Can a monopoly be efficient and increase the welfare for society?

Doron Laveea,b,*; Uri Regevc

aDepartment of Economics and Management, Tel-Hai College, Upper Galilee, 12210, Israel.bPareto Group Ltd., Netanya, 7 Hamelacha st., PO Box 8772, ZIP 4250553, Israel.cdeceased.

*Corresponding author: E-mail: doron@pareto.co.il

Cc E-mail: doron@pareto.co.il

Tel: 972-9-8361000

Fax: 972-9-8857667

Abstract

In economic literature, a monopoly is generally considered to be a factor that reduces social

welfare. The main reason for this is the ability of the monopoly to exploit its status and set a

high price for its products. While monopoly profits are growing the consumer welfare is

falling. There are unique cases where a monopoly can increase social welfare, For example,

in extreme cases of significant economies of scale (electricity, gas, water). In this article we

will look at another reason for the advantages of monopoly - markets with high level of

uncertainty. We will show that the market of competitive firms cannot cope with uncertainty

and therefore consumers refrain from entering the market. On the other hand, a monopoly

that guaranties to stabilize the market over the long term, will bring new consumers into the

market and under certain conditions, consumer welfare will increase, Even though the

monopoly takes advantage of its status and sets a high price for its consumers. The article

presents a theoretical model and its application in the waste and recycling market.

Keywords: Uncertainty, Monopolistic market, Recycling, Municipal solid waste

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1. Introduction

Monopolization is generally associated with economic inefficiency, market contraction and

welfare reduction relative to a competitive market structure. However, the establishment of

a single buyer (monopsony) that purchases the product from the producers and stabilizes

the market price, may encourage more producers to enter the market; and thus may

increase the supply of that product. This increase of the supply side may increase the

aggregate profits and the welfare of the producers. An intuitive example is a factory's choice

of matching machinery to raw materials, when there are two alternative raw materials: one

with low efficiency and a fixed price and the other with a high efficiency and price volatility.

Changing the production line, from an inferior raw material to a more high-quality raw

material, requires a high initial investment, which together with the price volatility

discourages the factory from making the transition. A monopoly that guarantees to stabilize

the price of the high-quality raw material (even if it takes a monopolistic price), may

motivate the factory to make the transition.

In many cases, without a price assurance, a market is not created at all. In Israel, for

example, markets developed for private electricity producers, desalination plants and toll

roads, only after an assurance of a fixed long-term price for the product. If this markets did

not have a monopsony condition, a situation of under-supply of the public product might

have been created, following the uncertainty and the destructive competition which

reduces the market volume. Thus, the benefit of ensuring a long-term stable price may

overcome the damage caused by the exploitation of a monopolistic power.

The literature shows that in some particular cases, a centralized market structure may be

justified from a welfare perspective. These are markets with economies of scale, supporting

research and development, markets with negative externalities and cases of incomplete and

asymmetric information (e.g. Auriol, 1998; Boccard and Wauthy, 2010; Marette et al., 1999;

Stole, 1995; Tangerås, 2009). These studies argue that when consumers have incomplete

information on a product's quality, a cartel may improve their welfare. Schulz and Stahl

(1996) showed that in markets with heterogenic and substitute products, a monopoly may

increase consumers' surplus due to reducing searching costs. Using a similar model, Chen

and Riordan (2008) suggested a theoretical explanation to the result found in some

empirical studies such as Perloff, Suslow, and Seguin (1995), Ward et al. (2002) and

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Thomadsen (2007). Other studies (e.g., Jansen, 2008; Jin, 1996; Malueg and Tsutsui, 1996;

Shapiro and Varian, 2013; Xu, 2010), present models in which firms can reduce information

collection costs by sharing information and thus increasing production and welfare. This

result was empirically supported by other studies of particular markets, such as Doyle and

Snyder (1999) in the motor vehicle industry. Bearne (1996), suggested that a monopoly

might increase consumers' surplus due to the relatively high advertisement investment,

which may also raise the information level in the market.

Demand uncertainty is an additional factor which may justify the existence of a centralized

market from a social welfare perspective. This uncertainty may cause economic inefficiency

in competitive markets and at the same time may give monopolization advantages in

increasing welfare. Deneckere et al., (1997) for instance, presented a model in which a

monopolistic manufacturer is selling to competitive retailers. The retailers must order

inventories before the realization of the demand uncertainty. The study showed that

determining minimum Resale Price Maintenance (RPM) by the monopoly may in some cases

increase both the total welfare and the consumer's welfare. The monopoly in this case

prevents destructive competition between retailers when the demand realization is low.

Deneckere et al., (1997) showed with a similar model that in an uncertain demand

environment, a manufacturer who prevents the emergence of discount retailers through

imposing RPM, may increase the retailers' inventory and the consumer welfare under

specific conditions. This issue of price and inventory management in supply chain was

actually analyzed by many studies (e.g., Bernstein and Federgruen, 2004, 2007; Dana, 2001;

Dana and Spier, 2001; Deneckere and Peck, 1995; Hall and Porteus, 2000; Kim and Sim,

2015; Krishnan and Winter, 2007, 2010; Li, 1992; Li and Lee, 1994). These studies

demonstrate that monopolistic actions such as vertical control of price and inventory made

by the manufacturer, may lead to improvements in total welfare as well as consumer

welfare. More generally, Dobbs (2004), Earle et al. (2007), Grimm and Zöttl (2010) and

Schwenen (2014), show that under demand uncertainty an imposition of price caps in

monopolistic markets (Cournot competition), may not lead to production and welfare

increase as it does under deterministic demand. By contrast, (an increase in) cancellation of

the price cap might be welfare improving in cases when the price cap is close to the

marginal cost. These theoretical studies describe a monopoly that has no impact on either

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the demand function, or the level of uncertainty. In general, uncertainty may have an

impact on the market size and this is due to its role as a barrier for firms to enter the market

(Segal et al., 2015). This conclusion is well established in the literature which reveals that

firms may postpone their investment because of uncertainty about demand, prices or costs

(e.g. Dixit and Pindyck, 1994; Huisman and Kort, 2015).

In a previous study, Lavee et al. (2009) demonstrated that price uncertainty in the waste

recycling market is one of the important factors of the municipalities' decision to enter the

market. The empirical results of that study for the case of Israel reveal that uncertainty has

indeed a significant impact as an entry barrier; thus it could be argued that reducing

uncertainty reflected by price stability may broaden the market by promoting new

municipalities to enter recycling and encourage current recycling firms to add additional

materials for recycling. However, it should be mentioned that some current recycling

municipalities may lose and even withdraw and stop recycling due to the lower price they

receive from the monopsonistic firm.

