Electronic copy available at: http://ssrn.com/abstract=2016860Electronic copy available at: http://ssrn.com/abstract=2016860

1

Artist and art dealer as a marketing channel*

ROBERTO CELLINI and TIZIANA CUCCIA

University of Catania, Faculty of Economics

Corso Italia, 55 – 95129 Catania (Italy) tel. +39-0957537728, fax +39-0957537710 e-mail: cellini@unict.it, cucciati@unict.it

Abstract: We study the relationship between artist and art dealer, interpreting them as the members of a marketing channel, as defined by the industrial organization and marketing science literature. The results for both parties depend on the individual efforts of each of them. Uncoordinated efforts lead to inefficient outcome. The efficiency of different institutional settings and agreements are studied. Different ways to reach efficient outcome are suggested and discussed, with specific reference to the case of visual arts. Keywords: Marketing channel, effort, mechanism design. JEL Codes: Z-10, L-83, L-13. RUNNING TITLE: Artist and art dealer as a marketing channel CORRESPONDING AUTHOR: Roberto Cellini University of Catania, Dept. of Economics and Business Corso Italia 55 – 95129 Catania – Italy; e-mail cellini@unict.it

* We are indebt to Guido Candela, Isidoro Mazza, and Antonello E. Scorcu for helpful comments. The usual disclaimer applies.

Electronic copy available at: http://ssrn.com/abstract=2016860Electronic copy available at: http://ssrn.com/abstract=2016860

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Artist and art dealer as a marketing channel

1. Introduction

In economics and marketing science literature, marketing channel denotes the

set of actors, practices and activities, to transfer goods from the point of production to

the point of consumption. In the simplest case, a particular product is made by a

manufacturer, and delivered to a retailer who sells it in the final market. Manufacturer

and retailer are the two members of the marketing channel. If they act uncoordinatedly,

channel inefficiencies arise, in the sense that the outcomes of the channel members are

lower than they could be under coordination. This inefficiency is due to strategic

behaviour in the presence of interdependence between manufacturer and retailer.

Available literature suggests different ways to overcome inefficiency, using tools of

industrial organization and marketing practice.

Here, we shall study the relations between artist and art dealer, interpreting them

as the members of a marketing channel. Figurative artist and art gallery manager are our

main reference example. Singer (or performing art company like theatre company or

orchestra) and event organizer may represent different specific examples of marketing

channel in artistic fields. All these cases in arts share some features with the case of a

manufacturer and a retailer of industrial production: the success of artistic production

depends on the artistic effort of the “creator” (the manufacturer), as well as on the

promotion effort made by the art gallery manager or by the live event organizer (the

retailer, or the dealer) –in perfect symmetry with the success of industrial production

whose revenues depend on manufacturer’s and retailer’s course of actions.

Usually, the behaviours of each member of a marketing channel affect the final

sales, and hence the outcome for manufacturer and retailer. Industrial organization and

marketing studies and practice analyse the outcome of different institutional

arrangements between the channel members, and make suggestions of specific

arrangements, to improve the results of the channel. In the real world, a variety of cases

can be observed: marketing channel members can take their decisions simultaneously or

sequentially, with different roles of leader and follower. Either of the channel members

may take the role of leader (that is, the first-mover) and may set incentive schemes to

3

lead the follower to specific actions. Under particular cases, peculiar objective function

can be the true goal of the channel members, and sometimes altruistic behaviours are

observed: a channel member may aim at the maximum joint-result rather than at the

maximum individual profit.

At the same time, the artistic production presents peculiarities with respect to

industrial production. For instance, the production of arts provides the artist with utility

per se, and artist enjoys welfare from her own fame, apart from the economic results.

Even art dealers’ behaviours are sometimes characterized by art for art’s sake.

Furthermore, competition takes place in arts’ market under peculiar forms, and the role

of price competition or quantity competition needs to be specifically qualified as

compared to “standard industrial goods”. More importantly, peculiar arrangements are

observed between producer and retailer, in artistic fields: perhaps the most prominent

one is that sales sharing is the rule, rather than profit sharing, as documented by a large

body of evidence (see, e.g., Caves, 2000, specifically p. 41, or Velthius, 2011a,b).

Again, mechanism designs typical for industrial goods, like quantity discounting

schemes, are clearly inappropriate (if not impossible) in the case of arts.

Our goal is to provide a formal model, consistent with peculiarities of arts, but

inspired from industrial organization and marketing science literature, to show that the

marketing channel inefficiency is a feature also in the case of the arts, and –more

interestingly– to study the efficiency property of different arrangements, commonly

observed in the real world of arts. Finally, we aim to suggest mechanisms to overcome

the marketing channel inefficiency. We believe that the consideration of different

approaches, developed by industrial organization and marketing science, applied to the

study of the relation between artist and art dealer, may be fruitful, under both a

perspective of description of observed actions, and a normative point of view.

2. Insights from different research lines

In this paper, we bring together two research lines. On the one side, we consider

the marketing channel literature, developed by both marketing and economic literature.

Jeuland and Shugan (1982) can be considered the seminal model, even if several

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previous contributions could be listed, containing similar ideas (e.g., Bucklin, 1966).

The models within this research line consider the relation between a manufacturer of a

specific brand, and a retailer. In the simplest version, only one manufacturer interacts

with one retailer. A market demand function is assumed, depending on retail price, set

by the retailer, and other characteristics of the good related to choices (and efforts)

made by the manufacturer. Advertising can play some role. Thus, the choices of both

manufacturer and retailer affect the outcome of both. Early models focus on pricing

problems (Jeuland and Shugan, 1982, Moorthy, 1987). Subsequent contributions

underline that non-price aspects are equally important (e.g., Bergen and John, 1997). In

the absence of coordination, inefficiency arises, due to opportunistic behaviours.

