Optimal Leasing and Selling Strategies of Durable Goods Manufacturer Considering Consumers’ Capital Constraint

9th IFAC Conference on Manufacturing Modelling, Management and 9th IFAC Conference on Manufacturing Modelling, Management and Control Available online at www.sciencedirect.com 9th IFAC Conference on Manufacturing Modelling, Management and Control Berlin, Germany, August 28-30, 2019 9th IFAC Conference on Manufacturing Modelling, Management and Control Berlin, Germany, August 28-30, 2019 Control Berlin, Germany, August 28-30, 2019 Berlin, Germany, August 28-30, 2019

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IFAC PapersOnLine 52-13 (2019) 319–324

Optimal Leasing and Selling Strategies of Durable Goods Manufacturer Optimal Leasing and Selling Strategies of Durable Goods Manufacturer Optimal and Strategies of Goods Manufacturer Considering Consumers’ Constraint Optimal Leasing Leasing and Selling Selling Strategies Capital of Durable Durable Goods Manufacturer Considering Consumers’ Capital Constraint Considering Considering Consumers’ Consumers’ Capital Capital Constraint Constraint

Jian Li*. Zhiwen Deng** Li*. Zhiwen Deng** WenJian Zhang*. GuoqingDeng** Zhang*** Li*. Zhiwen WenJian Zhang*. GuoqingDeng** Zhang*** Jian Li*. Zhiwen Wen Zhang*. Guoqing Zhang*** Wen Zhang*. Guoqing Zhang*** Development, *Research Base of Beijing Modern Manufacturing *Research Base of Beijing Modern Manufacturing Development, College of Economics Management, Beijing University of Technology, *Research Base ofand Beijing Modern Manufacturing Development, College and Management, Beijing University of Technology, of Economics *Research Base of Beijing Modern Manufacturing Development, Beijing, China, (corresponding author, e-mail: [email protected]). College of China, Economics and Management, Beijing University of Technology, Beijing, (corresponding author, e-mail: [email protected]). College of Economics and Management, Beijing University of Technology, ** School of Economics and Management, Beijing University of Chemical Technology, Beijing, China, (corresponding author, e-mail: [email protected]). Beijing University of Chemical Technology, ** School of Economics and Management, Beijing, China, (corresponding author, e-mail: [email protected]). Beijing, China, (e-mail:Beijing [email protected]) ** School of Economics and Management, University of Chemical Technology, China, (e-mail:Beijing [email protected]) ** School of Economics and Management, University of Chemical Technology, ***Beijing, Faculty of Engineering, University of Windsor, Beijing, China, (e-mail: [email protected]) *** Faculty of Engineering, University of Windsor, Beijing, China, (e-mail: Windsor, Canada, (e-mail:[email protected]) [email protected]) *** Faculty of Engineering, University of Windsor, Windsor, Canada, (e-mail: [email protected]) *** Faculty of Engineering, University of Windsor, Windsor, Canada, (e-mail: [email protected]) Windsor, Canada, (e-mail: [email protected]) Abstract: In this paper, we analyze the profitability of a monopoly manufacturer that takes pure-selling, Abstract: In and this hybrid paper, strategy we analyze the profitability of a monopoly manufacturer that takes pure-leasing by considering the capital constraint of the consumers and pure-selling, the life span Abstract: In and this hybrid paper, strategy we analyze the profitability of a monopoly manufacturer that takes pure-selling, pure-leasing by considering the capital constraint of the consumers and the life span Abstract: In this paper, we analyze the profitability ofWe a monopoly manufacturer thatthe takes pure-selling, of the product in an indefinite time horizon model. find that the increase of consumers with pure-leasing andinhybrid strategy time by considering the capital constraint of increase the consumers and the life span of the product an indefinite horizon model. We find that the of the consumers with pure-leasing and hybrid strategy by considering the capital constraint of the consumers and the life span capital constraint has a more significant impact on the prices when the proportion of that group is small. of the product in has an aindefinite time horizon model. We findwhen that the theproportion increase ofof the consumers with capital constraint more significant impact on the prices that group is small. of the product in an indefinite time horizon model. We find that the increase of the consumers witha It will curb the development of the rentalimpact market; when the group reaches a certainofscale, then itisplays capital constraint has a more significant on the prices when the proportion that group small. It will curb the development of the rental market; when the group reaches a certain scale, then it plays capital constraint has a more significant impact on the prices when the proportion of that group is small. leading role the in the demand, which more manufacturers to take leasing In the hybridaa It will curb development of theencourages rental market; when the group reaches a certainstrategy. scale, then it plays leading role in the demand, which encourages more manufacturers to take leasing strategy. In the hybrid It will curb the development of the rental market; when the group reaches a certain scale, then it plays strategy, we insee explicitwhich increase in the overall profit. We find thea leading role thean encourages more manufacturers to the takeleasing leasingchannel strategy.dominates In the hybrid strategy, we insee andemand, explicit increase inThe the suppressed overall profit. Wechannel find leasing channel dominates the leading role thehelp demand, which encourages more manufacturers to the take leasing strategy. In to thekeep hybrid markets with the of C-type market. selling has to lower the price the strategy, we see an explicit increase inThe the suppressed overall profit. Wechannel find thehas leasing channel dominates the markets with the help of C-type market. selling to lower the price to keep the strategy,coverage, we see an explicit increase inwith thethe overall profit. We find thefindings leasingprovide channelnew dominates market which is independent market structure. These insights for markets with the help of isC-type market.with The the suppressed selling channel has to lower the price to keep the market coverage, which independent market structure. These findings provide new insights for markets with the help construction of C-type market. The suppressed selling