The current study deals with issues of demand uncertainty and examines in particular

whether a monopolistic firm that stabilizes market prices can increase the economy welfare

by expanding the supply side. In contrast to previous studies (e.g., Blanchard and Kiyotaki,

1987; Tullock, 1967; Salop, S. C. (1979), the current study suggests that under specific

conditions, a monopsony can reduce uncertainty and shift the supply curve to the right; this

increase in the supply could increase welfare, even though the equilibrium price is higher

than the competitive price, due to utilization of monopolistic power. This study focuses on

the waste recycling market and relies on the previous studies of Lavee (2007) and Lavee et

al., (2009), which developed an economic model of the waste recycling market. In particular,

this study presents a model which examines a large number of producers (municipalities in

this case) in the recycling market who face an uncertain price for their product (recyclable

waste). To this end, two alternative market structures are compared: a competitive market,

characterized by demand uncertainty; and a market with a monopsony which sets a fixed

price on an input as a result of its optimization problem, and thus absorbs the uncertainty in

the market. The monopsony may reduce uncertainty in the market and thus cause an

expansion in the supply through promoting other input suppliers to enter the market. On

the one hand, this increase in supply may increase welfare, but on the other hand a

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monopsony has social costs represented by a possible reduction in the equilibrium quantity.

This study investigates when, and under what conditions, a monopsonistic firm can increase

the total welfare or even the welfare of its suppliers. The theoretical model in this study is

applied to the Israeli waste recycling market, using data from 79 Israeli municipalities to

establish whether the foundation of a monopsony in this market is efficient (welfare

increasing).

It should be mentioned that although the current model focuses on the waste recycling

market, it also provides a good intuition and description to many similar situations in which

uncertainty plays a significant role in the markets, like marketing chains with monopolistic

power over their suppliers. The paper continues as follows: Section 2 presents the

theoretical model and Section 3 discusses the welfare analysis. The empirical application is

presented in Section 4 and Section 5 concludes the paper.

2. The model

The theoretical model presented in this study is based on the model described in detail in

Lavee et al. (2009). Consider a municipality that must choose between landfilling or

recycling its solid waste. The transition from landfilling to recycling (or vice versa if

necessary) requires a fixed large investment. The municipality must treat a constant amount

of waste per time period, of which only a given fraction can be recycled.1 The model's

planning horizon is infinite and time is divided into discrete periods (for instance, one year

periods). Every period the municipality must decide whether to implement recycling, or

continue landfilling. The transition between these two states is instantaneous and the

amount of waste may be sent either to recycling or to landfilling immediately once the

investment is made.

For each unit of waste delivered to the recycling plant, the municipality is paid a sum ofPR

by a recycling plant. The unit cost of recycling by the municipality is constant(CR). The plant

then uses the waste to produce raw material for the end product at unit costC. We assume

that PR is an independent stochastic variable, distributed according to a density functionf

and the cumulative distributionF that do not vary over time, with varianceσ 2. At the

1A certain part of the waste must be landfilled at any event, thus the discussion here focuses only on the part of waste which potentially may be either recycled or landfilled. However, the recycled fraction may depend upon the level of investment.

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beginning of each period the municipality observes the price (PR) and then has to decide

whether to continue with its existing system or make the transition to the alternative

system.

The model in Lavee et al., (2009) shows that a municipality currently using landfilling,

determines a threshold switching price γ, and will make the transition to recycling if the

realization of the price PR exceeds this threshold price γ. It has been shown in Lavee et al.,

(2009) that this threshold switching price consists of two elements, the cost element CR and

the uncertainty element, measured by the standard deviationσ . The impact of uncertainty

on the threshold switching price γ was labeled as “risk premium”. The greater the

uncertainty, the higher is the "risk premium" and therefore the threshold price γ is higher2.

Thus, the risk premium can be expressed by (σ )−γ (0 ) , where γ (0 ) is the minimum total

average cost for recycling under conditions of certainty. Furthermore, for a lower

uncertainty (σ ) and risk, the municipality may be willing to increase its investment and the

fraction of waste for recycling. This could be true in particular when uncertainty is

eliminated (σ=0) and a fixed price is guaranteed for a long time horizon.

Thus, the supply function of a currently non-recycling i-th municipality is:

(1) q iS (σ , PR )={ 0 if PR<γ i (σ ) , γi

' (σ )>0q i (σ ) if PR≥γi (σ ) , q' (σ )≤0

The supply of a currently recycling municipality is fixed at q i (σ ) as long asCRi<PR. See Figure

1. The "risk premium" element in the threshold price γirepresents the additional

compensation required by i-th municipality in order to make the investment necessary for

transition to recycling, in light of uncertainty. The required compensation will increase with

uncertainty, so that the threshold price γi increases with the uncertainty. When uncertainty

is high, the municipality may be willing to spend only a small investment to supply the less

costly elements of its waste for recycling. This willingness to invest in recycling will be

greater the lower the uncertainty is. Therefore, the quantity supplied to recycling (q i) is a

decreasing function ofσ , but independent of PR as long asPR>γ i. Since the threshold price γi

2 As discussed in Lavee (2009), when a municipality is already recycling, it could make a transition back to landfilling when the price PR falls beneath the threshold priceγ L that is lower than the threshold priceγ for switching from landfilling to recycling. The difference between these two threshold prices reflects the concept of "economic hysteresis". This issue is out of the scope of this paper. For further discussion see Dixit and Pindyck (1994, p.17).

6

increases with the uncertainty, once γi rises high enough it will deter the municipality from

switching to recycling, even though the costs of recycling is lower relative to the expected

gains. Uncertainty thus leads to less recycling and higher waste management costs.

----Figure 1----

The underlying assumption of the model is that at the beginning of the process, most

municipalities landfill their waste. For a higher price PR more municipalities enter the

recycling market and thus the aggregate supply function of waste is an increasing function

ofPR. The process is described as follows: each municipality has a different threshold price γi

. We arrange the municipalities in an upward order according to their threshold prices.

When the waste price PRis sufficiently low, no recycling occurs. As the price rises, the

municipality with the lowest threshold price makes the transition to recycling and will be

referred to as the "first municipality". The supply quantity in the market is then that of the

"first municipality" and its threshold price γ1 is the threshold price of the aggregate supply

and will be denoted byγ. When PR increases, the second municipality joins the market and

the supply quantity increases, and so forth.

