Product Design for Recycling and Recycling Industry
Makoto Tawada*

andAichi Gakuin University

Tomokazu Sahashi
Nagoya City University

ABSTRACT
Because of the fear of resource extinction and worsening of natural environment,
companies and households have been gradually promoting the activities of reducing,reusing, and recycling of natural resources by the slogan ‘3Rs’ representing those
activities. We need to achieve building an efficient recycling system to reduce the burdenof the environmental cost in production as well as consumption. In the production side,producers become conscious of the importance of renewable resource use and recycledmaterial use in addition to the effort to make more efficient use of natural resources. For
promoting recycling of end-of-life products and making efficient use of resources, one
important method is to adopt the designs of produced commodities which make easier torecycle the commodities after their use, so that waste disposal could be decreased.
We investigate a recycling model on the basis of Eichner (2005). Our paper isdifferent from his model in three aspects. First, in his paper it is the recycling firm rather
than the producers that determines the level of the product design. Since the recycling
firm determines the level of product design so that recycling cost is minimized, the social
optimum level of product design can be achieved in the market economy. Hence, external
diseconomies cannot be caused by product design. But our paper employs more realistic
model in which the producers determine the level of product design. In this case, theproducers decide the design level so as to minimize production cost. Therefore, we cannot
achieve the efficient level of product design because recycling costs increase and thus
external diseconomies appear. Second, since policy variables have been introduced in anarbitrary manner in Eichner (2005), it is hard to understand which policy can take careof which market failure. In our model there are three kinds of market failures, that is,monopoly, environmental externality, and product design externality. These three typesof market failures are related to the production amount of a consumption good, the levelof product design, and the recycling ratio, respectively. As policy instruments to resolvethese failures, we can consider a production subsidy for the recycling firm as amonopolist, a waste tax imposed on the discarded waste to promote recycling, and amaterial subsidy to encourage the product design suitable to recycling. Third, we provide
some comparative statics analysis so as to examine how the changes of the degree of anenvironmental damage caused by waste, the waste disposal cost of landfilled goods, andthe price of the recycled materials affect the level of production, the product design, andthe recycling ratio.
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Product Design for Recycling and Recycling Industry
Makoto Tawada*

andAichi Gakuin University

Tomokazu Sahashi
Nagoya City University

1. Model and Social Optimum
We employ the model which is partial equilibrium in nature. The amount of aconsumption good is denoted by y which is produced by the use of recycled materials,
virgin materials and labor. The producers determine the attribution of the consumption
good in addition to production level. The attribution of the consumption good is expressedby an index of product design q . It is assumed that the waste good can be recycled by alower cost according to a greater q . The cost function of the producer is given by

C ( y, q)  yF (q) ,(1)where F (q) is the unit production costs of the consumption good with recyclability
degree q and we suppose that Fq  0 , and Fqq  0 . For any consumption amount of thegood, the same amount of the waste good is supposed to be generated. We assume thatthe producers collect the waste good and bring them into a recycling firm. The recycling
firm produces recycled materials by the use of a part of the waste and discards theremaining by landfilling.
Then, for consumed amount of the consumption good y , we havey  r  w,
where

r and

(2)

w are the recycled and discarded amounts of the waste good,

respectively. Let  represent the recycling ratio of the wasted good. Then the followings
hold:r  y ,(3)w  (1   ) y .

(4)

Next we define the cost structure of a recycling firm. We assume that the recycling
cost function is represented by the following function:N  yG(q, ) ,(5)

where N is the cost to produce r ( y) units of recycle materials fromy units of

the waste good. As for the function G(q,  ) , we assume that G  G /   0 ,G  G /   0 , Gq  G / q  0 and Gqq  Gq / q  0 .
The consumption good market is supposed to be perfectly competitive and the
producers of the consumption good determine the quality of the product design andproduce the good by the use of recycled and virgin materials. These producers have an
obligation to collect the used consumption good from households and hand bring them2

into a recycling firm. In the recycling market, only one firm exists so that the firm canact as a monopolist. This recycling firm receives the used consumption good from theconsumption good producers and produce recycled materials which will be reused in the
consumption good production. The non-recycled parts of the used consumption good are
landfilled as waste. Finally the resource and material market is supposed to be perfectlycompetitive.
The linear inverse demand function of the consumption good is represented byP( y)    y where  and  are strictly positive parameters. The landfilling ofwaste is supposed to cause an environmental damage. We assume that the marginal
landfilling cost of end-of-life products is c w and the marginal environmental damage
by landfilling waste is c d . Both c w and c d are positive and constant. Then the social
welfare isy