channel has to lower © the2019 priceIFAC to keep the the operation of large machinery manufacturing companies. Copy-right market coverage, which is independent with the market structure. These findings provide newIFAC insights for the operation of large construction machinery manufacturing companies. Copy-right © 2019 market coverage, which is independent with the market structure. These findings provide new insights for the operation of large construction machinery manufacturing companies. Copy-right © 2019 © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rightsIFAC reserved. Keywords: durable goods, selling, leasing, capital constraint. the operation of large construction machinery manufacturing companies. Copy-right © 2019 IFAC Keywords: durable goods, selling, leasing, capital constraint. Keywords: durable goods, selling, leasing, capital constraint. Keywords: durable goods, selling, leasing, capital constraint. market, even though many small and medium enterprises 1. INTRODUCTION market, even though many and because medium enterprises (SMEs) are eliminated outsmall of that of capital 1. INTRODUCTION market, even though many small and because medium enterprises (SMEs) are eliminated out of that ofbusiness, capital market, even though many small and medium enterprises 1. INTRODUCTION constraint. And for companies interested in this For the firms that produce durable goods, the choice between (SMEs) are eliminated out of that because of capital 1. INTRODUCTION constraint. And for companies interested in this business, eliminated out need of that of capital For the and firmsselling that produce durableissue. goods, the achoice between there areareseveral questions to because be considered. An leasing is a concerned Over long period in (SMEs) constraint. And forquestions companiesneed interested this business, For the and firmsselling that produce durableissue. goods, the achoice between there are factor several to beisin considered. An constraint. And for companies interested in this business, leasing is a concerned Over long period in essential of the durable goods its life span. For the firms that produce durable goods, the choice between the past,and most of the firms choose selling strategy, and the there are factor severalof questions needgoods to beis considered. An leasing selling is afirms concerned issue. Overstrategy, a long period in essential the highly durable its span. are several questions need toproducts be considered. An the past,and most of mainly the choose selling andprice the Consumers usuallyofthink of the life.life However, leasing selling is a concerned issue. Over a long period in there existing research concentrates on the optimal essential factor the durable goods is its life span. the past, most of the firms choose selling strategy, and the Consumers usually think highly of the products life. However, essential factor of the durable goods is its life span. existing research mainly concentrates on the optimal price leasing company will spend of more on these life. more durable the past, most of ofthethe firms choose selling strategy, the the and production products. It is noted thatand many Consumers usually think the products existing research of mainly concentrates the optimal price the leasingsince company willhighly spend more on and theseredistributed moreHowever, durable usually highly the products life. However, and production the products. It on is noted thatoptimal many machines theythink need to be of retrieved at existing research mainly concentrates on thetooptimal price Consumers researchers have turned to pay attention the the leasing company will spend more on these more durable and production ofturned the products. It is noted thatoptimal many machines since they need to be retrieved and redistributed at the leasing company will spend more on these more durable to the researchers have to pay attention end of each time period. And he also has to cut down the and production ofof the products. It is notedCoase that (1972) many machines since they need to be retrieved and redistributed channel structures the durable manufacturer. at researchers have of turned to paymanufacturer. attention to Coase the optimal end of each time period. And he also has cut down the machines since bethose retrieved and to redistributed at channel structures thedurable durable (1972)a the leasing price forthey theneed goodtoof consumers with capital researchers havethat turned to paygoods attention to the makes optimal firstly claimed a monopolist the end of each time period. And he also has to cut down the channelclaimed structures of athedurable durablegoods manufacturer. Coase (1972)a leasing price for the good of those consumers with capital the end of each time period. And he also has to cut down the firstly that monopolist makes constraint who can but lease the machines, which impacts his channel structures of the durable manufacturer. Coase (1972) larger profit when leasing its products rather thanmakes selling leasing price for the good of those consumers with capital firstly profit claimed that leasing a durable goods monopolist who canthe but leaseof thethose machines, whichwith impacts his leasing for good consumers capital larger when its products rather than sellingaa constraint profit inprice the original market. firstly claimed that a durable goods monopolist makes them. It’s widely recognized that leasing strategy is important constraint who can but lease the machines, which impacts his larger profit when leasing its products rather than selling profit in the original market. constraint who can but lease the machines, which impacts his them. widely recognized that leasing is important larger profit when leasing products rather than selling if the It’s manufacturer wants toits make morestrategy profit when facing profit in the original market. them. It’s widely recognized that leasing strategy is important So far as we know, the capital constraint of the consumers is profit in the original market. if thechanging manufacturer wants make moredemand. profit when facing them. It’s widelymarket recognized that leasing strategy isGenerally, important the andto dropping far as we know, the capital preference constraint of the consumersby is if thechanging manufacturer wants to dropping make moredemand. profit when facing So hardly regarded as a consumer or heterogeneity the market and Generally, So far as we know, capital preference constraint of