On the other hand, when the uncertainty level is lower, the required "risk premium" is lower

and therefore the threshold prices of all municipalities would be lower as well. For every

waste price level PR , more municipalities (and higher level of waste of each municipality)

will make the transition to recycling, and therefore the supply quantity of waste to recycling

rises up. Accordingly, the aggregate long run supply function of waste is defined as follows

(2 )Qts (PR ,t , σ )=∑

i=1

N

q i ,t (PR,t ,σ ) , Andq i ,t=0 forPR,t≤γ i ( σ ),

Where γ i(σ ) represents the threshold price of the i-th municipality andq i ,t is the quantity

supplied by municipality i in periodt . As municipalities are arranged by an increasing order

of their threshold prices, the threshold price of the first municipality is thus the threshold

price for the aggregate supply and is denotedγ (σ ). The total number of municipalities is

denoted by N and Qts (PR,t , σ )is the aggregate supply of waste in periodt . Which is an

3 The difference in the threshold price γi between municipalities derives from the different level of waste collection costs like salaries, construction etc.

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increasing function of the waste price PR,t and a decreasing function of the standard

deviation of the waste priceσ . That is:∂Qt

s

∂PR, t>0 ,

∂Qts

∂σ<0.

2.1. Competitive equilibrium

In a competitive market, a large number of recycling firms purchase waste from the

municipalities. The recycling firms use waste as an input to produce raw materials y t, which

they can sell in the global market for priceP y , t. The price of raw material P y , t is an

independent stochastic variable. Each unit of waste can be turned to one unit of raw

material for a constant costc, which includes labor, energy and other costs. Hence, the

recycling firms' production function of raw material is:4

(3 ) y t=f (q t )=q t

And the total cost function of the recycling firms is:

(4 )T C t=(PR , t+c )q t

The aggregate demand for waste by the recycling firms is infinitely elastic, determined by

the world price of raw materials, so thatPR ,t=Py ,t−c . After the realization of raw material

price P y , t in period t is observed, every recycling firm purchases waste to maximize its profit,

given by:P y , t y t−(PR, t+c )q t.

Though the recycled waste price PR,t is determined outside the recycling market by P y , t , it

can change from period to period due to the uncertainty of the demand for the world price

of raw materialP y , t. The establishment of long-term fixed price contracts between the

recycling firms and municipalities, would stabilize the waste price for a sufficiently large

number of periods and thus eliminate this uncertainty in the waste recycling market (σ=0).

However, in a competitive market, any single recycling firm or municipality would not be

willing to commit to a long-term fixed price for in a competitive market, since if the world

raw material price P y , t drops, the price of the recycled waste PR,t will drop as well and the

recycling firm will have a strong incentive to break the contract and buy its waste from other

municipalities at a lower price. In the same way however, if the price P y , t rises, the

municipality will have incentives to break the contract and seek other recycling firms to sell 4The use of a general production function will lead to the same qualitative results. But, the specification used in the study is more intuitive and useful for the empirical application.

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at a higher price. The higher the uncertainty, the stronger is the incentive to break the

contracts for both agents, so that no fixed-price contracts could prevail in a competitive

market. Thus, fixed-price contracts are not feasible in a competitive environment.

We can demonstrate that in every realization in a competitive market both:

The revenues of the municipal authority after the transition to recycling in period t :

Ei=PR ∙ qi

The profit of a competitive manufacturer in period t :

π i=P y ∙ y i−PR ∙ qi−TVC−FC

y i=qi ,TVC=c ∙q i

thus:

π i=(P y−PR−c)∙ q i−FC

The competitive producer maximizes its profit as follows:

∂π i

∂q i=P y−PR−c=0

Hence the competitive price in period t is:

PR=P y−c

The price PR is the price stipulated in the contract between the waste producer and the

municipal authority, in period t . SinceP y N (μ ,σ ), in period t+1, there may be two

situations (the situation where the price does not change is trivial and therefore we will not

refer to it):

Situation A: P y , t>Py ,t+1 In this case, the competitive manufacturer would prefer to break its

contract with the municipal authority, and work with another authority, as its potential

profits with another authority at a new price are higher. That is, π Ai , t+1<π

Ci ,t+1

π Ai , t+1=P y ,t+1∙ q i−PR,t ∙ qi−c ∙q i−FC

πCi ,t+1=P y, t+1 ∙ qi−PR, t+1 ∙ qi−c ∙ q i−FC

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P y , t+1 ∙ qi−PR, t ∙ q i−c ∙qi−FC<P y ,t+1∙ qi−PR ,t+1∙ q i−c ∙q i−FC

π Ai , t+1<π

Ci ,t+1

If a manufacturer decides to comply with the contract's terms, for small enough values of P y

in period t+1, the manufacturer will have a negative comprehensive income. That is

π Ai , t+1<0

π Ai , t+1=P y ,t+1 ∙ q i−PR,t ∙ qi−c ∙q i−FC<0

P y , t+1<PR,t+c+FC

Situation B: P y , t<Py ,t+1 In this case, the municipal authority would prefer to break the

contract and deliver waste to another manufacturer, at a new price:

EAi ,t+1=PR,t ∙ q i=(Py ,t−c ) ∙ qi

ECi , t+1=PR, t+1 ∙ qi=(P y ,t+1−c )∙ q i

EAi ,t+1<E

Ci ,t+1

However, for a monopsonistic recycling firm (a single large firm) this price stabilization could

be achieved in the market. The monopsony market is examined in section 2.2. Three

reasons can be specified for a viable long term contract when there is a monopolistic firm in

the market: First, as mentioned above, in a competitive market with a large number of

firms, fixed-price contracts are not feasible since municipalities and firms will always have

an incentive to violate the contract and sell/buy from a different firm. However, when there

is a monopsony, the municipalities cannot do so, as there are no other firms to sell their

product to (or other municipalities to buy from).

Second, the monopsony is a long-term plan, as opposed to a competitive firm (Price taker)

who plans in the short term. Repeated interactions between a monopsony and the

municipalities constitute an incentive for players to fulfill the contract in order to maximize

future profits. There is much literature on the difference between finite game equilibrium

and repeated game equilibrium. Aumaan and Shapley (1994) showed with the "Prisoner

Dilemma" and "The Folk theorem" the difference between the equilibrium in finite and

infinite game .In the finite Prisoner Dilemma, both players cooperating is not a Nash

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equilibrium, in the infinitely repeated version of the game, there is a Nash equilibrium such

that both players cooperate on the equilibrium path. In our case, the long term contract

between the monopsonist firm and the municipalities give the motive to both parties not to

brake the contract. Only a long term fixed price will encourage new municipalities to enter

the market. For a competitive player there is no interest in the market growth, only in the

price level. But for a monopolistic firm, the capacity of the market is a major factor which

determines the level of profit.

