rice discrimination. Contrary to Bulow s results, this analysis shows that a monoolist has actually too high an incentie to introduce the new roduct relatie to the socially otimal leel. Both the monoolistic rofit and the social welfare are lower under lanned obsolescence. The reason for this outcome is time inconsistency, i.e. the monoolist fails to internalize in a later eriod the imact of his decision on earlier eriods. This is in contrast to the role of lanned obsolescence in Bulow 986, in which

13 6 time inconsistency could be considered a cure to restore socially otimal leel of durability. Choi 994 considered the case of lanned obsolescence when the monoolist could not rice discriminate and found similar results to Waldman s 99. There are also studies arguing that lanned obsolescence may not always be social welfare decreasing. Instead, lanned obsolescence could become the engine of technological rogress and increase the seed of innoation. Bond and Samuelson 986 show that when roducing durable goods, a monoolist might deote more resources to innoation, which is socially otimal, to exloit the residual demand. In Fishman, Gandal and Shy 99, excess durability is associated with technological stagnation in that it blocks continuous innoation. As a result, the only euilibrium is the roduction of durable goods without innoation for a certain range of cost. In this sense, lanned obsolescence, or the roduction of non-durable goods, might be a necessary condition to achiee continuous technological rogress. Waldman used a similar two-eriod model in 996 where lanned obsolescence is still the result of a monoolist facing time inconsistency. Because the monoolist cannot commit to future R&D inestment, the oerall monoolistic rofit falls. oweer, when taking into account how rosectie behaior would affect the rofitability of the current and reious generations of goods, the monoolist s lack of commitment actually hels to increase its de facto R&D inestment, as well as the corresonding social welfare through an enlarged oerall social consumtion. In both Waldman 996 and Choi 994, the uality increase of the new durable goods is discrete, i.e. the decision on R&D inestment the monoolist faces is binary: inestment or no inestment at all; a new roduct of certain higher uality or no

14 7 roduction at all. The monoolist does not hae the otion to choose the actual leel of its R&D inestment. But what if the monoolist CAN choose the uality of its next generation of durable roduct that suersedes the rior ones? What if the monoolist CAN control the leel of R&D inestment? Will Waldman s results still hold? Another characteristic of durable goods is that roduct uality may not be obsered at the time of urchase. Strausz 9 builds a reeated game with a single consumer who reuires at most one functioning unit of the roduct. Consumer and social welfare deend on both a uality ariable and a durability ariable, which can be both exerience elements that cannot be obsered by the consumer till the urchase is made. Strausz shows that when there is comlete transarency between the consumer and the roducer, the otimal uality is increasing in durability, i.e. the two are comlements. Both the uality and durability outcomes are socially efficient, which is consistent with the original conclusion by Swan 97. oweer, with unobsered uality, uality and durability can change to substitutes when the durability is relatiely large. Unobserability reduces the euilibrium uality, durability and rice to below the otimal leel. Strausz argues that reduced durability may be in the interest of consumers because the roducers hae an incentie to roide adeuate uality although not otimal uality in other dimensions. Planned obsolescence may be considered a ositie factor in this sense. When unobsered uality attributes are imortant, lanned obsolescence may be needed to roide the roducer with the right incenties. This assumtion eliminates the Coasian time inconsistency roblem of durable goods monoolist.

15 8 I.. Secondary arket In both Bulow 986 and Waldman 996, there exists a erfect secondary market so that consumers could sell their used units. By doing so, roducers of durable goods must comete with reious generations of their own roducts. It is imortant to understand the role of secondary market to the theory of lanned obsolescence. Swan 97 argues that since a good s initial rice reflects the rice at which it will change hands in the second-hand market in the future, the aailability of used units does not reduce the oerall rofitability of a monooly seller. oweer Waldman 996, 997, Fudenberg and Tirole 998, endel and izzeri 999 all argue that because of otential substitutability across different generations, the aailability of used units lowers the monoolist s new unit rice. One resonse is for the monoolist to reduce the durability of new units to reduce substitutability and to increase the rice for new units Bulow, 986. Another resonse is to reduce or een eliminate the aailability of used units, e.g. lease-only olicy. alueg and Solow 989 shows that with non-linear demand cures, the euilibrium under rental may Pareto dominate that under sales. Waldman 997 further shows that een when haing the otion to reurchase and scra the used units, if the firm cannot commit to the subseuent reurchase rice when selling new units, then the reurchase-and-scra strategy fails because of time inconsistency. Een if a firm can contractually commit to a high reurchase rice, the lease-only olicy is still referred as long as there is a ositie robability of bankrutcy, which means full commitment is imossible.