consumersby is if the manufacturer wants to make more profit whenreasons. facing hardly leasing goods appeals to the consumers for three regarded as a the consumer orofthe heterogeneity the changing market to andthe dropping demand. Generally, So far as we know, the capital constraint the is former researchers. So is the wealth levelof theconsumers market and leasing goods appeals consumers for three reasons. hardly regarded as a consumer preference or heterogeneity by the changing market and dropping demand. Generally, First, they can get a relatively higher utility because the former researchers. So is the wealth level of the market and leasing goods appeals to the consumers for three reasons. hardly regarded as a consumer preference or heterogeneity by consuming patterns. So In this paper, we level build of an the analysis model First, they canare getless a relatively utility because the former researchers. is the wealth market and leasing goods appeals tolikely the consumers for three reasons. leased goods to higher be out-of-dated. Second, patterns. In some this paper, weon build an the analysis model First, they canaregetless a relatively higher utility because the consuming former researchers. So is the wealth level of market and and manage to shed lights these questions. We leased goods likely to be out-of-dated. Second, consuming patterns. In this paper, we build an analysis model First, they can get a relatively higher utility because the leasing is moreare flexible. Consumers can use the products as and manage to shed some lights onbuild these questions. We leased goods less likely to be out-of-dated. Second, consuming patterns. In this paper, we an analysis model consider a market composed of two groups of consumers, one leasing is and morereturn flexible. Consumers use the products as and manage to shed some lights on these questions. We leased are less to be out-of-dated. Second, they likegoods it tolikely the firm if can it’s dispensable. Third, a market composed two other groups of consumers, one and manage to shed some lights on these questions. We leasing is and morereturn flexible. Consumers can use the products as consider with capital constraint andof the without, and then they like it to the firm if it’s dispensable. Third, consider a market composed ofthe two other groupswithout, of consumers, one leasing is more flexible. Consumers can use the products as with the rental price is always much lower than the selling price. capital constraint and and then they like and return it to the firm if it’s dispensable. Third, consider a market composed of two groups of consumers, one compare three marketing strategies of the manufacturer, purethe pricereturn is always much lower than the selling price. with capital constraint and the other without, and then they like it to the if it’s dispensable. Third, Thisrental is a and major forfirm those with capital three constraint marketing the manufacturer, the rental price isattraction always much lowerconsumers than the selling price. compare with capital and the of other without, and purethen selling, pure-leasing, andstrategies a hybrid strategy, to investigate its This is a major for those consumers withstrategy capital comparepure-leasing, three marketing strategies of the manufacturer, purethe rental price isattraction always much lower than the selling price. selling, constraint. Therefore, the leasing strategy or a hybrid and a hybrid strategy, to investigate its This is a major attraction for those consumers with capital compare three marketing strategies of the manufacturer, pureperformance. Our main research questions are:(1) Is the constraint. Therefore, the leasing strategy or a hybrid strategy selling, pure-leasing, and aresearch hybrid strategy, to are:(1) investigate its This is a major attraction consumers withforcapital of leasing and selling can beforanthose alternative solution some performance. main questions Is the constraint. Therefore, the strategy orsolution a hybridfor strategy pure-leasing, and a hybrid strategy, to investigate its relatively smallOur leasing market in China reasonable? How do of leasing and selling can leasing be an alternative some selling, performance. Our main research questions are:(1) Is the constraint. Therefore, the leasing strategy or a hybrid strategy manufacturers, especially when the consumers are reluctant relatively small leasing market in China reasonable? How do of leasing and selling can be an alternative solution for some performance. Our main research questions are:(1) Is the the marketsmall structure andmarket productinquality the company’s manufacturers, especially when the consumers are for reluctant leasing China affect reasonable? How do of leasing and selling can be an alternative solution some relatively to pay. marketsmall structure andmarket product affect company’s manufacturers, especially when the consumers are reluctant the relatively inquality China reasonable? How do decision? (2) Is leasing the hybrid channel always the the better choice? to pay. the market(2) structure and product quality affect the company’s manufacturers, especially when the consumers are reluctant decision? Isrelationship the hybrid channel always the the better choice? to pay. the market structure and product quality affect company’s What is the of two channels in the hybrid Given decision? (2) Isrelationship the hybrid channel the in better to pay.the above, it’s obvious that leasing channel has played What is the of two always channels the choice? hybrid decision? (2) Is the hybrid channel always the better choice? Given the above, it’s obvious thatgoods leasing channel has played strategy? an important role in the durable market. In China, we What is the relationship of two channels in the hybrid Given the above, it’s obvious that leasing channel has played strategy? is the relationship of two channels in the hybrid an important role it’s in durable market. In has China, we What Given the above, obvious thatgoods leasing channel played have long seen a the small construction machinery leasing an important role in durable goods market. In China, we strategy? have long seen a the small construction machinery leasing an important role in the durable goods market. In China, we strategy? have long seen a small construction machinery leasing have long seenIFAC a small construction machinery leasing 2405-8963 © 2019, (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