W ( y, q,  )   (  s)ds  yF (q)  yG (q,  )  (c w  c d )(1   ) y  yp r ,0(6)

where p r is the price of resources and materials for production.
Our first task is to demonstrate the socially optimal allocation which follows fromthe maximization of (6) with respect to y , q and  . Then the first-order conditions
are obtained as  y*  F (q*)  G(q*, *)  (c w  cd )(1   *)   * p r ,(7)

Fq  Gq  0 ,(8)G  c w  c d  p r .

(9)where y * , q * and  * are those of optimal values. If G(q,  ) is convex for (q,  ) ,the second-order condition is satisfied. (See Appendix for this.)
The efficient allocation of the consumption good is determined by equation (7). It
means that the consumers’ marginal payment for the consumption good which is the
LHS of (7) equals the sum of its unit production cost, the net unit recycling cost
( G(q*, *)   * p ), the marginal landfilling cost and the marginal environmentalrdamage. Equation (8) shows that, for the recycling activity, the marginal cost of thedesign expressed by Fq should be equal to the marginal benefit from saving the recycling
cost exhibited by  Gq . Equation (9) implies that the marginal cost to raise the recycling
ratio is equal to the sum of the marginal landfilling cost, the marginal environmental
damage, and the price of the recycled materials.
32. Market Equilibrium
In this section we investigate the market equilibrium. Our model introduces theconcept that the consumption good producers have a responsibility to collect the-end-of
life consumption good from households after consumption and to bring it to the recycling
firm. When the collected end-of-life consumption good is brought into the recycling firm,
the consumption good producers must pay a fee to the recycling firm for recycling service
provided by the recycling firm. Japan and some countries in Europe, for example, adopt
this system.
Since perfect competition prevails in the consumption good market, the profit
maximizing behavior of a typical consumption good producer is formulated asmax  y  ( p y  p) y  yF (q)   m qy ,

(10)

y ,q

where pyis the price of the consumption good, p is the price of the wasted goodbrought into the recycling firm and  m is a product design subsidy. The first-orderconditions are given byp y  p  F ( q)   m q  0 ,(11)

Fq   m .

(12)

The second-order condition also holds. The amount of the produced consumption good
and the quality of product design are determined from (11) and (12). Especially the levelof product design is determined as qm

 q( m ) by (12). Then, in view of (11) and thedemand equation p    y , the price of the recycling service is determined asyp    y  F (q m )   m q m  P( y, q m ) .

(13)

Next we consider the behavior of the recycling firm as a monopolist. The behaviorof the firm is to maximize its profit with respect to y and  subject to (13), so that the
optimization problem of the firm is described asmax  r  [( P( y, q m )   y ] y  yG (q,  )  ( p w   w )(1   ) y  p r y ,

(14)

y ,

where pw

is a landfilling charge, yis a subsidy for recycling service and 

w

is a

waste tax. Local government plays a role of discarding the non-recycled wastes bylandfilling, so that the government charges p to the recycling firm for this one unit ofw

cost. This means p  c . The first-order conditions for maximizing profit of thew

w

recycling firm are given by  2y  F (q m )  G(q m ,  )   y   m q m  ( p w   w )(1   )  p r ,G  p w   w  p r .
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(15)