16 9 The textbook market can be considered as another examle of using new editions to kill the used coies. Iizuka 7 conducted an emirical study using a discretetime surial model and aroximately,5 obserations in economics textbook market during semesters between 996 and. The outcome shows that ublishers are indeed more likely to reise editions as the market share of used books increases, which is consistent with the iew that textbook ublishers introduce new editions to kill-off used textbooks. Ding, icks and Ju conducted an analysis to study the role of secondary markets to lanned obsolescence in the ideo game industry. It shows that the monoolist deliberately reduces the resale alue of its reious generation of durable goods by introducing new generations with large uality imroements. Emirical eidence from the US ideo game market confirms the existence of lanned obsolescence. I.. Planned Obsolescence and cometition In Bulow 986, in addition to lanned obsolescence under monooly market structure, Bulow also studies the oligoolistic or euialently a monoolist facing certain entry in a subseuent eriod maximization roblem, entry deterrence and collusion between roducers. It is found that while monoolists will select inefficiently short useful lies, oligoolists may choose either too short or too long roduct life sans deending on their technologies and market conditions. There is an incentie to increase durability to deter entry. In other words, in contrast to lanned obsolescence, cometition may induce ostoned obsolescence.

17 Grout and Park 5 studies lanned obsolescence under cometition and argues that it is ossible that a durable goods firm cannot surie in a cometitie market unless its roduct exhibits lanned and known obsolescence. This form of obsolescence is necessary to minimize the lemons roblem in a cometitie market where information asymmetry is resent. Strausz 9 also argues that lanned obsolescence may arise under cometition in a similar fashion i.e. unobsered uality to Grout and Park 5. Wantanabe 6 uses a dynamic stochastic game with discrete time horizons and ertical roduct differentiation to study the toic of lanned obsolescence by duoolists, which can be extended to the case of multile firms. Wantanabe argues that sooner or later duoolists start to renew their roducts i.e. roduction of the next generation roduct for a certain cost that suersedes the rior intages in the same time length efficient for consumers regardless of the initial difference. The more tolerant of the delay of renewal consumers are, the earlier each firm makes its roduct renewal in time length best for them, i.e. the more obious is lanned obsolescence. If consumers are fussy about roduct renewal, only one firm renews its roduct. iao studies another form of lanned obsolescence under cometition. It intends to exlain icrosoft s tying behaior i.e. bundling the alication with the new oerating system instead of selling the alications searately, which does not reuire a hysical tie inoling incomatibility with a rial s roduct, nor does it rely on the entry deterrence effect of tying. This study endogenizes the monoolist s choice of comatibility and generates the lanned obsolescence outcome without the tyical assumtion of new consumers i.e. all consumers urchase the system in eriod, i.e. the monoolist will sell a tying new system that is only backward comatible, howeer

18 the oerall rofit maximization choice is to commit to either selling the alication alone or selling the tying new system that is fully comatible. iao further considers a cometition case using the standard linear city model and finds that tying becomes a rofitable strategy because it turns the cometition between two alications into a cometition between two systems, which lowers the rices of alications thus allowing the system maker to charge a higher rice for the original system. This outcome lowers social welfare because forward incomatibility reduces total network benefits and because it distorts some consumers urchase decisions and increases their transortation costs. I. Conclusion With regard to the deeloment of lanned obsolescence literature, it can be seen that there are at least three asects of lanned obsolescence of durable goods worth further inestigation: uality choice and its social welfare imlications, the role of a secondary market and the interaction between lanned obsolescence and cometition. This dissertation follows the set u of Waldman 996 assuming that the outcome of innoation is uality increases in next eriods. It focuses directly on the effect of lanned obsolescence in relation to the monoolist s R&D inestment and uality choices. The monoolist is not choosing whether or not to introduce a new roduct of imroed uality at a gien leel, but rather how much uality the new roduct should hae, or in other words, how long the continuous R&D inestment should last. Planned obsolescence of uality in this context is defined as the case where the