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The remainder of this paper is organized as follows. Section 2 presents the model and assumptions. We compare the three marketing strategies in Section 3 and the analyses on the effects of the parameters are presented in Section 4. Then the paper concludes with Section 5 2. MODEL FORMULATION In this section, we describe the basic model framework and the assumptions about the consumers, products and the manufacturer. We establish a model involving a monopoly manufacturer selling a durable product to customers. And the firm operates over an indefinite time horizon, which is similar to the models in some other literatures on durable goods (Agrawal et al. 2012, Lacourbe 2016). At the begin of each time period, the monopolist will decide the leasing and selling price, and consumers make their decision based on their utility function. At the end of the time period, the leased products will be returned and repaired for the next transaction. 2.1 Product To better understand the durable goods market, we take the construction machinery industry as an example. Apparently, other durable goods such as cars or web servers also fit. For a machine newly introduced, it has a quality VN = 1 . And its life span is N. We take it as an exogenous variable which is determined by monopolist’s production technology. When the machine is sold, the depreciation rate is 1 −  s  ( 0,1) ,

s

Vs =

t

s

t

s

price at period t, and p st is the per-period expense

the beginning of period n. Consequently, when the machine is purchased, the aggregated average quality is + N −1 1− N = N N (1− )

At the begin of every period, the consumers make their decisions to purchase, lease or do nothing based on their perceived utility and personal preference, which are widely employed in earlier researches (Desai and Purohit 1998, Yin 2010). Similarly, we assume that the consumer’s per-period utility is given by U =   V − p . It comprises the product quality V , the quality evaluation  and the per-period expense p . Compared with the pure-leasing model, the consumers’ decision in a concurrent leasing and selling market is more convoluted. Consumers who lease the good just have to consider the current price and quality in one period. Yet sold products last for N periods and the gross quality value and price are generated. To compare the two utility functions, we use the per-period expense rather than the leasing and selling price to unify the two utility functions. The expense of leasing a product for one period equals the leasing price. And the per-period expense of each sold machines is usually calculated as the annuity (Dasgupta 2007). In this paper, we simply assume the per-period expense is the average, i.e. P = Np . P stands for the selling t

which means the quality of the used machine is Vsn =  sn −1 at

1+ +

 is uniformly distributed in [0,1] . And  of the C-type consumers is uniformly distributed in [w-1,w](0
correspondingly. While taking the interest rate into consideration may unnecessarily complicate the analysis and won’t change the insights concluded in this paper.