Coordination hardly may emerge endogenously, because the best reply of each channel

member to the cooperative choice of the counterpart is not the cooperative choice: a

typical prisoner dilemma occurs. It is true that, in the presence of repeated transactions,

cooperation could emerge tacitly, along the lines of the Folk-Theorem story, but the real

world documents that explicit contracts are often signed, introducing explicit

mechanisms that clearly aim to mitigate inefficiency. A number of mechanisms can be

observed, and studied under a theoretical point of view: we may mention a variety of

pricing schemes, including quantity discounts, quantity surcharges, two-part tariffs;

specific rules of profit sharing among the channel members; advertising allowances, or

subsidies to promotion costs. Jorgensen and Zaccour (1999, 2002) deal with the

dynamic optimal problem of a marketing channel, and present some models taking a

differential game perspective. Dynamic mechanism designs are proposed, based on

incentive schemes regarding price setting or advertising efforts (see also Jorgensen,

Sigue and Zaccour, 2000, 2001; Jorgensen, Taboubi and Zaccour, 2006). It is worth

mentioning that the marketing channel can be also interpreted as a particular case of

team production (à la Alchian and Demsetz, 1972), in which there is no firm owner, but

the team members share the joint result deriving from their personal skills and efforts:

Levin and Tadelis (2005) and Kaya and Vereshchagina (2009) study how the properties

of the productive process determine the optimal contract design, and the optimal sorting

patterns among many agents. The conclusions of these lines of research can be

summarised, by stating that a number of price- and non-price mechanisms are available

5

to channel members, to overcome inefficient outcomes due to opportunistic behaviours,

both in static and in dynamic framework.

On the other hand, cultural economics shows that artistic production shares a lot

of aspects with standard industrial production, but presents at the same time important

peculiarities, so that the results developed by industrial economics can be extended to

cultural sectors with caution. Production and distribution channels are clearly present in

many artistic sectors: artists, managers, representative agents, gatekeepers and retailers

play important roles: Caves (2000), Sacco (1998), Throsbe (1994a), just to mention a

few, have studied the relations among the subjects in production and distribution

channel of artistic productions; Velthuis (2011a) reviews the specific literature on art

dealers.

Here, it is particularly important what Caves (2000, Ch. 2) or Velthius (2011b)

report: they describe the main aspects of the relationship between artists and dealers,

with particular reference to the visual arts sector.1 Common features of observed

contracts or arrangements in arts’ marketing channels are:

- Artist and dealer typically make informal agreements concerning their “efforts”;

formal contracts are generally avoided (even if formal contract are more and more

frequent in recent times);

- Artist’s effort can hardly be defined, but number and type of works proposed are

objects of the agreements, and can be interpreted as proxy variables for artistic

effort; dealer’s efforts mean advertising and information campaigns, organisation of

meetings or events, and other possible forms of promotion of artistic production;

- In agreements or contracts between artist and dealer, the rule is the gross revenue

sharing, rather than the profit sharing;

- Sometimes artists are called to participate to the financial efforts for promotion

campaign;

- Fixed payments from dealer to artist are rarely observed (such cases were more

frequent in past times and for well-known artists).

All these points will be ingredients of the model we are going to present. As far

as we know, a formal model borrowing from the marketing channel literature has not jet

proposed, with specific reference to the arts, and we aim at filling this gap.

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It is worth noticing that the focus on the channel of creation and distribution of

artistic goods leads us to disregard the secondary or resale markets of arts, and the

dynamics of price in such market segments. Hutter et al. (2007) or Shonfeld and

Reinstaller (2007), among many others, stress that the determinants of prices in

secondary markets are different, as compared to primary markets. However, the

research line on the evolution of prices in secondary markets is immaterial to our

present study, even if -admittedly- expected future prices of artistic goods are relevant

on current demand, so that a cautionary note has to be posed, as long as there is no role

for expectations on future prices, in our present model.

3. The basics of the model

We present a model, where an artist produces a good, that is sold to final consumers by

an art dealer.

The artist (A) chooses her artistic effort a; her fame, g, is a positive function of

the artistic effort, and some exogenous variable, z0, according to the simple linear

function .0,0 >+= ααazg Artistic efforts entail a cost for the artist, assumed to be

quadratic: .0,2 >= AAA uauc

The retailer (P), that is, the art dealer in this specific case (let us think of an art

gallery manager, for instance), makes a promotional effort, p, to promote the sales of the

artistic production manufactured by A. Promotion efforts entail a quadratic cost for the

retailer, .0,2 >= pPP upuc

The final sales (S) of the artistic production depend on the retailer’s efforts, and

the artist’s fame, according to a function like 0,0with, >≥⋅⋅+= βθβθ gpS . (This

formulation is clearly inspired by Jorgensen, Tabouti and, Zaccour, 2006). We assume

that the fraction π (with 10 ≤≤ π ) of the revenues from the sales goes to the artist, and

the fraction )1( π− goes to the dealer. Clearly, the larger is π , the larger the share of

sales accruing to the artist. At the moment, π is an exogenous parameter; in the real

world, π is a contracted variable, depending on the relative fame of artist and dealer.