19 realized final uality is lower than the otimal leel the monoolist would hae selected. The otimal uality leel refers to the uality the monoolist would hae chosen without time inconsistency issues. A lower uality is associated with the remature introduction of the new roduct. As a result, the old roducts become obsolete earlier than they should hae and the R&D rocess ends sooner than when it could hae. If the realized actual uality is too high on the other hand, then ostoned obsolescence of uality is said to occur. It is worth noting that the focus of this dissertation is not on whether it is socially otimal to introduce a durable roduct of higher uality, which has already been studied by the literature of lanned obsolescence intensiely, but rather on what this socially otimal uality should be and the corresonding social welfare imlications. The analysis includes two arts. First I introduce a simlified model based on Waldman 996 with ste-function demand and three discrete uality choices. Second I generalize the analysis with continuous uality otions and a continuous and decreasing consumer demand. Results from these analyses are highly consistent that a monoolist would inest too little in R&D and roduce a uality that is too low to maximize its oerall rofit because of time inconsistency. In other words, there exists lanned obsolescence of uality for a monoolistic comany. oweer from a social lanner s ersectie, when a monoolist does not commit, time inconsistency, or lanned obsolescence of uality, naturally hels to correct at least artially the roblem of too much uality and increases social welfare through increased social consumtion in a similar fashion to Waldman 996 and Choi 994. Although I am focusing on the uality increase of durable goods in the form of a new roduct that suersedes the older generations, the imact on consumer ercetions

20 and behaior changes are uite similar to the comatibility analysis by iao. The conclusion is also similar to Strausz 9, which argues that reduced durability may be in the interest of consumers because of unobsered uality, therefore the roducers hae an incentie to roide adeuate uality although not otimal uality in other dimensions. In addition, when continuity of uality is resent, Waldman s 996 result can be considered as a secial examle where ositie uality increase is always suerior to no increase at all. It is in fact this binary uality choice that has led to the different conclusion of Waldman 996 from Coase 97 and Bulow 986. Once the uality choice becomes continuous, with lanned obsolescence, the final leel realized will always be lower than under the commitment case. In this sense, the literature of time inconsistency conerges in terms of the meaning of lanned obsolescence: deliberately reduced roduct life or roduct uality. Although lanned obsolescence of uality demonstrates aealing social welfare indications, it still cannot sole the social lanner s roblem comletely. Innoation subsidies may be considered as a otential solution roided that the cost of ublic interention is less than the gain in social welfare. The cost of subsidy is smaller when the marginal cost of roduction is smaller. This dissertation continues to rely on the existence of a secondary market in conducting the theoretical analyses. It is imortant to note that the monoolist would not choose to articiate in the secondary market, gien that it would actually increase the suly of cometitie roduct in the latter eriod, and this in turn negatiely affects its roduct rices in both rior and current eriods. The indication that used good rices are

21 4 indirectly decided by firm leel decisions concerning their next generation roducts is consistent with the simulation outcome by Ding, icks and Ju.

22 5 Chater II. A Simle odel Waldman 996 roides a simle two-eriod model to study the toic of lanned obsolescence and the uality choice of durable goods. In his model the monoolist has a binary choice to whether or not increase the uality of its durable goods in the second eriod. The monoolist faces a time inconsistency roblem: the inestment decision to maximize its current i.e. second eriod rofit does not maximize its oerall rofit. As a result, the monoolist will roduce too much uality; howeer the social welfare is higher with lanned obsolescence. A simle model is build uon Waldman 996 setu in this chater to further extend the study of uality imlications of lanned obsolescence. II. The odel Setu There are three eriods,, and, in which a monoolist is selling a durable roduct of a certain uality K, where K =,,, and < <. The monoolist starts with in Period and inests in R&D at the same time to imroe the uality of its durable goods to either medium or high leel in the following eriods. For simlicity, assume that once an inestment is made, it is always successful in imroing future uality. A roduct of uality is a minor imroement and reuires