Other reasons may be that a large firm will have economic resilience in times of losses,

while small firms do not. A firm that commits to a long-term fixed-price may suffer losses in

periods that the world price of raw material decreases. Large firms have a higher ability to

absorb this loss. The monopolistic firm's resilience will convince new municipalities to switch

to recycling, due to a security of a long lasting price for their waste.

2.2. Monopsony

As an alternative, we examine a market structure with a single recycling firm that operates

as a monopsony.5 From a welfare point of view, it is obvious that if the monopsony has no

constraint on the price determination, it would reduce the municipalities' welfare by using

its market power. Nevertheless, we assume that the establishment of the monopsony firm is

subject to a commitment of the monopsony to determine a fixed waste price for a long-

term6, denoted by PRM (how this price is determined will be demonstrated later). This

commitment is established by long-term contracts between the municipalities and the

monopsony firm.

The monopsony still faces uncertain prices for its product in the global market, thus it

actually absorbs the uncertainty in the waste market. As shown above, the supply of

recycled waste is a decreasing function of price uncertainty. Therefore, the monopsony

commitment for a fixed price induces more municipalities to join the recycling market, and

thus increases the supply. Furthermore, every municipality has a better incentive to increase

its part of recycled waste. This increase of the supply will increase the aggregate surplus of

the municipalities. On the other hand, the monopsony firm still has its market power in the

5 The monopsony firm has the same production technology as a competitive firm. 6 The monopsony commits to a fix price in order to convince municipalities to enter the recycling market. It can also be assumed that the regulator agrees to allow a monopolistic firm to operate only if it commits to a long term price, but doesn't intervene in the price level or can't know what the competitive price is.

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waste market that permits it to decrease the recyclable waste price to maximize its

expected profits; and thus may reduce the municipalities' surplus. Therefore, the study

attempts to identify the conditions in which monopolization increases the municipalities'

welfare, and thus making it worthwhile for the municipalities to prefer a monopsony with

fixed price over a competitive market structure with price uncertainty.

The market equilibrium for both market structures, competitive and monopsony, is shown

in Figure 2 for a linear approximation of the market supply.

--- Figure 2-----

As shown, the demand curve depends upon the global price of raw materials Py , t which is

assumed to be a random variable, but independent of the recycling market. The demand

curve, and thus the waste price, may vary over time. This is reflected in Figure 2 by the shifts

of the demand curve upward and downward arrows. The expected equilibrium price in a

competitive market is EPR(Point D in Figure 2). In contrast, the monopsony determines a

price to maximize its profits; particularly, its optimization problem solution reveals that this

price fulfills the condition MFC=Py , t−c (See Figure 2). Nevertheless, the monopsony must

set a constant price ex-ante to the realization of the global price of its productP y , t. Assuming

that the monopsony is risk neutral, it is reasonably assumed that the price the monopsony

determines PRM is the price which fulfills the condition in expectationMFC=EP y−c .

The equilibrium in the monopsony case is described by Point B in Figure 2. As can be seen,

the monopsony reduces the equilibrium price of waste relative to the expected price in the

competitive solution. But on the other hand, the supply curve shifts to the right due to the

absence of uncertainty. The question then is which market structure do the municipalities

prefer? And for which alternative is the social welfare higher?

The monopsony obviously increases its own welfare. But, do the municipalities necessarily

suffer welfare loss? Since price reduction by the monopsony reduces the municipalities'

surplus, but the reduced risk increases it. It could be concluded that in general, when the

benefit for the municipalities associated with the risk reduction is higher than the loss

associated with the price reduction, then the municipalities will have net welfare gains.

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It should be mentioned that the municipalities' welfare are examined rather than the total

economy welfare, since there could be a situation in which the total welfare increases while

the municipalities' welfare decreases. The municipalities' welfare is important since it

represents the consumers' welfare in this case. In addition it should be noted that the

aggregate welfare is examined, so even when monopsonization is a welfare increasing

process, there are some municipalities that could be harmed and some may even quit

recycling. The total effect on the recycling level depends mostly on the initial level of the

price uncertainty. The higher it is, the lower will be the recycling and price stabilization will

lead to higher increase of the recycling market. In section 3 we will analyze it for an

individual municipality.

A linear market supply curve is assumed (for simplicity the index t is omitted in the

forthcoming analysis):

(5 )Qs= 1(1+σ )

β ( Δ(σ )+PR ) ;∧QS=0 for PR≤ γ (σ )β>0 ,

where β is a constant parameter andΔ (σ )=−γ (σ ), is the threshold price, as can be seen by

inverting the supply function. Thus,

(5')Qs= β

(1+σ )(PR−γ (σ ));QS=0 for PR≤ γ (σ )

When uncertainty (σ) increases, the supply curve (inverse supply function) will become

steeper and with higher intercept (see Figure 2).

Qs= β

(1+σ )∙PR−

β(1+σ )

∙ γ (σ )

β(1+σ )

∙ PR=Qs+ β(1+σ )

∙ γ (σ)

PR=(1+σ )β

∙Qs+γ (σ )

In a world of certainty, namely when σ=0

PR=1β∙Q s+γ (0)

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Since σ>0 and γi' (σ )>0 (and therefore γ (σ )>γ (0 )), it can be seen that the supply curve of a

world of certainty conditions is always under the supply curve of a world of uncertainty

condition. Namely,

(1+σ )β

∙Qs+γ (σ )> 1β∙Qs+γ (0 )∀Qs

The coefficient 1

(1+σ ) represents the effect of the uncertainty (σ ) on the supply function. As

shown above, the supply function of every municipality is a decreasing function of the

standard deviation of the price and so is the aggregate supply.

The higher is the parameter σ , the greater is the effect of uncertainty in reducing the

supply. The increased risk reduces the supply of each municipality in two ways: first, by

raising the threshold price γi(σ ) for entering recycling and second by reducing the recycled

quantities supplied at each price level. The coefficient1

(1+σ )∈ (0,1 ], so that in case of a fixed

price, the standard deviation equals zero and the coefficient equals one. While in the case of

a random price, when the standard deviation rises, the coefficient (and the quantities

supplied for recycling) drops and may go to zero for infinitely high uncertainty. Consistently

with the underlying model, when the uncertainty level decreases the supply curve shifts to

the right (see Figure 2); this shift emanates from the entry of more municipalities to the

market and the increased quantities for recycling by every municipality (see equation 1).

The relationship between the price standard deviation and the quantity of recycling was

studied in Lavee et al., (2009). The supply function is set to match the simulations of this

relationship that was carried out in Lavee et al., (2009). In particular, the supply function

specification in equation (5') is determined in a form that mimics the supply elasticity

observations in these simulations.7

The monopsony must determine a constant price over time for a unit of waste, denotedPRM.