Note also that the hypothesis that sale-share are contracted, rather than profit-share is

7

typical to the arts sector (see Caves, 2000). We finally assume that the art dealer cares

only on his net result, 2)1( puSR PP −−= π , while the artist cares also on his fame, and

her net result is: gauSR AA δπ +−= 2 ; the positive parameter δ describes the

importance that her own fame plays into the net result perceived by artist: the presence

of such a term in the utility function of artist is common in cultural economics models,

consistent with the fact that artists care not only on the monetary outcome of their

activity, but also on non-monetary, intangible recognition, like fame (Frey, 1997; see

also Throsby, 1994a, 1994b and, more recent, the formal model of Cuccia and Cellini,

2009).

Without loss of generality, and for the sake of simplicity, we will develop the

model under the following parameter assumptions: 2/1,2/1,0 ===== PA uuβαθ ,

so that the model can be summarised by the following equations:

[1] azg21

0 +=

[2] pgS ⋅⋅=21

[3] 22

121

221 2

0

2 aazpaggpRA −

+

+⋅=−+⋅= δπδπ

[4] ( )22

1121

221)1(

2

0

2 pazpppgRP −

+−=−⋅⋅−= ππ

Artist aims at maximising [3], setting her choice variable a, while the art dealer aims at

maximising [4], setting his choice variable p. However, the result of each player (i.e.,

marketing channel member) depends also on the choice of the other player, so that a

strategic interdependence situation is operative. The specific choices of players will

depend on the “institutional framework” at work. For instance, we could imagine that

the choices will be set simultaneously and independently by artist and dealer, or we

could imagine that the choices are independent but sequential, with the possibility that

the first-mover is the artist or the dealer. Again, we could imagine that artist and dealer

agree on their choices, aiming at the joint result maximization. All these different

settings will be analysed in what follows. From the point of view of the realism of

8

different settings, we note that it would be too easy (and hence false) to say that in the

real world, firstly the artist sets her efforts, and then the dealer sets his promotion

efforts: this situation clearly may happen, and perhaps it is the rule in most cases, but it

is far from true that this arrangement covers all cases: in some cases –for instance, in

the performing art shows– advertising campaign for a show starts before (or during) the

show is under construction. The different institutional settings provide different

ordering of individual and aggregate results for the channel members.

4. Results

4.1. The simultaneous game

Let us imagine that artist and dealer set their decision simultaneously. We denote this

setting as the “Cournot setting”, borrowing the label from the oligopoly theory. The

artist maximizes objective function [3], with respect to a, and derives the following

optimal rule, which represents her reaction function:

[5] 4

2 pa ⋅+=

πδ

The dealer maximizes function [4], with respect to p, and derives the following reaction

function:

[6] 4

)1()1(2 0 azp

⋅−+−=

ππ

The optimal effort of the artist depends positively on the promotional effort of the

dealer, and the promotional effort of the dealer is a positive function of the artistic effort

of the artist: the reaction functions are positively sloped, so that the choice variables are

strategic complements, in the terminology of oligopoly theory. The Nash equilibrium is:

9

[7] 16

)]1(4[22

0

+−−+

=ππ

ππδ za COU

[8] 16

)1)(4(220

+−−+

=ππ

πδzpCOU

where the superscript COU stays for “Cournot”, i.e., simultaneous choice setting; note

that both variables in equilibrium are positive, and increasing in δ and z0;

correspondingly, the maximum outcomes reached by artist and dealer, in equilibrium,

are respectively:

[9] 22

200

)16(]32(4)][1(4[2

+−+−+−+

=ππ

ππδππδ zzR COU

A

[10] 22

20

2

)16()4()1(2

+−+−

=ππ

δπ zR COU

P

The result obtained by the dealer is strictly decreasing inπ (the higher the revenue share

for the artist, the lower the equilibrium result for the dealer), while the result obtained

by the artist is increasing in π for 0<π <½ , reaches its maximum in π =½ and is then

decreasing over ½<π <1: for high levels of π , further increases of this share parameter

lead the dealer to lower his effort to such an extent, that the artist’s result decreases.

4.2. The sequential games

We firstly consider the case in which the dealer sets his promotional effort after having

observed the artistic effort chosen by the artist: in this case we are in a sequential game,

à la Stackelberg, where the artist is the first-mover (or leader) and the dealer is the

second-mover (follower). The leader can anticipate the choice of the follower, and can

insert such a reaction function into her objective function: this amounts to saying that

the artist-leader maximizes her objective function [3], considering the constraint

represented by the reaction function of the dealer-follower [6]. The solution of the

leader’s problem provides:

10

[11] 8

)]1(2[22

0

+−−+

=ππ

ππδ za STAL

.

(where the superscript STAL stays for “Stackelberg, with artist leading”), and the choice

of the dealer-follower is:

[12] 8

)4)(1(2

0

+−+−

=ππ

δπ zp STAL

The efforts exerted by both the artist and the dealer are larger than the respective efforts

in the simultaneous choice case. Thus, it is not surprising that the individual results

obtained in equilibrium by both parties are larger in this Stackelberg case, as compared

to the Cournot equilibrium. Equilibrium results, when the artist is the first-mover, are:

[13] 8

8)1(22

20

20

+−++−

=ππ

δδππ zzR STAL

A

[14] 22

20

2

)8(2)4()1(

+−+−

=ππ

δπ zR STAL

P

The opposite case of sequential moving, in which the dealer is the first-mover, and the

artist follows, is conceivable as well. In some cases, the promotion campaigns for shows

or specific events start before the preparation of the show is finished, so that it is true

that the artistic effort is set after the promotion effort is made. In such a case, the dealer

is the leader, and he can anticipate the choice of the artist-follower. Analytically, the

dealer-leader maximizes his objective function [4] under the constraint represented by

the reaction function of the artist [5]. The optimal choice of the dealer turns out to be:

[15] 8

)4)(1(2

0

+−+−

=ππ

δπ zp STAF

11

where superscript STAF stays for “Stackelberg with artist following”, and the reaction

of the artist, in equilibrium is

[16] )8(4

)1(4)16(2

02

+−−++−

=ππ

ππππδ za STAF

The artist is led to make an effort, as second-mover, larger than the effort set as a first-

mover. As far as the art dealer is concerned, his effort, as the leader of the Stackelberg

game, is equal to the effort made as the follower of the Stackelberg game.