23 6 only one eriod of R&D inestment in the first eriod. If the comany decides to continue with the R&D inestment in Period, it will then come u with a roduct of uality roduct of uality in eriod, which is considered a reolutionary relacement of the original. An imortant assumtion here is that the roducts of uality and are substitutes and mutually exclusie. This means that it is not ossible for the monoolist to manufacture roducts of uality in Period while continuing inesting in R&D to come u with uality in Period. This scenario is true when the two R&D inestment otions rely uon significantly different technologies and the monoolist has limited resources to afford only one tye of inestment within a certain time frame. Once uality is selected, there will be no roduct to be deeloed in the future and ice ersa. For examle, a car manufacturer could consider two cometing innoation ideas. One is to send one year inesting in an imroed model of the existing gas-fueled ehicle; the other is to send two years inesting in electric cars. With limited financial resources and research caability, this car manufacturer can only choose one strategy to follow instead of deeloing both. Another imortant asect of the monoolist s R&D inestment is the timing of its decision making rocess. Assume that the initial R&D inestment for both uality otions is the same in Period and at least one eriod of R&D will take lace because een the minor imroement is sufficiently aluable. For simlicity, further assume that the Period inestment leel is zero. The monoolist could announce its uality lan at the beginning of Period, but the actual uality strategy i.e. the Period R&D inestment decision cannot be obsered by consumers till the end of Period or the

24 7 beginning of Period. In other words, it is ossible for the monoolist to hae announced a strategy at the beginning of Period but actually adot a different one at the end of Period or the beginning of Period. The marginal cost of roduction is assumed to be a constant, c, for all ualities. This is esecially true when the alue drier of the durable roduct is intellectual roerty instead of raw material and labor. In this case the R&D exense is the rimary comonent of the cost of roduction. The uality of goods deends more on the R&D exenditure than on hysical roduction cost. The discount rate between eriods is δ. et the otential R&D inestment in Period be R and R. There is no further R&D inestment in Period gien it is the last eriod and there is no reward for continuous inestment any more. et the monoolistic oerall rofit from the three eriods be achieed and K = or. K where K is the final uality There are two grous of consumers with marginal utility of uality and, haing a mass of n and n resectiely with density. For simlicity, assume that n n. A consumer j s ayoff of consumtion in each eriod is K j, where j = or and K = or. Assume and in articular, n n n so that the monoolist will refer to sell a gien uality only to the consumers if both and are ready to urchase in each eriod, howeer it would still sell to the consumers when they re the only grou aailable. The latter reuires an additional assumtion that This assumtion ensures that a determinate ositie euilibrium rice can be achieed on the secondary market.

25 8 c min[, ]. When a new roduct becomes aailable, a second-hand market may form between the and consumers. Consumers are forward-looking and can always obsere the monoolist s R&D inestment behaior in each eriod and act accordingly. All arameters are common knowledge. II.. Decision Tree Using a game theory aroach, the flow of the monoolist s decision making rocess is shown in Figure. There are four otential aths the monoolist could follow. ow to decide the rices for roducts with different ualities will be exlained later in section II... This assumtion means that the marginal cost of roduction is always smaller than the lowest rice the consumers are eer going to ay for any uality, so that a transaction is always ossible in any eriod.

26 9 Figure : The onoolist s Decision Tree Sell to Path I R > Not sell to No business Path II, and Secondary market R =, Secondary market Path III No business Path IV Period Period Period Period : The monoolist sells the roducts of original uality and inests in R&D to imroe uality in the following eriods. Since n n n, only consumers will urchase the goods in this eriod. As described in the model setu, the monoolist faces two R&D inestment otions at the beginning of Period : a relatiely limited uality imroement in Period which only reuires one eriod of inestment, i.e. R = ; or a more drastic uality increase to be achieed in Period after a continuous R&D inestment through both Period and, i.e. R >. For reference conenience, these two otions are called the -otion and -otion resectiely where reresents uality and uality. Deending on the monoolist s inestment