(16)
By virtue of (16),  is determined. This, together with (15), determines y . Then p y
is obtained from (11).
In this market equilibrium, there are three types of external diseconomies. Firstis the monopoly power of the recycling firm. Second is the environmental damage causedby landfilling the non-recycled waste. Third is the low quality of the product design toreduce the production cost. These three types of failures reveal that production, y , thelevel of product design, q , and the recycling ratio,  , tend to be lower under the market
equilibrium than the socially optimal levels. In order to attain the socially optimal levelsof these variables under the decentralized economy, we can use three policy instruments.
They are a subsidy  y for the recycling service, a product design subsidy  m , and awaste tax,  w to reduce the land filling of the waste good. If these policies areappropriately introduced, economic efficiency is achieved in the decentralized economy.
The following proposition presents the levels of these policies for the market equilibrium
to be efficient.
3. Propositions
PROPOSITION 1. If we set y  y  Gq q m  p r , w  cd  0 , m  Gq  0 ,then the market equilibrium becomes efficient, implying that the welfare can be
maximized.
PROPOSITION 2. The market equilibrium level of the product design is lower than thatthat of the social optimal level. And, if Gq  0 , the market equilibrium recycling ratio
is lower than that of the social optimum.
PROPOSITION 3.

For the market economy to be efficient,  y should be a subsidy(tax) when the undersupply due to monopoly power is larger (smaller) than theoversupply due to free riding on the environment in the recycling service and landfilling.

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PROPOSITION 4. Concerning the socially optimum, increases in the landfilling cost andthe environmental damage lessen the production level of the consumption good y * , andraise the level of the product design q * and the recycling ratio  * .

PROPOSITION 5. At the social optimum, a rise in the price of the recycled material

enhances the consumption good production y * , the level of the product design q * , andthe recycling ratio  * .
PROPOSITION 6. In the market equilibrium, an increase in the landfilling cost of thewaste decreases the amount of the consumption good y m , and increases the recycling
ratio  m , but does not affect the quality of product design q m .
PROPOSITION 7. In the market equilibrium, a rise in the price of the recycled material

expands the consumption good supply y m , as well as the recycling ratio  m , but does
not influence the level of product design q m .
4. Conclusion
In our paper, we construct a model where the perfectly competitive producers of
the consumption good choose the product design which affects the recycling cost and themonopolistic recycling producer determine the volume of the recycling service andrecycling ratio of the used consumption good. Economic efficiency cannot be attainedsince there are three types of market failures which are the lower level of the productdesign, and the smaller recycling ratio and the over or under supply of the recycling
service. Thus we introduced three types of policy instruments, each of which corresponds
to each type of the market failures and investigated how these market failures are solvedby these policy instruments.
Then we examined the comparative static analysis on how changes in therecycling cost, the landfilling cost and the price of the recycled materials affect theconsumption good supply, the recycling ratio and the level of the product design. By the
analysis we showed that increases in the landfilling cost and the environmental damage
by the waste reduce the socially optimal amount of the consumption good while anincrease in the price of the recycled material expands it. We also showed that theincreases of these exogenous variables necessarily raise the socially optimal levels of therecycling ratio and the product design. In the market equilibrium, the environmental
damage by the waste has no effect on the equilibrium. The effects of the landfilling cost6

and the recycled material price have the same effect to the consumption good supply andthe recycling ratio as in the case of the social optimum. However, these exogenous
variables have no impact on the level of product design.
We can extend the present analysis to a various cases. For example, we consider
the case where the consumption good producer is a monopolist and the case where there
is a cost of the collection of the used up consumption good and thus only a part of theconsumed amount of the consumption good is collected. More importantly, we should
extend the model to a general equilibrium framework. These are our future topics.
References
Calcott, K. and M. Walls, “Can downstream waste disposal policies encourage upstream
design for environment?,” American Economic Review, Vol.90, 2000, pp.233-237.
Choe, C. and I. Fraser, “An economic analysis of house hold waste management,”

Journal of Environmental Economics and Management, vol.38, 1999, pp.234-46.
Einchner, T. and R. Pething, “Product design and efficient management of recycling andwaste treatment,” Journal of Environmental Economics and Management, vol.41,
2001, pp.109-34.
Einchner, T., “Imperfect competition in the recycling industry,” Metroeconomica, Vol.56,
2005, pp.1-24.

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