This price is set such that the monopsony's profit is maximized. The expected profit function

of the monopsony in a representative period is given by:

7The elasticity of the recycled quantity with respect to the price standard deviation (Lavee's et al., 2009) was found to be an increasing function of the standard deviation. Accordingly, the supply function specification in equation (5) stands in line with this result.

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(6 )EΠ=[E P y−c−PR ]Q s (PR , σ )

The first part in equation (6) is the expected profit per unit of waste and the second part is

the waste quantity. Since PR=P y−c=¿E P y−c=EPR ,

(6 ' )EΠ=[E PR−PR ]Qs (PR , σ )

the price that maximizes monopsony's profit satisfies the following first order condition:

(7 ) ∂E Π∂ PR

= ∂Qs

∂ PR∙ [EPR−PR ]−Q s(PR , σ )=0

Appling the supply function in equation (5'), we see that ∂Qs

∂PR= β

(1+σ ) . Since the waste price

(PR¿ determined by the monopsony is constant over time, the standard deviation in the

supply function (σ ) equals zero and the coefficient of the supply function (5') becomes

1(1+σ )

=1. Thus, the fixed price PRM set by the monopsony for the municipalities, is

determined by equation (7) and given by (see point B in Figure 2):

∂E Π∂ PR

= β(1+σ )

∙ [EPR−PRM ]− β(1+σ ) [PRM−γ (σ ) ]=0 [EPR−PRM ]−[PRM−γ (0 ) ]=0

2 PRM=EPR+γ (0)

(8 )PRM=EPR+γ (0)

2

3. The welfare of the municipalities

The recycling firms will clearly gain from merging into a single monopsonistic firm. However,

the impact on municipalities' welfare, which is conventionally negative, is ambiguous here

due to its effect on eliminating uncertainty. Next we examine under what conditions

monopsonization increases the municipalities' welfare.

Analyzing a single municipality, it will obviously gain if it switches to recycling as a result of

monopsonization. That is, as a result of eliminating uncertainty, its threshold price drops

below the monopsony price so thatγi (0 )<PRM . The threshold price under conditions of

certainty γi (0 ) is simply the average total costs atq (0).

15

The ith currently recycling municipality will gain from monopsonization if its expected profits

increase. Using equation (1) and given thatPRM−CRi>0, this will happen if:

(9 )V (q i)=q i (0 ) [PRM –C Ri]−qi (σ ) [EPR−CRi ]≥0, or

(10) EPR−CRi

PRM−CRi≤qi (0 )qi (σ )

The RHS of inequality 11 reflects the relative increase in the recycled quantity as a result of

eliminating uncertainty.

From the last inequality, one can get (by subtracting 1 from each side and dividing by EPR)

the condition for the maximum (percentage) price reduction that will leave a currently

recycling municipality better off:

(11) EPR−PRM

PRM−CRi≤q i (0 )−q i (σ )

qi (σ )→

EPR−PRM

EPR=∆ PR

EPR≤

∆q i

qi (σ )(EPR−CRi)

EPR

One interpretation of inequality (11) could be that it sets an upper bound for the price it is

willing to pay for eliminating uncertainty. Another interpretation of the expression

∆PR

EPR/∆q i

q i ( σ ) would be as a sort of demand elasticity for certainty. It should be less than 1 if

CRi=0, but will have to be smaller for higher CRi in order for a currently recycling

municipality to gain from a monopsonistic environment that eliminates uncertainty.

To sum up the arguments, the three important parameters are the initial size of uncertainty,

and the effect of eliminating it on the threshold price and on increasing the fraction of the

recycled waste. The price set by the monopsonyPRM, will also play a crucial role in attracting

more municipalities to switch to recycling.

4. Empirical application

The analysis is based on data collected in Israel during 2000 – 2004 (Lavee, 2007). Data were

collected via a detailed questionnaire sent to all municipalities in Israel, consisting of

questions on all relevant aspects of the waste management system (the full questionnaire

appears in the appendix of Lavee, 2007). Lavee (2007) estimated the cost parameters of

waste management in 79 Israeli municipalities whose waste accounts for over 60% of all

16

municipal solid waste (MSW) in the country, presenting a thorough analysis of landfill vs

recycling costs and the potential economic gains resulting from the change in disposal

method.

Lavee (2007) considered a combination of waste components - an ‘‘average waste bundle’’.

The bundle is comprised of different types of recyclable waste, each weighted according to

its share (measured in mass units) of total recyclable MSW in Israel. The waste components

that have been found suitable for recycling in Israel include: paper of different types (white

paper, newspaper and other paper), cardboard, glass, Polyethylene Terephthalate plastic

(PET) and other plastics (mainly HDPT – high-density Polyethylene). Lavee (2007) identified

the municipalities for which it would be economically beneficial to adopt full recycling. In

this paper we also analyze the economic benefit for partial recycling (depending on the level

of the price of recycled waste - PR).

Lavee et al., (2009) used the same data to study the impact of uncertainty on the

municipalities’ adoption decisions. An estimate of the risk premium was preformed, and

used to examine quantitatively the effect of price uncertainty on recycling adoption. In this

paper we broaden the analysis for different levels of uncertainty were each municipality has

to choose the level of recycling (some will recycle all the potential waste components, some

only part, and some will not recycle at all). Then we calculate the total benefit from

switching to recycling (for each level of uncertainty). In the last stage we compare the

benefit to municipalities in a monopolistic market with an assurance for a long term fixed

price via an uncertain competitive market (with different levels of uncertainty). We also

analyze the number of municipalities that will benefit from the transition of the market (an

uncertain competitive market to a certain monopolistic market).

4.1. Benefits from transition to recycling

In order to calculate the benefits from transition to recycling five stages are carried out:

First, we rate the different types of waste according to the level of the net return (PR)

expected from their sale to the recycling plant (from high to low), as every waste product

has a different value. The return equals the price that can be received for a kg of waste for

recycling. However, since the return is not guaranteed and depends on changing market

prices, the net return is calculated by deducting the risk premium (the risk premium

17

obtained from Lavee et al., 2009). The volatility reduces the authority's desire to separate

and sell the recyclable waste. As the price volatility increases, a higher price is required to

motivate the authority to switch to recycling. The extra price for the "risk premium" was

quantified at Lavee et al., (2009). Table 1 displays the full return (in a world of certainty), the

risk premium analyzed in Lavee et al., (2009) and a sensitivity analysis of how the net return

changes in levels of higher (UP) or lower (DOWN) volatility.

Table 1 Sensitivity analysis for the price of recycled components under various uncertainty conditions.