27 decision made, it could follow four different aths through Period and as described below. Period : If the monoolist has chosen the -otion, the comany would also need to decide whether to sell the goods to the consumers who hae not urchased in Period. If -otion has been chosen, the monoolist would sell the goods to the consumers and a secondary market would form between the and consumers for the goods. The monoolist would also sell the roduct in this eriod to the residual consumers that did not articiate in the secondary market gien n n. Period : If the monoolist has chosen the -otion, the roduct of uality will be sold only to the consumers in this eriod. If the roduct has already been sold to the consumers in Period, there would not form a second-hand market in Period Path I. Otherwise, a secondary market forms between the and consumers Path II. Note that the monoolist would also sell the roduct to the residual consumers in Period under Path II gien n n. If the monoolist has chosen the -otion instead, the only otential business remaining in Period is the sale of goods to the consumers who hae not urchased before. No secondary market forms in this circumstance Path III. The monoolist can also choose not to sell to the consumers in Period if it is concerned about the imact of such behaior on the rice of roduct back in Period Path IV.

28 II.. Price Structure The rice u to which a consumer j can afford in each eriod deends on his or her marginal utility of uality j and the uality of the durable goods, i.e., the consumer surlus. The rice a consumer is willing to ay for a certain uality today euals the forgone utility from waiting till later when the exected rice is reduced. This rice is also the final euilibrium rice the monoolist will charge gien the ste-function demand it faces. If the monoolist has chosen the -otion, it would choose between Path I and Path II, i.e. whether or not to sell the roduct to the consumers in Period. The rice schedules of the two aths are outlined below resectiely 4 : I. Sell the roducts of uality to the consumers in Period. P P P II. Do not sell roducts to the consumers in Period. P P P 4 See Aendix A for roof.

29 K where P is the rice of the roduct of uality i j K sold to the j consumers in eriod i, i =, or ; j =, ; and K =, or. All notations are the same in the following analyses. It can been seen intuitiely from the aboe rice structure that in Period, is the ayoff of uality increase to the consumers as they are the only grou who would ugrade to in Period. The difference between the Path I and Path II roduct rices is exactly the forgone rice for selling to the consumers in Period, i.e.. If the monoolist has chosen the -otion instead, it then has a choice between Path III and Path IV, i.e. whether or not to sell the roducts of uality to the consumers in Period. The rice schedules of the two aths are outlined below resectiely 5 : III. Sell the roducts of uality to the consumers in Period. P P P P IV. Do not sell the roducts of uality to the consumers in Period. P P P 5 The roof is in Aendix B.

30 uality Comare the roduct rices. If the monoolist does not sell the roducts of to the consumers in Period, the additional amount it could charge in Period is. The first comonent is the additional ayoff to the consumers from the secondary market. The second comonent is the additional ayoff of uality increase to the consumers if the consumers do not hae the oortunity to also ugrade to the Period. uality in II.. Definition of Commitment The monoolist will announce its uality otion at the beginning of Period. To maximize its oerall rofit, the monoolist would calculate its total exected rofit from each ath and comare to ursue the otimal otion. If it is obsered to follow this otimal strategy otion when it reaches Period, the monoolist is said to commit and this scenario is called the commitment case. Otherwise, if after reaching the end of Period, the monoolist considers the ast as water under the bridge, it could choose to only maximize its exected oerall rofit from that moment on and the actual otion selected may not be the same as the original one announced. If the monoolist is found to deiate from the original strategy once it enters Period, it s said not to commit and this scenario is called the non-commitment case.

31 4 II. The Commitment Case II.. The onoolistic uality Choice If the monoolist could commit, it would determine its otimal strategy at the beginning of Period by comaring its total exected rofit from each ath. Secifically, the monoolist would first need to comare the rofits from Path I and II if it shall continue inesting in R&D in Period ; and the rofits from Path III and IV if it shall settle with roducts of uality emma resectiely. in Period. The results are shown in emma and emma : If the monoolist is going to continue with the R&D inestment in Period to come u with the high uality goods in Period, with commitment, the comany would choose Path II oer Path I, i.e. it would not sell the roducts of uality to the consumers in Period. 6 emma : If the monoolist is going to cease R&D inestment in Period and come u with the roduct of uality, with commitment, the monoolist would choose Path IV oer Path III, i.e. it would not sell the roducts of uality to the consumers in Period. 7 6 The roof is in Aendix C. 7 The roof is in Aendix D.