By straight substitutions into the objective functions, we obtain the results of

both parts in equilibrium, when the dealer leads and the artist follows:

[17] )8(32

)]1(4)16()][16()3233(4[2

0222

0

+−−++−+−++−

=ππ

ππππδππδππ zzR STAF

A

[18] 22

20

2

)8(16)4()1(

+−+−

=ππ

δπ zR STAF

P

By simple comparisons, we can state that, for any π (with 10 << π , that is excluding

the limit cases),2 the following relations hold:

;

;

;;

STAlP

STAFP

COUP

STAFA

STALA

COUA

STAFSTALCOU

STAFSTALCOU

RRR

RRR

pppaaa

<<

<<

=<

<<

This means that each player prefers any sequential settings to the simultaneous choice

setting, and –in the sequential settings– each of the players prefers to be the follower

rather than the leader. This ordering of individual outcomes is consistent with analogous

results obtained in games in which choice variables are strategic complements.

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4.3. The cooperative setting (joint result)

If channel members aim at the maximum joint result, they face the following problem:

[ ]220,

22)2)(2(41 papazRRRMax PA

JOINT

pa−−++=+= δ

We could label this setting as the coordinated setting (or the cartel setting, borrowing

from oligopoly theory). From the first order conditions we obtain:

[19] 15

)4(2 0zp JOINT +

=δ

[20] 15

)4(2 0za JOINT +

=δ

Some comments are in order. First, the efforts of each part are the highest, with

respect to all considered settings. This means that the maximum joint result requires the

highest efforts by both parts. Second, both the Cournot setting and the Stackelberg

settings provide the players with individual equilibrium results whose sum is smaller as

compared to the sum of results they can obtain in the coordinated setting. In other

words, strategic interaction leads to inefficient outcomes; this result is well known by

marketing channel literature. Third, parameter π disappears from the problem of the

coordinated setting, consistently with the fact that π captures an aspect related to the

division of a common result, that is immaterial to the maximum of the common result in

itself.

Of course, the problem of the division of the common result remains open, after

the coordinated choices are set. As far as the division of result is concerned, we assume

that the artist obtains the share π of the sales, and the dealer obtains the complement

share π−1 , while the term aδ goes entirely to the artist; needless to say, this is only one

–rather obvious– assumption concerning the division of the “cartel result”. Under the

above mentioned rule of sharing, the dealer and the artist obtain the following

individual results:

13

[21] [ ])216)(7()132(2252 2

020 δδππ +++−= zzR JOINT

A

[22] 20 )4)(21(

2252 δπ +−= zR JOINT

P

and hence, under the above mentioned rule of sharing, the cartel situation provides the

artist a higher result with respect to the Cournot situation for any π >0.1350, and

provides the dealer with a higher result as compared to the Cournot situation for any

π <0.24085. Similar comparisons can be readily made with respect to the Stackelberg

settings. In any case, apart from the cartel situation, any other setting is Pareto-

inefficient – in the sense that a different situation can be found, with appropriate sharing

of the result, where each player can be better off.

As is well-known, the choices associated with the efficient outcome do not

represent a Nash equilibrium, at least in the one-shot game. This amounts to saying that

informal or non-binding agreements concerning socially efficient levels of individual

efforts are not self-enforcing. In Section 5 we study how it is possible to replicate the

efficient outcome, on the basis of more-complex self-enforcing agreements. Eventually,

we will discuss the degree of efficiency of different types agreements, observed in the

real world of arts’ markets. Remember that formal binding contracts (ideally replicating

the efficient outcome) are rarely observed in the filed of arts, also because their

enforcement is difficult, due to the fact that relevant key variables (like the artistic

efforts) are hardly definable and measurable.

5. Replication of efficient outcome

The available literature on marketing channel has suggested several contract designs,

able to lead the parts to replicate the choices associated to the efficient outcome. In the

cases of industrial goods, for instance, specific profit share designs, advertising

allowances, quantity discount schemes, are possible solutions: it is a well-established

14

result that a multiplicity of effective solutions exist, to overcome the inefficiency of

decentralised decisions in marketing channel situations. In order to make such

arrangements self-enforcing, it is necessary to assure that each part obtains a larger

result, as compared to the individual result obtained in uncoordinated setting.

Here we focus on the case at hand and we limit to propose two different

solutions: the first one has a theoretical interest, but it is hardly implementable in the

real world; it is appropriate for the context in which choices are set simultaneously. The

second one is appropriate when the artist set her artistic efforts firstly, and the dealer

follows –a situation more frequently observed in the real world; for this reason we will

spend more attention on it.

The relevant question can be posed specifically as follows: How is it possible to

lead the artist to set her effort at the efficient level given by [20], and the dealer to set

his effort at the efficient level [19]?

5.1. Linear subsidies in the simultaneous choice setting

Consider the case in which artist and art dealer set their choices simultaneously.