Change from cornet level of certainty (USD/ton)e

Certainty (USD)d

Risk premium

cost (USD/ton)c

Risk premium bType of product a

150%100%50%0% f-10%-25%-50%

136.6140.2143.7147.3148.0149.0150.8154.47.14.6%PET

51.656.361.065.866.768.270.575.39.512.6%White paper (WP)

16.023.130.237.338.740.844.451.514.227.6%Other Plastic (OP)

14.115.016.016.917.117.417.918.81.910.0%Glass (G)

-5.11.07.213.414.616.519.625.712.348.0%Cardboard (C)

-9.4-4.60.24.95.87.39.614.49.566.0%Newspaper (N)

5.712.118.525.026.228.231.437.812.934.0%Average

a Type of recycled product; b The risk premium in accordance with the standard deviation of the price as

calculated in Lavee et al., (2009); c The change in USD per ton depending on the risk premium; d The price of

the recycled product in a world of certainty; e The price in USD per ton, given the change in the risk premium; f

The current price, the columns on the left show the risk premium in USD per ton when the price volatility

declines, the columns on the right show the risk premium in USD per ton when volatility the price increases.

The first column indicates the type of waste, the second column shows the risk premium

from Lavee et al., (2009) (in accordance with the standard deviation of each product), the

third column translates the premium into cost and the fourth column shows the price of the

recycled product in a world of certainty PR. The remaining columns show the net return in

accordance with the expected level of uncertainty in the market. For instance column 5

shows how a 50% reduction in volatility reduces the risk premium by 50%. For example, the

PR of cardboard in a world of certainty is USD 25.7, while in a level of uncertainty estimated

18

at Lavee et al., (2009) the price drops to USD 13.4 and in a volatility higher by 50% the net

PR falls to USD 7.2.

In the second stage, the return expected to the authority from recycling a group of

recyclable goods is calculated, when the authority begins to recycle the most advantageous

product, up to the point it recycles the entire recyclables. After calculating the net return

from each waste component separately and ranking their feasibility from highest to lowest,

a group of recyclable products is created according their feasibility level. First, we examine

the waste component that is the most feasible to recycle (PET), then we add the next

feasible waste component (WP) and consider the net return from recycling those two

component, then three components, etc. As we begin to expand the recycling "basket" from

the most feasible component, the more types of components we add, thus the average

return per kg decreases. Table 2 shows the calculation for each level of uncertainty.

Table 2 Sensitivity analysis of the average price of the recyclables basket under various uncertainty conditions

Change from current level of certainty (USD)cAverage Prices (certainty condition)

(USD)b

Aggregate basket by recycled components a

150%100%50%0%-10%-25%-50%

136.6140.2143.8147.

2147.9149.0150.8154.4PET

95.699.8103.9108.1108.8110.1112.

2116.2PET+WPd

34.841.247.654.055.357.160.566.7PET+WP+OP

31.236.541.947.648.650.253.058.4PET+WP+OP+G

20.225.731.437.338.340.143.048.5PET+WP+OP+G+C

5.712.118.525.026.228.331.437.8PET+WP+OP+G+C+N

a An aggregate basket of recycled components, where each row contains the components above; b The average

price of the basket in certainty conditions; c The change in the average price of the basket based on the change

in the risk premium; d Names of recycled components as listed in Table 1.

The first row displays the net return from PET, given various levels of price volatility. The

second row displays the return from a combination of PET and white paper, the third row

displays the combination of PET, white paper and other plastics, etc. The calculation displays

the return for each group according to the expected volatility level in the market, where, in

19

certainty conditions, the average return per kg of all recycled components stands on USD

37.8, while for the volatility estimated at Lavee et al., (2009), the price is lower by about

34% as a result of the risk premium.

In the third stage, the treatment cost of waste intended for recycling was calculated. When

the expected cost of separation and treatment of recyclable waste components is CR, the

treatment method is performed using recycling centers, namely, the residents bring their

waste to the centers located throughout the authority. The recycling center has a separate

retention container for each waste component (PET, NP, etc.). A transport company collects

each container separately – one truck collects only newspaper, another truck collects only

plastic, etc. For each type of waste, the CR varies depending on the container costs, the

frequency of removal, truck capacity etc. In an authority which recycles only one waste

component, the recycling center will have a single container, if it recycles all six

components, the recycling center will include six containers. In this recycling method, there

is no economy of scope, i.e., if only PET is recycled, the cost CR per kg does not change

depending on the recycling volume in the authority.

In the fourth stage, the authority's expected savings from sending waste to recycling is

calculated. The authority's expected savings, from a separate treatment of waste for

recycling, is driven from the alternative costs of landfilling CL. The expected savings are not

linear, that is, when only a certain type of waste is recycled – for instance, PET, the PET

removed from the mixed waste reduces the volume of waste intended for landfills.

However, the elasticity rate between the volume of recycled waste and the disposal cost is

less than 1. Recycling 5% of the waste volume does not save 5% of landfill disposal costs, as

it is not possible to reduce the costs at the same scale due to inflexible expenses. In order

for a local authority to reduce costs as a result of a transition to recycling, it must reach a

critical mass of reducing waste to landfill. That is, the savings are gradual rather than

continuous. In a large authority, which operates hundreds of waste collection vehicles, the

transition between the steps is quicker, as even a 5% reduction in the entire authority can

spare one truck and more. However, for a small authority, it will be required to reduce a

higher percentage of waste in order to save on waste collection vehicles, for instance, an

authority with two collection trucks will be required to reduce 50% of its waste in order to

spare one truck. To examine the feasibility of the transition to recycling, the authorities in

20

the sample were divided into four groups based on the size of the authority (in terms of

population) and the level of density (city or council). The average savings for each group was

estimated based on the cumulative amount of recycling. Table 3 summarizes the expected

savings, depending on the type of authority and amount of recycled products.

Table 3 The savings rate from a transition to recycling, by recycling rates and size of the municipal authority

PET+WP+OP+G+C+NPET+WP+OP+G+CPET+WP+OP+GPET+WP+OPPET+WPPETAggregate basket by recycled componenta

100%69%48%40%9%5%

Savings ratecSaving forb

100%68.7%41.2%26.5%4.8%1.4% Big city

100%59.1%32.1%19.0%2.7%0.9%Small city

100%46.0%28.5%11.5%1.6%0.5%Regional Council

100%33.0%13.9%7.0%0.9%0.0%Local council

a Aggregate basket of recycled component, where each column contains the previous components; b The savings from a transition to recycling by the size of the municipal authority; c The savings from a transition to recycling by recycling rates and the size of the municipal authority.