32 5 uality From emma, Path II is the monooly s otimal choice when roducts of are roduced in Period. The oerall monoolistic rofit from this ath is n [ ] n[ ] n n R [ n n n] c From emma, if the roduct of uality is roduced instead, with commitment, Path IV in Figure will be selected. The oerall monooly rofit is then: n [ ] n[ ] n n [ n n n] c. Comare the two rofits: R n n n n D D n ] where [ c D and D. In this euation, R is the discounted extra R&D inestment cost if the monoolist continues with the R&D inestment in Period to roduce the instead of the roducts. n n n contains two comonents: n and n. n reresents the rice adantage of the roducts oer the roducts because under Path II, haing no business in Period, the monoolist can extract all consumer surluses from the consumers back in Period. While in Path IV, the monoolist is not able to extract such surluses from the consumers in Period gien that they could exect to sell their used goods to the consumers in Period. oweer, by following Path IV instead of Path II, the monoolist would extract additional n surlus from the consumers in Period. Therefore, the sum

33 6 n n n reresents the relatie income adantage from extended R&D inestment and roducing high uality comared to the medium uality. It could also be considered as a reward to a reolutionary uality imroement oer eolution. The art n D D is the discounted forgone income of the in Period since uality roducts would hae a much higher alue increase as well as rice remium. n c is the discounted cost adantage of selecting the because the roduction cost would not occur until Period. roducts oer et n n n n D D n c A, which is the net total benefit of the goods roduction and it is easy to see that A >. Then R A. This outcome is summarized in emma. emma : When the monoolist commits, if the additional inestment cost of the goods roduction is smaller than the total net benefit, i.e. R A, Path II would be selected as the otimal uality otion and the roduct of uality would be roduced in Period. Otherwise, uality Period. would be roduced in II.. The Social Planner s uality Choice Assume there exists a social lanner that engages in maximizing the total social surlus. Based on emma and emma, if the monoolist commits, Path II will be chosen if the roducts are to be selected, otherwise Path IV would be selected and

34 7 uality would be roduced in Period. Denote the discounted oerall social surlus from the three eriods as K S where K is the realized final uality and K or. The total social surluses from the two situations are then: S S n n n nc n n c R, and n n n n c n n c. Comare the two social surluses: S S R n D n D n n ]. [ c Substitute in A n n n n D D n c and rewrite this euation as S S [ R A E], where E n. When the monoolist commits to its future uality choice at the beginning of the game, if the additional inestment cost reuired for uality is less than A-E, it would be otimal from a social ersectie to continue with the R&D inestment in Period and follow Path II. Otherwise, the goods roduction and Path IV would be referred from a social lanner s ersectie to maximize the social welfare. Proosition : If the monoolist commits, for R&D inestment cost R that A E R A, there would exist too much uality in the society from a social lanner s ersectie.

35 8 Figure : The Discreancy between the onoolist and the Social Planner in the Commitment Case Social Planner onoolist Path II, Discreancy Path IV, A-E A R In Figure, the ertical arrows reresent the social lanner or the monoolist s uality choice deending on the leel of R&D inestment reuired. To the left of the arrows, i.e. when the Period R&D inestment R is relatiely small, continuous inestment and the realization of uality early termination of the R&D inestment and uality will be referred. To the right of the arrows, will be referred. Note that there is a discreancy between the monoolist s strategy choice and the social lanner s. For an inestment cost R that is in the interal A-E, A, the social lanner would refer the monoolist to choose Path IV and uality and ersectie. instead of Path II, i.e. there would exist too much uality in the society form a social lanner s

36 9 II. The Non-Commitment Case II.. The onoolistic uality Choice Contrary to the commitment case, when the monoolist does not commit, it would not simly follow the original strategy announced at the beginning of the game, but rather consider the ast as water under the bridge and only maximize its exected future rofit from that oint on. Because all arameters are common knowledge and the consumers are forward looking, they could erfectly redict the monoolist s otential deiation in adance thus make behaior adjustments accordingly. In a game theory analysis, such ractice is called sub-game erfect strategy. Secifically, the monoolist would make Nash Euilibrium choices in each sub-game and utilize backward induction to calculate its demand in each eriod of the game. The reliminary results are shown in emma 4 and emma 5. emma 4: If the uality were to be roduced, without commitment, i. if the marginal roduction cost is sufficiently small that n n n c, the monoolist would choose Path I and sell the roducts to the consumers in Period ; and