Assume that artist has to pay a subsidy ψ to the dealer for each unit of promotional

effort he makes; at the same time, the dealer has to pay a subsidy ω to the artist for

each unit of artistic effort she makes. The problems of artist and dealer can be written,

respectively, as follows

[23] apaazpRMax Aaωψδπ +−−

+

+⋅=

221

21 2

0

[24] ( ) appazpRMax Ppωψπ −+−

+−=

2211

21 2

0

From the first order conditions, the following reaction functions can be easily derived:

[25] 4

42 ωδπ ++⋅=

pa

15

[26] 4

4)1(2)1( 0 ψππ +−+⋅−=

zap

The corresponding equilibrium efforts are:

[27] 16

])1()42(2[22

0

+−−+++

=ππ

ππωδπψ za

[28] 16

))]1(4(2)1)(4[(22

0

+−−++−+

=ππ

πωψπδzp

Appropriate levels of ψ and ω can be computed, to render the effort levels [27] and

[28] equal to the efficient levels [20] and [19], respectively; the solution is:

[29] 15

)4(2 0 δπψ

+=

z

[30] 30

)4)(1( 0 δπω

+−=

z

The subsidy levels given by [29] and [30] lead each member of the channel to set the

individual choice that replicates the efficient outcome of the maximum joint result. Note

that the higher is the share for the artist, the higher the amount of unit subsidy that she

has to give to the dealer. By appropriate substitutions, it is possible to compute the

individual results obtained by channel members under such arrangement, and to

compare them with the result obtained in the uncoordinated Cournot setting. It is

immediate to verify that only over a limited range of parameter configuration, each

member receives a larger outcome as compared to the uncoordinated setting; outside

that range, appropriate transfer are necessary to make the socially efficient arrangement

convenient even for each members under a strictly individualistic point of view.

It is also interesting to note that: (a) in the limiting case where 0=π , the

efficient levels of unit subsidies become 0=ψ and 30/)4( 0 δω += z : this arrangement

describes a situation in which all revenues from sales go to the dealer, but he commits to

give the artist a subsidy for her artistic effort; (b) in the limiting case where 1=π , the

16

efficient outcome is reproduced by the subsidy scheme 0=ω , 15/)4(2 0 δψ += z ,

which means that all revenues from sales go to the artist, but she commits to give the

dealer appropriate subsidy for each unit of promotional effort of his. Also in these

limiting cases, the efficient solution is reproduced, but appropriate lump-sum transfer is

necessary to make the arrangement dominant for each member also from a strictly

individualistic point of view.

The real implementation of the subsidy design in this simultaneous moving

setting, however, should require that artistic efforts are definable and measurable – a

hardly tenable assumption. One could also observe that if this mechanism design is

implementable in the real world, no reason exists why a formal contract concerning

directly the efficient levels of efforts is not implementable. The substantial obstacle to

contract enforcement in the case of arts rest on the possibility of defining and measuring

artistic efforts. Such obstacles can be avoided in the sequential setting, if artist set her

efforts firstly.

5.2. Quadratic subsidy in the Stackelberg setting, with artist leader.

Consider the case that the artist sets her artistic effort firstly, and then the art dealer sets

the promotional effort; equilibrium levels of efforts in the uncoordinated setting are

given by [11] and [12], which represent an inefficient allocation from a marketing

channel point of view.

Imagine that the artist commits herself to give a subsidy )( pσ to the dealer

(with 0≥σ ), for each unit of promotional effort of his, so that the total subsidy from

artist to dealer is 2pσ . The net result of artist and dealer, under such an agreement are

respectively:

[31] 22

0 221

21 paazpRA σδπ −−

+

+⋅=

[32] ( ) 22

0 2211

21 ppazpRP σπ +−

+−=

It is immediate to find the reaction function of the dealer:

17

[33] ( )( )

21,

)21(421 0 <−

+−= σ

σπ az

p

This reaction function has to be inserted in the in the leader’s problem, and

different cases could be taken into account.

Case I (Digression). The artist aims at her own maximum, and sets σ and a

accordingly. We denote this case as the case of a selfish artist. It is easy to check that

the maximum private result for the artist requires

[34]

≤≤≤<+−

=3/100

13/1)1(2/)13(π

πππσ

forforSQS

[35] ;3/10

13/1263

]16)1([22

20

≤≤

≤<−−++

=π

πππ

δπ

fora

forz

aSTAL

SQS

(superscript SQS stays for “selfish quadratic subsidy”). This means that the artist finds

it convenient to give a positive subsidy to the dealer only for sufficiently high levels of

π . Clearly, for 3/10 ≤≤ π , that is, in the situation of the corner solution corresponding

to nil subsidy, optimal choices replicate the simple situation à la Stackelberg (without

subsidy) with the artist as the leader, and individual results coincide with [13] and [14].

For 13/1 ≤< π , subsidy is positive, and individual results are:

[36] 2

20

220

263]432)1([2

ππδδπ

−−+++

=zz

R SQSA

[37] 22

20

2

)263()4)(1(16

ππδπ

−−+−

=z

R SQSP

whose sum is smaller than the cartel outcome. It is interesting to note that, for high

levels of π , it is in the interest of a selfish artist to provide the dealer with a subsidy for

18

the promotional effort: RASQS turns out to be larger than RA

STAL for any π included in the

range (1/3,1].

Case II. The artist sets σ in order to lead the follower to replicate pJOINT, and

sets a=aJOINT. This case can be denoted as the case of a cartel-oriented artist (or

benevolent artist, in the sense that he takes care of the whole marketing channel). From

the dealer’s reaction function [33], it is immediate to find that p= pJOINT requires:

[38] 2/πσ =

with 0<π <1 and hence 0<σ <1/2. Correspondingly, the channel members’ net results

are:

[39] )]14()14(8)116([2252 2

020 ++++−= πδπδπ zzRCQS

A ,

[40] )]4)(1[(2252

0 δπ +−= zRCQSP

where superscript CQS stays for “cartel quadratic subsidy”. Of course, the sum of the

results given by [39] and [40] coincides with the efficient joint result. However, from an

individualist point of view, each channel member is ready to implement this agreement,

only if it provides a larger individual result as compared to decentralised decisions.