The values in Table 3 indicate the relative savings that can be reached by recycling. In a case

of recycling all six components, the savings equal (100%) to the amount calculated in Lavee

(2007) (the calculation was carried out specifically for each authority, and calculated

assuming that all six components are recycled). As can be seen in Table 3, the elasticity

between the amount of recycled waste and the relative savings is less than 1. If only some

of the waste components are recycled, the savings from landfill reduction is lower than the

rate of recycled waste. For instance, if a large city recycles PET, WP, and OP, we reach 26.5%

in savings despite recycling 39.55% of the waste components for recycling. In addition, the

smaller the locality is, the lower are the savings, due to diseconomies of scale. For instance,

a local council recycling only PET products cannot save on any component cost of the

authority; however, a large city can reduce the number of retention containers and even

employees.

In the fifth stage of implementing the model, the transition cost is calculated. In Lavee et al.,

(2009) the transition cost W R was calculated and normalized to transition cost per ton.

21

When only part of the materials are recycled, on the one hand the total average cost is

lower, for example, it is required to lay off fewer workers and therefore the layoff cost is

lower. However, there are also fixed components such as the establishment of a recycling

monitoring system and the publicity cost, which are divided on a smaller amount of waste,

meaning the saved costs per ton are lower. In the calculations carried out, it appears that

the fewer the recyclable waste components are, the transition cost per ton is higher. The

larger the authority is, the transition costs are more flexible, thus the additional cost of the

transition will be lower, as shown in Table 4. For example, for a local council that decided to

recycle only PET, the transition cost per ton is three times higher than in a situation where it

recycles all of its recyclables. However, for a big city that decided to recycle only PET, the

transition cost is higher only by 160% from the transition costs of recycling all recyclables.

Table 4 Transition cost per ton from a transition to recycling according to the recycling rates and the size of the municipal authority

PET+WP+OP+G+C+N

PET+WP+OP+G+C

PET+WP+OP+G

PET+WP+OP

PET+WPPETAggregate basket

by recycled componentsa

100%69%48%40%9%5%

Transfer costs ratecTransfer costs forb:

100%105%115%120%140%160% Big city

100%110%130%140%160%180%Small city

100%120%150%160%200%250%Regional Council

100%140%180%200%250%300%Local council

a An aggregate basket of recycled component, where each column contains the previous components; b The

cost of transferring to recycling by the size of the municipal authority; c The transition cost per ton regarding a

state of recycling all components according to recycling rates and the size of the municipal authority.

Using the above five stages, it is possible to calculate the recycling cost for each authority

and for any amount of recycled waste (according to the formula of Lavee et al., 2009).

¿U¿−CR+CL−W R>0

In the simulation ran for the recycling feasibility of each authority in Israel, two major

components were taken into consideration:

22

1. Different levels of uncertainty for PR, where 0% is the level of uncertainty that appears in Lavee et al., (2009), whereas we checked higher (UP) and lower (DOWN) uncertainty levels.

2. The waste components that an authority would want to recycle in order to maximize their benefits – for convenience reasons the six recycling components were grouped into 2 groups: full recycling and partial recycling.

The simulation results are displayed in Table 5.

Table 5 Sensitivity analysis of a transition to recycling under various uncertainties

Change from current level of certaintyb

Certainty conditiona 150

%100%50%0%-10%-25%-50%

54%58%61%65%68%73%81%89%The amount of recycling authorities

18%23%24%34%35%41%46%53%Full recycling

37%35%37%30%33%33%35%35%Partial recycling

58%62%65%69%72%77%86%95%The volume of total recycling

42.044.547.149.850.551.352.953.8Benefit from recycling (USD

millions per year)

a Recycling rates under certainty conditions; b Change in recycling quantities according to the uncertainty change from the current situation.

In a world of certainty regarding the prices of recycled waste, 88.6% of the authorities will

move to recycling, out of which 53.2% will recycle all six components and 35.4% will recycle

only part of the components (for instance, only PET and white paper), and therefore will

reach only 10% of the potential recycling. The total volume of recycling reaches 95% since in

a world of certainty only small authorities do not recycle, while the large authorities engage

in full recycling. However, when uncertainty rates increase by 150% above the level of

uncertainty in Lavee et al., (2009), only 54.4% of the authorities will recycle, out of which

only 17.7% will recycle all six components.

The last row in Table 5 presents the authorities average benefit from a transition to

recycling. The benefit is calculated based on the authority's ongoing savings generated each

year, minus the transition cost which is normalized per ton. Thus, an authority which

decided to move to partial or full recycling, benefits from the cost differences. As the level

23

of uncertainty increases, fewer authorities will recycle (or will partially recycle) and

therefore the overall benefit decreases.

It is important to note that an authority that moves to recycling gains the difference

between landfill cost and recycling cost, and the risk premium in the calculation is relevant

only for the decision whether to move to recycling or stay in the current situation. The risk

premium does not affect the savings level, as it is assumed that an authority which moved

to recycling, will receive the expected value of recycling in the long run.

4.2. Monopsony market

A monopoly commits to a fixed and guaranteed long-term price. Therefore, it benefits from

a transition of many authorities to recycling, and waste supply substantially increases

compared to a situation of a competitive market. As the level of uncertainty in a competitive

situation is higher, guaranteeing a fixed price raises the number of recycling authorities

relative to the competitive situation. The monopoly's economic calculation is a standard

calculation, which considers the supply curve and determines the price that maximizes its

profit. Assuming that the competitive price of waste is the monopoly's cost price (under the

assumption that the monopoly has no economies of scale), the monopoly's profit is the

difference between the competitive price and the monopoly's offering price (as a fixed and

guaranteed price). The simulation results appear in Table 6.

Table 6 A simulation of the feasibility of a monopsony entering the recycling market in Israel

90%80%74%60%50%40%30%20%10%0%Rate of price reduction19%22%24%34%44%52%61%66%75%89%Authorities recycling ratea

41%46%59%66%72%75%81%83%91%95%Rate of recycled wasteb

10.310.811.310.09.37.76.44.93.30.0Monopsony surplus profit (USD millions per year)

40.641.642.444.746.348.149.951.953.053.7Authorities benefit from recycling (USD millions per year)

a Authorities recycling rate, depending on the price change from certainty conditions; b Amount of recycled waste depending on price change from certainty conditions.

The simulation shows that in the level of uncertainty in Israel, a transition to a monopsony

will reduce the volume of recycling by 8% and the price of a ton of waste by 74% from the

market price in competitive conditions. At the monopoly's price, only 24% of authorities will

24

choose to recycle, but at that price the monopoly would maximize its profits from the price

differences. By analyzing the results, it appears that there are several relatively large

authorities that will transfer to full recycling, even at a very low price of recycled waste, and

some of these authorities will transfer even if PRis negative. This result creates a bias in the

results, such that at a 74% decline in price, 59% of the waste will still reach recycling. Only at

a reduction of more than 74% part of the large authorities will not recycle, therefore by

lowering the price by 80%, only 46% of waste will be recycled and therefore the monopoly's

profit will decline.