37 ii. if the marginal roduction cost is sufficiently large that n n n c, the monoolist would choose Path II and not sell the roducts to the consumers in Period. 8 emma 5: If the uality were to be roduced, without commitment, the monoolist would always choose Path III and sell the roducts to the consumers in Period irresectie to the size of the marginal cost of roduction. 9 emma 4 indicates two situations when the goods are roduced. Denote the non-commitment monoolistic exected rofit in these two cases as NC i where i = I or II, corresonding to Path I and Path II resectiely; NC refers to the non-commitment situation. Note that NC i is the sum of Period rofit and the discounted eriod rofit only. It s not necessary to include the Period rofit because it is not related to the subgame erfect strategy decision of the monoolist. If n n n c, the monoolist will sell the roducts of uality to the consumers in Period, thus ursuing Path I. The non-commitment monoolistic exected total rofit from Period and is then : NC I n n R n n c. 8 The roof is in Aendix E. 9 emma 5 is obious because otherwise there would be no business for the monoolist to engage in and hence nil exected rofit in eriod.

38 If n n n c, the result becomes exactly the same as in emma under commitment. The corresonding non-commitment exected rofit is then NC II n[ ] n n R n n n c. If the medium uality is roduced instead, from emma 5, Path III would be followed irresectie to the size of the marginal cost c. The non-commitment monoolistic exected rofit from Period and is NC n[ ] n n n n n n n c, where NC refers to the non-commitment situation as well. Comare the aboe three monoolistic exected rofits. If the marginal cost is relatiely small so that n c, n n. Note: R is the ure extra cost of the goods roduction oer the goods. n n c the discounted additional cost of roduction if the monoolist selected the is uality instead of in Period. n D is art of the discounted forgone rofit from Period due to the reduction of the final uality achieed if the goods were to be roduced in Period. n n D is the other art of the discounted forgone rofit from Period due to the change of consumtion base from the consumers to the consumers if uality were to be roduced in Period. The sum of n D and n n reresents the total forgone rofit of the D goods roduction relatie to the roducts due to the roduct uality reductions and a lower marginal consumer

39 reference for uality. n D on the other hand, is the relatie benefit of selling the roducts in Period, or the oortunity cost of the goods roduction in Period. The total of n D is n c nd n n D n hence the net forgone rofit of the roduction. Rewrite this net benefit of uality goods roduction, or the net benefit of uality roduction as: A n n n D [ nc n n c], where A n n n n D D n c as defined in the commitment case. et n n n D nc n n c B. Thus NC NC I R A B, whereas if the extra R&D inestment cost R reuired to roduce uality in Period is smaller than the net benefit A-B, uality roduced. Otherwise, roducts of uality the sign of B is not decisie. would be would be roduced in Period. Note that If the marginal cost is large enough that n n n c, there is NC NC II R n c n nd n D n n n D. R again, is the inestment cost saing of uality relatie to uality. n c is the roduction cost disadantage of the roducts of uality because without commitment, Path II would be followed where no roduction occurs in Period. n reresents the net rofit adantage of the goods roduction by

40 extracting the consumers surlus indirectly. n D is D nd n n n also the net rofit adantage of the of the oer roducts. goods roduction due to the different alue added Rewrite n D as c n nd nd n n n A [ n n n D n nc]. et C n n n D n n c. Note that C B when n n n c, otherwise, B C. Therefore R A C, where the total net benefit of uality NC NC II roduction is A C. If the extra inestment cost R reuired to roduce the roducts in Period is smaller than the total net benefit A C, the high uality goods would be roduced in Period. Otherwise, roducts of uality Period. These results are summarized in emma 6. would be roduced in emma 6: When n n n c, without commitment, the monoolist would follow Path I and roduce the roducts of uality if R A B ; otherwise, the monoolist would ursue Path III and roduce uality. When n n n c instead, without commitment, the monoolist