From the dealer’s point of view, result [40] is higher than results [14] or [37], for

any 0<π <1. This means (quite obviously) that the dealer prefers the situation in which

the artist is cartel-oriented rather than selfish.

From the artist’s point of view, we have to distinguish, according to π be larger

or smaller than 1/3.

(i) If 3/10 ≤≤ π , the result [39] is higher than result [13] only for levels of π

higher than a threshold level. More precisely,

)8(225)4)(112262(

2

20

23

+−+−−+

=−ππ

δπππ zRR STAL

ACQSA is positive only for

19

0112262)( 231 >−−+≡ ππππf , that is, 07.01 ≈≥ ππ . This means that for

3/11 ≤≤ ππ , it is in the interest of a selfish artist to implement the cartel allocation.

The result that a manufacturer, under given parameter conditions, may find it

convenient to pursue the maximum of the channel is not a novelty in the marketing

channel literature (see, in a different framework, Jorgenson et al., 2006, Section 4). For

10 ππ <≤ , in order to make the cartel choice convenient for the artist, a further lump-

sum transfer from the dealer to the artist must be required. Let τ denote such a transfer

from the dealer to the artist. If we compare the outcomes (under the quadratic subsidy

and transfer) with the case of nil subsidy, in order to make the arrangement self-

enforcing, we have to fix τ in a way such that: STALP

CQSP

STALA

CQSA RRRR >−>+ ττ and ,

which means:

[41]

22

20

234

2

2

20

23

1

21

)8(450)4)(311616884)(1(

,)8(225

)4)(112262(;

+−++++−−

=

+−+++−−

=

<<

ππδπππππ

τ

ππδπππ

τ

τττ

z

z

(note that 1τ is positive for any level of 07.01 ≈< ππ ).

(ii) For π included in the interval [1/3, 1], it can be easily checked that

RASQS>RA

CQS, and (RASQS+RP

SQS)<(RACQS+RP

CQS). Thus, a transfer (from the dealer to the

artist) has to be designed, to lead the artist (who sets σ and a) to behave in the interest

of the channel. Specifically, a lump-sum transfer 0>η can be found, from dealer to

artist, such that SQSA

CQSA RR >+η and SQS

PCQSP RR >−η . Simple computations permit to

find that the two conditions correspond to

[42]

22

20

234

2

2

20

23

1

21

)263(225)4)(216920521224)(1(2

,)263(225

)4)(183516(2;

ππδπππππ

η

ππδπππ

η

ηηη

−−++−−+−

=

−−++−+

=

<<

z

z

20

One can interpret η as the price that the dealer has to pay to the artist, in order to lead

the artist to behave in the interest of the channel, instead of in a selfish way. In words,

the story can be told as follows. If the artist is the leader of the marketing channel, an

arrangement can be identified, which leads to the efficient outcome, and which is self-

enforcing in the sense that it is impossible to find alternative outcomes in which both

members are better off (i.e., no room for convenient deviation does exist); the

arrangement is as follows: (i) the sales are divided according to the positive fractions π

and π−1 , for artist and dealer respectively, with π >1/3; (ii) the artist gives the dealer

the subsidy 22 )2/( pp πσ = , linked to the promotional efforts of his; (iii) the dealer

gives the artist the fixed sum 21 ηηη << , conditional on the fact that the artist set

a=aJOINT. Under such conditions, the artist finds it optimal to set the efficient effort

a=aJOINT, and the best reply of the dealer is p=pJOINT.

In sum, we have found that for some parameter values ( 3/11 ≤≤ ππ ), it is in the

(individualistic) interest of the artist, to behave in the interest of the cartel; outside such

a parameter range, a self-enforcing mechanism is found, able to replicate the efficient

outcome. In such a mechanism: (i) sales are shared among artist and art dealer, (ii) the

artist receives an additional fixed amount from the dealer; (iii) the artist pays the dealer

for his promotional effort. The mechanism is efficient because each member replicates

the choice associated with the joint-maximization case, and the mechanism is self-

enforcing, because each channel member has no incentive to deviate from the efficient

choices.

6. Comments and concluding remarks

Here we have pointed out that artists and art dealers constitute a marketing channel, in

the sense defined by economics and marketing science literature: in several cases, for

industrial goods, a good is manufactured by a firm, and sold to a retailer which sells it in

the final market; the result for both subjects –producer and retailer, that is, the channel

members– depend on the efforts made by each of them. Like in the more general case of

team production, strategic interdependence and incomplete information generate room

21

for inefficient results, if subjects act in a uncoordinated manner, and each actor is

oriented to his/her individual maximum result. The situation in the arts’ markets is very

similar. Artist and art dealer benefit from results which depend on the efforts of both.

We have shown that the theoretical results obtained by industrial organization and

marketing science hold, by and large, for the arts markets as well. In the arts markets,

however, specific characteristics are worth taking into account.

History and the current real world document a variety of agreements between art

makers and art dealers, in different arts’ markets (visual arts, performing arts, and so

on).3 For instance, employment, direct acquisition and consignments are alternative,

possible forms of agreements in the case of visual arts; however, in current day

experience, the consignment is the most frequent form of agreement. Caves (2000,

especially Chs. 2 and 3) and Velthius (2011a,b), with particular reference to the case of

visual arts, provide a list of “typical” behaviors in the to-day relations between artists

and art dealers. These characteristics have shaped the specific model we have presented

in this paper.