. And for the leased products, the

monopolist will remanufacture the machine after the machine being returned for the next order. We assume that the remanufactured machines have the constant quality value Vl .

2.3 Market and strategy

In practice, when the service life is over, the machines, whether it’s sold or leased, are usually recycled by the manufacturer for remanufacturing, which can save the cost (Yi 2016). Thus, the salvage of every product can be subtracted from its production cost, and we assume we assume the residual value is 0 to simplify the analysis. In addition, two types of cost are taken into account: marginal production cost c , and marginal recycling and maintenance

Two marketing channels are considered in this model. In time period t, consumers who don’t own the goods make their decisions in accordance with the utility function. Those who have purchased in the previous periods take no action. We assume that every consumer can have at most one unit. So, the quantity of newly introduced products can be derived from the demand. In time period t, the demand from the Ctype and N-type market is denoted by Qct and Q nt respectively,

cost in one period c m .

and Q nt is further decomposed into leasing quantity

t

Qnl

and

t

selling quantity Qns . After many scrapped products go out of

2.2 Consumer

the market, the quantity of products the monopolist offers for t t the three markets are qct , qnl and qns , respectively. Then we

Apart from the monopolist manufacturer, two heterogeneous groups of consumers are involved, who are distinguished by capital constraint. In other words, the market is composed of the consumers with capital constraint (type C) and the consumers without capital constraint (type N). And we denote the proportion of C-type consumers in this market by m . We use the parameter  to represent the consumers’ quality evaluation of the product. For the N-type consumers,

can obtain that the production is subject to satisfy the N −1

equation Q

t i

=  qi (i = c, nl , cs ) . The monopolist can t− j

j =0 t

both lease and sell products at the price of P and P L

t

S

respectively. Since there is no physical separation between the two markets, the leasing price in the two markets is 325

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in the two markets is set to be the same, the demand is determined by the wealth level of the market. We calculate the demand in the two markets, and it can be derived that demand in the N-type and C-type market Q is nl = 1 − pl / Vl

supposed to be the same. By choosing the optimal prices of P and P , the monopolist maximizes its profits. t

t

L

S

3. THE MONOPOLIST’S STRATEGIES

and Q

In this section, we analyse three cases where the monopoly firm can choose lease or sell or the hybrid strategy. Consistent with those literature focusing on the durable goods in an indefinite time horizon, we study the steady state equilibrium in which the monopolist won’t change the price in each period. This is reasonable because the machinery may be not in the market for a long time before upgrading, and the manufacturer prefers to lever the production. Then the price shall be constant as well (Tilson et al. 2009). So, we take out the notation t in the monopolist’s decisions. In the steady state equilibrium, the price of leasing and selling don’t change over time. Then the utility function of consumers in both markets is determined, so is the demand. For a good with a longevity of N periods, the quantity of the newly manufactured products satisfies the equation t i

c

= w − pl / Vl . Equivalently, we have the profit function

max  L = (1 − m)[( Pl − c )  qnl + ( Pl − cm )  (Q

pl

− qnl )]

+ m[( Pl − c )  qc + ( Pl − cm )  (Q c − qc )]

(3)

Lemma 2. The optimal price and quantity and monopolist’s profit with pure-leasing strategy are: Vl c + ( N − 1)cm (1 − m + mw) + 2 2N 1 + m − mw c + ( N − 1)cm L − Qnl = 2 2 NVl Pl L =

N −1

Q

321

=  qi (i = c, nl , cs ) for any starting point t. Similarly, t− j

QcL =

2 w + m − 1 − mw c + ( N − 1)cm − 2 2 NVl

L =

( NVl (1 − m + mw) − c − ( N − 1)cm ) 2 4 N 2Vl

(4)

j =0

we simply ignoring the production swing during these periods, and assume that the quantity of the newly manufactured products is supposed to be 1/N of the total demand.