41 4 would follow Path II and roduce the roducts of uality if R AC ; otherwise, the monoolist would ursue Path III and roduce uality. II.. The Social Planner s uality Choice Based on the monoolist s uality choices without commitment, deending on the size of the marginal cost of roduction, there also exist two situations when calculating the total social welfare. et the oerall social welfare in the non-commitment case be K S NC, where K is the final uality realized and K or. NC means noncommitment. Note here that three eriods. If the roducts of uality K NC S is the sum of the discounted social welfare from all were to be roduced, from emma 4, when the marginal cost is relatiely high so that n n n c, Path II would be followed and the result is the same as in emma under the commitment case, where the oerall social welfare is S and: S n n n n c n n c R. When the marginal cost is relatiely low instead, i.e. n n n c, Path I would be chosen and the oerall social welfare becomes: S NC n n n n n n c R.

42 5 If on the other hand the goods were to be roduced, from emma 4, Path III would be chosen and the oerall social welfare is then c n n n n n n n n n S NC ] [. Comare these situations. When n n n c, ] [ ] [ G A R c n n D n n D n R S S NC NC, where c n c n c D n n n n G. When n n n c, ] [ ] [ F A R c n D n n D n R S S NC, where c D n n F. If the monoolist does not commit, the social lanner would refer a comany with relatiely low marginal cost of roduction i.e. when n n n c to follow Path III and manufacture the roducts of uality if and only if the additional inestment cost R reuired is greater than A-G; otherwise, the roducts and Path I become the social lanner s faorite. If on the other hand, the monoolist turns out to hae a relatiely high marginal cost of roduction, i.e. n n n c, uality and Path II are referred by the social lanner if and only if the additional R&D inestment cost R is smaller than A-F; if this cost is higher than A-F, the uality and Path III are desired instead.

43 6 Note that G < F, therefore A F AG. For the R&D inestment cost R where A F R AG, it is socially otimal for an industry with relatiely low marginal cost of roduction to follow Path I and manufacture the roducts of uality ; while for an industry with relatiely high marginal cost of roduction, the socially otimal choice would be for the monoolist to select Path III and roduce uality. If the inestment cost R is smaller than A F or bigger than A G, then irresectie to the size of the marginal cost of roduction, the social lanner would strictly refer Path II with uality and Path III with uality resectiely. II.. Comarison between the onoolistic and the Social Planner s uality Choices Comare B and G, C and F resectiely: B G n n n D nc n n c n n n n D c nc nc C F n n n D n nc n n D c Therefore A G A B and A F A C. Proosition : There is discreancy between the monoolist and the social lanner when the monoolist does not commit. i. When the marginal cost of roduction is relatiely small, i.e. when n n n c, for the additional R&D inestment cost R in the range of A-G, A-B, the social lanner would refer the uality to

44 7 be roduced, while the monoolist would select the goods roduction. In order words, there exists too much uality in the society when A G R A B. ii. When the marginal cost of roduction is relatiely large, i.e. when n n n c, for the additional R&D inestment cost R in the range of A-F, A-C, the social lanner would refer the roduced, while the monoolist selects the uality to be goods roduction. In other words, there exists too much uality in the society when A F R AC. Proosition is illustrated in Figure and Figure 4. Figure : The Discreancy between the onoolist and the Social Planner in the n Non-Commitment Case when c n n Social Planner onoolist Path I, Discreancy Path III, A-G A-B R

45 8 Figure 4: The Discreancy between the onoolist and the Social Planner in the n Non-Commitment Case when c n n Social Planner onoolist Path II, Discreancy Path III, A-F A-C R In Figure and Figure 4, the ertical arrows reresent the social lanner or the monoolist s uality choice deending on the leel of R&D inestment reuired. To the left of the arrows, i.e. when the R&D inestment R is relatiely small, continuous inestment and the realization of uality early termination of the R&D inestment and uality will be referred. To the right of the arrows, will be referred. Discreancy exists when A G R A B when the marginal cost of roduction is relatiely small and A F R AC when the marginal cost of roduction is relatiely large that the social lanner would refer the roduction of uality while the monoolist would select uality instead. to maximize social welfare II.4 The Role of Commitment From the aboe analyses, without commitment, the monoolist s ractice is euialent to the sub-game erfect strategy in a game theory analysis. Comared to the