First, formal contracts between artists and art dealers (especially in the cases of

painter and art gallery) are generally avoided, in real world: informal deals (and moral

obligations) are more common forms of agreements. The reasons why formal contracts

are rare can be easily understood: complete terms are difficultly stated in a contract;

monitoring activities are difficult to be conducted; litigations are expensive and

financial compensation from successful litigations nearly impossible to be obtained.

Nevertheless, in recent years, a larger use of written contracts is claimed (especially by

artists) and observed (Vinick, 1997). The absence of a large body of detailed contracts

makes a robust analysis of contracts impossible, and the comment have to focus on

episodic or anecdotic evidence.

Second, the typical agreement has the form of ‘consignment contract’: the artist

consigns her artworks to the dealer (who exhibits them), in order to be sold. The

agreement could prescribe number and type of artworks to be delivered. The dealer

receive a share of the revenues, as a counterpart of his activity of promotion. Pay in

advance and/or regular wage are very uncommon.4

Third, as a matter of fact, the role of the art dealer is more complex than just

selling the artistic items: an art dealer acts as an agent (both for the artist, and for

22

institutional buyers like museums or private collectors): for this reason, the assumption

that the dealer makes efforts to promote the artistic production is meaningful, in the case

of the arts, and the promotion actions in the hands of an art dealer are wider and

potentially more effective as compared to the typical actions available to a retailer in the

case of industrial goods. An art dealer is expected: to provide information to critics,

certifiers, art writers, museum curators, and media; to organize exhibitions; to provide

items for temporary exhibitions; to compose books and further editorial catalogs; to

make (traditional) advertising campaigns in journals and specialized reviews; to spend

time with prospective clients articulating the artist’s intent (Caves, 2000, p. 38): all

these activities define the dealer’s efforts. Especially in contemporary arts, we can say

the efforts of the dealer contribute to the definition of the characteristics of artistic

product.

Fourth, it is worth stressing, once again, that revenue share, rather than profit

share, is the rule. This aspect is of particular importance, since it entails that the channel

members are not reimbursed for specific expenses. Documented exceptions are rather

limited: in the case of visual arts, for instance, one can seldom observe a participation of

artist in expenses of dealer, e.g. for advertising, catalogues and framework.

Fifth, it is difficult (if not impossible) that dealer can participate to the artistic

effort exerted by the artist. Artist’s effort is hardy observable, and the observable result

of her are weakly linked to the effort (whatever “effort” could mean in artistic fields). In

observed agreements, efforts are at generally linked to the number of pieces that the

artist commits to deliver to the dealer, in a time interval.

Sixth, artists typically complain about the limited efforts of dealers, and dealers

complain about the limited efforts of artists. In the specialized newspaper Art World

News we can read: “An artist fails to deliver quality works in sufficient number. A dealer fails

to promote an artists' work. These are only two types of claims that have recently led to disputes

between artists and dealers” (Vinick,1997, p. 1).

The perceptions of each member of the marketing channel that the other member

does not exert a sufficient level of effort are really very common. The fact that these

perceptions may be well founded is supported by our present theoretical model. The

above mentioned characteristics of typical agreements between artist and dealer lead to

a situation in which each part exerts a lower amount of effort as compared to the

23

efficient level: this is due to the strategic interdependence. Possible agreements

concerning socially-efficient levels of individual efforts are not self-enforcing, as long

as each actor has an incentive to free-riding. Thus, in our interpretation, the true root of

inefficiency does not rest on asymmetric information (which in any case, does exist, and

explains why it is nearly impossible to sign formal binding contracts), nor in agency-

type, i.e., principal-agent relationship (which in any case could be appropriate for

describing some aspects of the relations), but simply in the team-type production

process which is relevant for artistic items, as they are sold in today markets, where

marketing channels are really relevant.

We have shown that specific designs for contracts would be able to overcome

inefficiency. Many efficient contracts are in principle possible. Reciprocal cross-

subsidies have been shown to met the efficiency condition, in a situation in which artist

and art dealer exert their efforts simultaneously. A further example has been provided,

for the case in which artist and art dealer take their decisions sequentially (with the artist

leading), and in which artist and art dealer split the revenues from sales: in such a case,

the artist may be required to participate to the promotional efforts of dealer (according

to a quadratic subsidy), and receives a lump-sum transfer; the amount of the lump-sum

transfer has to be linked to the values of the agreed revenue-share, and to the amount of

the subsidy to promotional efforts. Interestingly enough, in accordance with available

results in marketing channel literature, we have found that –under certain parameter

configuration, and specifically under given values of share according to which revenues

are split– there is no conflict between individual and collective incentive, in the sense

that it can be in the egoistic interest of a member of the channel to act in the interest of

the whole channel.

As far as we know, this type of contracts are not used in to-day arts’ market, at

least in the case of visual arts. Under this perspective, our paper may provide useful

suggestions to artists and dealers.