3.3 Hybrid strategy If both strategies exist in the market, the monopolist sets both Pl and Ps . And the consumers make their decision based on their utility and preference. For one monopolist that provides two types of products, we make an implicit assumption that Vl  Vs . This is held in many existing literatures. As

3.1 Pure-selling strategy When the monopolist takes pure-selling strategy, the consumers in C-type market are not taken into consideration. Since the monopolist don’t change its price, the overall demand from the N-type market do not change. Based on the utility function of consumers in N-type, we can derive that the overall demand Q ns = w − p s / Vs . Recall the profit function

discussed in section 1, leasing is more flexible when it comes to the product’s price and usage period. Convenience and flexibility have appealed to a number of consumers. In addition, compared with the average per-period utility of purchasing, the per-period utility of leasing is higher as a result of the regular maintenance. The difference goes bigger as the N increases. It’s generally regarded that a company that can handle two marketing channels is able to keep the quality of leased product at a high level. Thus, we have Vl  Vs .

of the monopolist for period t. We can derivative the profit in pure-selling market is

max  S = (1 − m)( Ps − c)  qns

(1)

Solving the problem, we get the following results:

For the N-type market, the consumers are divided into three parts by two available marketing channels. We introduce 1

Lemma 1. The optimal price and quantity and monopolist’s profit with pure-selling strategy are: NVs + c P = 2 S s

S =

NVs − c Q = 2 NVs S ns

and  2 as the two consumer threshold. 1 is the boundary between leasing and selling, and  2 separate the consumers

(2)

who choose to buy and those who take no action. In summary, we have 1Vl − Pl = 1Vs − Ps and  2Vs − Ps = 0 . In this

(1 − m)( NVs − c) 2 4 N 2Vs

market, if the consumer’s quality evaluation is larger than 1 ,

3.2 Pure-leasing strategy

he will choose to lease rather than purchase, and consumer with a quality evaluation between 1 and  2 prefers to buy.

When the monopolist adopts the pure-leasing strategy, both markets make the same performance. At the begin of each time-period, all the consumers will return the machines and make another decision in leasing. Thus, we can easily investigate the demand for one period. Since the leasing price

For those consumers whose evaluation is below  2 , they do nothing. The demand is expressed as Qnl = 1 − 1 , Qns = 1 −  2 . For the C-type market, the consumers can

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only choose to lease. We define  3 as the consumer threshold

line stands for corresponding vl . as expected, a bigger C-

who is indifferent between leasing and non-consumption, as shown in fig 1. Therefore, we have  3Vl − Pl = 0 . Similarly,

type market absolutely reduces the profits of both strategies. For pure-selling strategy, it only cut down the overall demand in the whole market. While by spending extra operation cost to handle the product turnover, leasing companies gain the opportunity to make profit from the C-type market. The deduction in quantity is smaller because of the supplement of the C-type market, but the increase of the capital constraint consumers forces the manufacturer to decrease the leasing price at the same time. Therefore, the wealthy level of the Ctype market is the fatal issue for the leasing company to lessen the loss with an increasing m. considering a poor Ctype market,  L −  S will decrease because of the lower

demand is determined asQ

c

= w −  3 .The overall profit

function is

max  H = (1 − m)[( Pl − c)  qnl + ( Pl − cm )  (Q

nl

− qnl )]

+ m[( Pl − c)  qc + ( Pl − cm )  (Q c − qc )]

(5)

+ (1 − m)[( Ps − c)  qns ] Lemma 3. The optimal price and quantity and monopolist’s profit are as follows: c + (1 − m + mw) NVs P = 2 Vl c + ( N − 1)cm H Pl = (1 − m + mw) + 2 2N ( N − 1)cm c H Qns = − 2 N (Vl − Vs ) 2 NVs

leasing price as the m is small. The effect of quantity deduction dominates when the proportion grows and  L −  S begin to increase. When the C-type market is close

H s

QnlH = 1 − QcH =

(6)

enough to the original market, a slight decrease on the leasing price has little effect on the profit. Then we can see an everincreasing profit difference. Then we take a look at the product quality. An increase on the quality of sold goods absolutely stimulates the monopolist to take pure-selling strategy. But the initial difference (when m=0) is determined by the relationship between v s and vl .

N (1 − m + mw)(Vl − Vs ) + ( N − 1)cm 2 N (Vl − Vs )

2Vl Nw − (1 − m + mw)Vl N − c − ( N − 1)cm 2 NVl

4. ANALYSIS OF THE MODEL In this section, we compare these strategies to explain the market change in China and analyse the performance and market features. We pay attention to the steady state equilibrium, in which the prices don’t change over time. 4.1 Comparison between pure-selling strategy and pureleasing strategy For the monopolist, the primary goal is to figure out the optimal channel structure. We firstly analyse how the market structure, which is represented by m and w, and the quality difference, which is marked as v s , affect the decisions. Since Fig. 1. Effect of the market structure and product quality

most companies take pure-selling strategy, we divert attention to product quality of sold ones, and denote vl as a reference. This won’t change the insights and makes the conclusion more intuitive. Proposition 1.(1) there is a m * such that if m  ( m*,1) then L