What is the level of uncertainty for which an existents of a monopoly it is most worthwhile

for the authorities rather than a free competition? According to the above calculation, the

feasibility exists only when the level of uncertainty in the market is very high, specifically it

should increasing by 140% from the situation calculated in Lavee et al., (2009). Thus, at least

according to the empirical data in this study, it is feasible to allow a monopoly to operate

only in situations of extreme uncertainty. The result actually depends on the ratio between

the authorities' sensitivity to the price compared with their sensitivity to uncertainty. As the

transition cost from one state to another (from recycling to landfilling and vice versa) is

higher, the level of sensitivity to uncertainty increases. In the empirical model used in this

study, the largest authorities have a relatively low transition cost (per ton), as most of their

expenses are almost linear (they can benefit from a partial transition to recycling, by cost

savings from cutbacks on part of the employees or vehicles). However, very small

authorities are most sensitive to uncertainty. From an examination carried out only for small

authorities, at a similar uncertainty level that exists in Israel as calculated by Lavee et al.,

(2009), it appears that an equilibrium result will exist by reducing the price by 24% from the

competitive price.

Thus, the feasibility to approve a monopoly that reduces prices – but assures it on the long

term – is highly dependent on the specific market conditions and particularly on the level of

the uncertainty of waste treatment elasticity, as well as on the authorities' transition costs

from one situation to another, which reflects the adaptability of an authority to price

volatility. As an authority's uncertainty rises, its ability to cope with these changes

decreases, thus it is more advisable to work with a monopoly that sets the price, even if the

proposed price is much lower than the price of a competitive market.

25

5. Summary and conclusion

There is extensive literature dealing with the benefits of a monopoly, particularly economies

of scale and reducing information costs. This paper shows, for the first time, that in some

situations, a centralized market is more efficient than a competitive market as a result of

price stabilization. This study examined the effect of a monopsony in a market with entry

barriers or high transition cost and demand uncertainty. As shown in Lavee et al., (2009),

price volatility in a competitive market, with high entry / transition cost, may reduce the

market size in relation to a situation of price stability. The new equilibrium in the market

was created by price stability, which led to a decrease in the risk premium taken by the

economic agent in the decision-making process prior to entering the market. A

monopsonistic price may motivate a player to make an investment / market entry, which

would not have been carried out without a stabilization of the prices. Thus, although there is

a monopolistic profit, the social benefit increases in relation to a situation of uncertainty

due to an increase in market trading.

Creating certainty is possible only by a monopsony, due to the confidence built following the

repeated interaction between the players and the transition costs, which reduce the

feasibility of each player to deviate from the contract due to fear of future punishment. A

market with a large number of firms cannot produce the same level of reliability, therefore

the market will not develop (will not grow). The benefit from a monopsony's entry is

influenced by the risk aversion of the players and the transition costs between the different

states. The results of the case study of the waste recycling market in Israel, showed that

within the scope of recycling and the level of the market's uncertainty, a monopsony entry

will adversely affect the recycling scale. In an event where uncertainty rises, a monopsony

entry will improve the social welfare. When considering the impact of a monopsony's entry

to a market with small local authorities – which avoided recycling due to the large price

variance – the monopsony's entry will essentially increase recycling volumes. The benefit of

a single authority from a transition to a monopsony market is influenced by the initial

recycling rate, as the shift in the demand curve affects only the authority's decision whether

to enter the recycling market, and to what extent.

To determine whether an authority benefited or lost from the market change following the

monopsony's entry, the authorities were divided into three main groups: non recycling

26

authorities, partially recycling authorities and full recycling authorities. If an authority

previously did not recycle and started to recycle, the authority's benefit is inevitably

positive, and the authority will benefit from the price stabilization by a monopsony. The

benefit of a partially recycling authority is influenced by the change of the ratio in the

recycled waste versus landfilled waste, and thus requires an individual examination. An

authority which recycled all of its waste, will inevitably lose from the monopsony's market

entrance. Thus, the monopsony solution is usually not Pareto efficient, however in some

cases it may be affected by the Kaldor-Hicks efficient by increasing the social welfare. In the

case shown in Israel, creating a regulation that allows larger authorities to sell the waste at

competitive prices (international market prices) and allows small authorities to recycle at a

monopsony price, will lead to improved social welfare. The novelty of this study stems from

the proof that a monopsony may increase the market size in markets with high levels of

uncertainty, thus increasing the consumers benefit. A monopsony creates "certainty

benefits" by reducing the risk premium arising from price fluctuations and the entrance of

new players, and although it gains excessive profits, the benefit of reducing uncertainty may

be greater than the loss of a monopolistic exploitation.

Acknowledgment

The authors would like to thank Sefi Bahar for comments and editing.

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Figures

Figure 1 the supply of a single municipality

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EPR

qi

PRM

PR

qi(ϒ) qi(0)

γi (0 )

CRi

γi (σ )

Figure 2 Competitive versus monopsony recycling market

SUC- Waste supply curve in a market with uncertainty (competitive structure).

SC- Waste supply curve in a certain market (monopsony market).

MFC - The marginal factor cost of the monopsony.

EPR- Expected equilibrium price of waste.

PRM – profit maximizing price for the monopsony

D- Equilibrium in a competitive market.

B- Equilibrium in a monopsony market.

γ (σ ) - the threshold price for uncertainty conditions

γ (0) - the threshold price for certainty conditions

Note that

1. The threshold price γ (σ ) of each municipality decreases to γ (0) in certainty conditions, so that for any fixed price level more municipalities will enter the market. Furthermore, the quantities of each municipality in the market could only increase, since q i (0 )≥qi (σ ). Therefore, the aggregate supply curve under certainty conditions, SC , is placed to the right

of the supply curve in uncertainty conditions SUC.

2. The upward and downward arrows represent fluctuation of the waste price over time in an uncertain price.

3. The area covered by vertical lines represents the municipalities' surplus in the competitive market, while the area covered by horizontal lines represents the municipalities' surplus in the monopsony market.

4. comparison of the vertical and horizontal areas shows that even without any regulatory intervention the municipalities as a whole could gain from monopsony pricing. However, there could be municipalities that still lose.

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SUC MFC

SC

EPR=EP y−cD

Pw , t−c

Pw , t−c

PRM

P

Q

B