24

REFERENCES Alchian A. – Demsetz H. (1972) “Production, Information Costs and Economic Organization”, American Economic Review, vol. 62, pp. 777-95. Alper N.O. – Wassall G.H. (2006), “Artists' Careers and Their Labor Markets”, in V. A. Ginsburgh – D. Throsby (Eds.), Handbook of the Economics of Art and Culture, North Holland, Amsterdam, pp. 813-64. Bergen M. – John G (1997), “Understanding cooperative advertising participation rates in conventional channels”, Journal of Marketing Research, vol. 34, pp. 357-69. Caves R. E. (2000), Creative Industries. Contracts between Art and Commerce, Harvard University Press, Cambridge, Ma, Us. Cuccia T. – Cellini R. (2009), “Workers’ Enterprises and The Taste for Production: The Arts, Sport and Other Cases”, Scottish Journal of Political Economy, vol. 56, pp. 123-37. De Marchi N. – Van Miegroet H.J. (2006), “The History of Art Markets”, in V. A. Ginsburgh – D. Throsby (Eds.), Handbook of the Economics of Art and Culture, North Holland, Amsterdam, pp. 69-122. Frey B. S. (1997), Not Just for the Money, Edward Edgar, Cheltenham. Hutter M. – Knebel C. – Pietzner G. – Schafer M. (2007), “Two Games in Town: A Comparison of Dealer and Auction Prices in Contemporary Visual Arts Markets”, Journal of Cultural Economics, vol. 31, pp. 247-61. Jeuland A. P – Shugan S. M. (1983), “Managing Channel Profits”, Marketing Science, vol. 2, pp. 239-72. Jorgensen S. – Zaccour G., (2003), “Channel Coordination over Time: Incentive Equilibria and Credibility” Journal of Economic Dynamics and Control, vol. 27, pp. 801-27. Kaya A. – Vereshchagina G. (2009), “Moral Hazard and Sorting in a Market for Partnership”, Mimeo, Arizona State University. Levine J. – Tadelis S. (2005), “Profit Sharing and the Role of Professional Partenership”, Quarterly Journal of Economics, vol. 120, pp. 131-71. Menger P.M. (2006), “Artistic Labor Markets”, in , in V. A. Ginsburgh – D. Throsby (Eds.), Handbook of the Economics of Art and Culture, North Holland, Amsterdam, pp. 765-811. Moorthy K. S. (1987), “Managing Channel Profits: Comment”, Marketing Science, vol. 6, pp. 375-79. Sacco P. (1998), “La selezione dei giovani artisti nei mercati delle arti visive”, in: W Santagata (Ed.), Economia dell’Arte, UTET, Torino. Schonfeld S. – Reinstaller A. (2007), “The Effects of Gallery and Artist Reputation on Prices in the Primary Market for Art: A Note”, Journal of Cultural Economics, vol. 31, pp. 143-53. Tamperi T. (2006), La vendita di opere d’arte fra tutela e mercato, Clueb, Bologna.

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Throsby D. (1994a), "The Production and Consumption of the Arts: A View of Cultural Economics", Journal of Economic Literature, 32, 1-29. Throsby D. (1994b), "A Work-Preference Model of Artist Behaviour", in A. Peacock - I. Rizzo (eds.), Cultural Economics and Cultural Policies, Kluwer Academic Publishers, Dordrecht, pp. 69-80. Velthuis O. (2011a), “Art dealers” in Towse R. (ed.), A Handbook of Cultural Economics, Second Edition, Edward Elgar Cheltenham. Velthuis O. (2011b), “Visual Arts” in Towse R. (ed.), A Handbook of Cultural Economics, Second Edition, Edward Elgar Cheltenham. Vinick P. A. (1997) “Art Dealers Need Written Contracts Specifying All Aspects of Dealer-Artist Agreements”, ArtWorldNews, February (also downloadable from the website http://www.fphlcc.ca/downloads/art dealers-need-written-contracts.pdf, Dec. 2011).

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NOTES

1 Caves (2000), in a different chapter, considers also the cases of writers (editorial industry) and singers (disco industry), which we overlook in the present paper. 2 Relations in the limiting cases are trivial. For 0=π , 2/δ=== STAFSTALCOU aaa , and

8/)4( 0 δ+=== zppp STAFSTALCOU , so that the individual results coincide across the different settings; for 1=π , 2/δ=== STAFSTALCOU aaa , and 0=== STAFSTALCOU ppp , so that also in this case individual results are the same across the considered regimes. 3 A short history of the relations between artists and dealers can be found in De Marchi and Van Miegroet (2006, Section 4). The variety of employment status and careers of artists are dealt with by, e.g., Menger (2006) and Alper and Wassall (2006). 4 Velthius (2011b), lists three main possible forms of agreements between artist and art dealers, in the case of visual arts: (1) employment with stipend, (2) direct acquisition, and (3) consignment. However, employment is not common today (exceptions are the low-tail of the market where artists copy standardized artworks for mass markets); famous cases of employment with fixed wage concern artists in past times: for instance, art dealer D. H. Kahnweiler paid (young) Picasso on a regular stipend, believing him as potential well-gifted artist; similar contracts were used by dealers Russo for Giorgio De Chirico (at the beginning of XX century) and by L. Castelli for promising young pop-artists in New York around 1960. Under such an agreement (also known as contrat-mecenat –see Tamperi, 2006), the artist commits to deliver a certain number of pieces in a given period of time, and receives a fixed salary, e.g., on monthly base; the art dealer usually keeps all the revenues from artworks’ sale. Alternatively, under direct acquisition contract, the dealer buys artworks from the artist and then decides when and at what price to sell them; such a system (also refereed as ‘the French system’, since it was common in the late XIX century in France) requires large (capital and financial) resources from the dealers, since they have to buy the artworks, and implies that the dealer runs the risk that the economic value will be never realized; it is rare in the today world. The largest part of today agreements base on consignment: the artist consigns her pieces to the dealer (who exhibit them); if and when a piece is sold, artist and dealer split the revenues, on a previously agreed terms. We have thought of this kind of agreement, in building the present model.