  S for any available vs ; otherwise  L   S if and

only if vs  vs1 for a threshold vs1 . Proposition 1.(2) when the C-type market is wealthy enough w  w1 ,  L −  S increases as m increase; but for market that have w  w1 ,  L −  S decrease first and then increase

Fig. 2. Effect of the market wealth

with increase in m. In addition, a wealthier C-type market, which is denoted by an increasing w, also contribute to the difference. And the impact of adding w on the difference is much steady, compared with that of m (as shown in fig 2). Hence, when the

This proposition depicts the inhibiting effect of the C-type market and product quality, as shown in fig 1, and the red

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323

C-type market just emerges, rather than choose pure-leasing strategy, more manufacturers prefer to take pure-selling strategy.

market by serving these consumers with capital constraint. Secondly, in N-type market, two channels are established to make a price discrimination strategy and stimulate the

Proposition 2. For leasing companies, as the maintenance cost increases, the profit of pure-leasing strategy decreases, so do the quantities in both types of market, and the leasing price increases.

demand. Seeing that Pl

H

= Pl L , it can be indicated that the

stimulating effect of C-type market performs much more significant than the latter. In the C-type market, consumers can only choose the leasing channel because of the capital constraint. And it’s not affected much by the introduction of selling channel. In the N-type market, due to the competition between two channels, the market coverage both declined. While with the help of N-type market, the leasing price remains the same, and the selling price decreases to attract consumers with low quality evaluation. Thus, compared with the leasing companies, manufacturers taking pure-selling strategy may be more willing to take full control of the marketing channels.

Generally, an increasing c m have pushed up the average cost of the products. And the cost pressure drives the manufacturers to raise leasing price, resulting in a decrease in market coverage. In fact, a well-established leasing distribution channel calls for a lot of money as well as management effort, which has restricted the development of leasing companies in China. In recent years, as an important part of the aftermarket, the leasing channel building has witnessed a rapid growth, especially on the equipment management and talent cultivation. A decreasing operational cost strengthens the development of leasing market, with a compound annual growth rate of 20%.

Proposition 5. When m increases, the gross profit of the manufacturer will decrease. Prices for both leased and sold products decrease. Demands for leased products in C-type and N-type markets both increase, while the selling demand remains the same.

Proposition 3. When the life span become longer, the profit of pure-leasing strategy increase, yet the profit of pureselling strategy increases at first and then decreases. The effect of life span on the profit of two strategies varies. For the selling companies, a longer life span increases overall demand, yet a large stock in the market surely suppresses the production in a single time period, which results in a profit decline. Meanwhile, if the life span is too small, consumers perhaps think lowly of it, and refuse to purchase. Then, to stimulate consumers to purchase and get more profit, a lot of planned obsolescence or trade-in strategies have been discussed. For leasing companies, compared with producing a new machine, spending more on maintenance to keep the machines in good condition is a more economical way. A longer life span will push down the leasing price, which appeals to more consumers. Hence, they are more willing to extend product life to get more profit. 4.2 The performance of the hybrid strategy In practice, it may be a better choice for these companies with sufficient money and powerful control over the market to take both channels. The combination of leasing and selling channels allow most consumers to choose the way they spend, which is conducive to the expansion of external markets. And leasing is considered to be effective way to discriminate across consumers as well (Desai and Purohit 1998). According to lemma 1,2 and 3, we can easily draw that  H is always greater than  S and  L , illustrating the contribution of the introduction of leasing channel on the manufacturer’s profit. Proposition 4. Leasing channels dominate in the hybrid strategy. Two effects have contributed to the increase of the total profit in the hybrid channel. Firstly, the leasing channel expands the 328

The proportion of the C-type consumers has a direct influence on the production. The demand from C-type market will increase proportionally with an increasing market size, so do those in the N-type market. Besides, the change in market proportion will affect the manufacturer’s pricing decision, which have an indirect impact on the demand in the competitive market. When the proportion of C-type market increases, the consumption capacity of the whole market decline because of the aggravated capital constraint. So, the leasing and selling price decrease accordingly. For the leased products, if we take a look at the two markets respectively, it can be found that the constraint in budget leads to a demand increase in both markets. But for the entire leasing market, we are more likely to see a decreasing demand due to the difference of wealth level of the two markets. The consumption capacity of consumers in the N-type market is much stronger. As N-type market shrinks, the impact of change on the consumer group is greater than that of price decline. For the sold products in N-type market, a bigger rate of capital-constrained consumers also pulls down the selling price. Since leasing prices decrease simultaneously, the demand for sold products in this market stays unchanged. To some degree, the selling channel can remain independent by cutting down the price to remain the market coverage. In total, more consumers with capital constraint literally affect the performance of the hybrid strategy, especially the leasing channels. Another important factor of the market structure is the wealth level of the C-type market, which is denoted by w. In a wealthier C-type market, consumers are more willing to lease products and, consequently, the price goes up. Similarly, demand for sold products doesn’t change when prices increase concurrently and proportionally, which suggests an independent selling channel. While for the leasing channel, a wealthier C-type market prompts the demand, and then drive up the leasing price. In turn, the demand of leasing channel in N-type market is inhibited.

2019 IFAC MIM 324 Berlin, Germany, August 28-30, 2019

Jian Li et al. / IFAC PapersOnLine 52-13 (2019) 319–324

Proposition 6. When the life span increases, the leasing prices decrease, consequently demand for leased products in both markets increase, the per-period expense decrease and the selling price increase, and the quantity of sold products decreases.

market in China during the past few years and has provided some management insights for companies. It must be admitted that this model is not without limitations. First, we don’t clarify the relationship between the maintenance cost and product quality of the leased goods. In practice, with more spend on the products’ inspection and maintenance, consumers' assessment of product quality will increase as well. Secondly, we regard the life span as an exogenous variable, ignoring the planned obsolescence of the monopolist. And the life span of the leased and sold products even don’t have to be same. It’s would be much more meaningful if we extend the model to take the life span as a decision variable.

Since the per-period expense and the price of sold products perform differently, we use the former to continue the discussion. As the total market is dominated by leasing channel, it is not surprising that increasing the life span is more profitable. As an effective way to reduce the product cost, increasing the life span can be used to squeeze down the leasing price. And whether a longer life span or a lower price for rent is a great appeal to consumers. Therefore, market coverage of leasing channel increases with longer life span. As for selling channel, even though the selling price decreases faster than leased ones, demand for sold products decrease with increase of N. As the life span increases, a quick decline in the quality evaluation of the sold products suppress the consumers sentiment (Since we cannot make the conclusion analytically, we did many numerical studies to show the trends, as shown in Fig 4). Therefore, for those companies who take the hybrid strategy, extending the product life span literally does harm to the maintenance of the selling channel.

ACKNOWLEDGEMENTS This research was funded by the National Natural Science Foundation of China (No. 71571010), and partly by GreatWall Scholar Training Program of Beijing Municipality (CIT&TCD20180305). REFERENCES Agrawal V V, Ferguson M, Toktay L B. (2012). Is leasing greener than selling. Management Science, 58(3): 523533. Coase R H. (1972). Durability and monopoly. The Journal of Law and Economics, 15(1): 143-149. Dasgupta S, Siddarth S, Silva-Risso J. (2007). To lease or to buy? A structural model of a consumer's vehicle and contract choice decisions. Journal of Marketing Research, 44(3): 490-502. Desai P, Purohit D. (1998). Leasing and selling: Optimal marketing strategies for a durable goods firm. Management Science, 44(11-part-2): S19-S34. Lacourbe P. (2016). Durable goods leasing in the presence of exporting used products to an international secondary market. European Journal of Operational Research, 250(2): 448-456. Tilson V, Wang Y, Yang W. (2009). Channel strategies for durable goods: coexistence of selling and leasing to individual and corporate consumers. Production and Operations Management, 18(4): 402-410. Yi P, Huang M, Guo L. (2016). Dual recycling channel decision in retailer oriented closed-loop supply chain for construction machinery remanufacturing. Journal of cleaner production, 137: 1393-1405. Yin S, Ray S, Gurnani H. (2010). Durable products with multiple used goods markets: Product upgrade and retail pricing implications. Marketing Science, 29(3): 540-560.

Fig. 3. Effect of the life span 5. CONCLUSION Faced with the rapidly changing market environment in China, machinery manufacturers are striving for chances for transformation and market development. As a challenging issue, the strategy between leasing and selling of durable goods has been extensively and fully discussed. In this paper, we learn from the existing research and build a model with two differentiated markets. Next, we explore how the market structure and product features influence the strategy decision of a monopoly manufacturer and try to explain the phenomenon of the development of construction machinery leasing industry in recent years in China. Finally, some managerial insights on channel selection and operation are proposed. Although we believe our model helps explain the development trend of the construction machinery leasing 329