Non-strategic entry deterrence in monopolistic competition

Toshihiro Atsumi
Faculty of Economics, Meiji Gakuin University

Discussion Paper No.17-01
May, 2017

Non-strategic entry deterrence in monopolistic competition

Abstract
I look into the entrepreneur model of monopolistic competition that has been used in several
different strands of literature. I show how the same model also speaks to entry deterrence andinequality: in the model, incumbent entrepreneurs can successfully deter entry in a non-strategic
way, which results in a lower entrepreneurial participation rate and inequality among members of
the economy, compared to the no entry deterrence/free entry equilibrium. Such entry deterrence
can occur in industries in which firms are producing sufficiently dissimilar goods or goods with
sufficiently low elasticities of substitution.

Keywords: entrepreneur, monopolistic competition, entry deterrence, inequality
JEL classification: L13, L51, D72

11. Introduction
Analysis of entry deterrence has largely focused on one-on-one situations in the industrialorganization literature using game theory. According to Wilson (1992), analyses on strategic
entry deterrence fall into the categories of preemption, signaling, and predation. Typicalsituations examined in preemption studies are those of monopolists acting to preserve theirpositions, that is, deterring entry, for example, by holding higher capacity than needed to supply
current demand. Signaling studies proceed by assuming that incumbents convey information(such as cost) that discourage entry. Predation studies focus on incumbent firms’ battles against
current entrants to deter subsequent entry.
In the present paper, I examine entry deterrence using the entrepreneur formulation ofmonopolistic competition in general equilibrium. I show that, under certain conditions,incumbent firms have incentives to deter entry, and they can do so if there is a procedure for themto influence entry regulation. In contrast to the vast existing literature on strategic entry
deterrence, the present paper shows entry deterrence by atomistic firms engaged in monopolisticcompetition that do not take any strategic actions. The entrepreneur formulation of monopolisticcompetition has been used previously in at least in two different strands of literature:
entrepreneurial risk taking and new economic geography.
Attitudes toward risks and their consequences have been analyzed by Frank (1990) andClemens (2006, 2008) using the entrepreneur formulation of monopolistic competition. Theirfocuses are on the impact of entrepreneurial behavior on macroeconomic fluctuations or
economic growth. Frank (1990), for example, assumes risk aversion by entrepreneurs which leads
to cautiousness in making employment decisions. This micro behavior explains low output, lowemployment, and low welfare as an equilibrium macroeconomic consequence.
In new economic geography, Forslid and Ottaviano (2003) analyzed a model ofmonopolistic competition in which geographically mobile skilled workers are needed to set up
firms. This model is now known as the footloose entrepreneur model and it explains the relation
between inter-regional trade costs and agglomeration created by the migration of skilled workers.
The model is included among the core models of the new economic geography literature.1

1

See Baldwin et al. (2003) that offer comprehensive introduction of the core models developed in the new economic
geography literature.

2

In the entrepreneur model in this paper, there are neither entrepreneurial risks nor
geographic mobility. Instead, unlike the above mentioned studies, I analyze both the equilibriumwith a fixed share of entrepreneurs within the population and the free entry equilibrium. By
comparing the two equilibria, it is shown that conflict of interest can exist between incumbent
entrepreneurs and potential entrants depending on the initial share of entrepreneurs. I then show
conditions under which incumbent entrepreneurs can successfully block entry by majority voting.
If entry gets blocked and the free entry equilibrium is not achieved, then inequality persists
within the economy.
In the next section, I derive the equilibrium with fixed share of entrepreneurs, which ingeneral exhibits inequality between entrepreneurs and their employees. This inequality leads toentry, and the resultant free entry equilibrium is shown in section 3. In section 4, the possible
conflict of interest between incumbent entrepreneurs and potential entrants is shown. I show in
Section 5 conditions under which incumbent entrepreneurs can successfully block entry bymajority voting. Section 6 summarizes and concludes.

2. Equilibrium for a fixed share of entrepreneurs
The population of the economy is denoted by L . Members are either entrepreneurs or workers.
The share of entrepreneurs within the population is denoted by e

0  e  1 and, following

Forslid and Ottaviano (2003), it is assumed to be fixed. Correspondingly, the share of workers is
1  e . The firms run by the entrepreneurs are assumed to be monopolistically competitive. Each

entrepreneur employs workers to produce a particular variety. It is assumed that c units ofworkers are needed per unit output.
The same population also comprises the consumers. The assumption for consumer
behavior is a standard one, originally developed by Dixit and Stiglitz (1977). All consumers havethe same preferences, which are defined as1nU   mi  di  ,
 0




where U is the composite of all the differentiated varieties, n is the mass of varieties, mi  is theconsumption of variety i , and  is the substitution parameter. It is assumed that 0    1 toensure that the varieties are imperfect substitutes.   1 1     1 represents the elasticity of3

substitution between any two varieties. Higher (lower)  means weaker (stronger) love ofvariety. Denoting the price of a variety as pi  , a price index
1

n
 1
1
G   pi  di 
 0




(1)

is introduced such that total expenditure is GU . G is an overall level of prices that each firmtakes as given.
In the above setting, consumers’ utility maximization leads to demand for each variety
being pi  G  1Y , where Y is aggregate income. Demand therefore depends not only on pi and Y but also on G . Y consists of total profits earned by the entrepreneurs and total earnings of
the workers. When  is the profit of each firm and each worker’s wage is set equal to 1,
Y  eL  1  eL .

(2)On the supply side, entrepreneurs of monopolistically competitive firms will set theirprices so that marginal revenues equal marginal costs:pi 1  1    c .

(3)This is known as mark-up pricing in which firms always set their prices above their marginal
costs, c . However, since rival firms are producing more or less substitutable varieties, the markup depends on  : when the varieties are close substitutes (or consumers’ love of variety is weak),i.e., when  is high, then consumers are sensitive to prices and the prices are closer to c . By
substituting Eq. (3) into Eq. (1), we find that the mark-up pricing by each firm leads to the priceindex being
1

G  n 1

c
,
 1

(4)

where
n  eL .

(5)

Further, denoting the output of each firm as qi  , since the profit of each firm (  ) ispi qi   cqi  , using Eq. (3), we havecq i  .
 1

4

(6)

We can now consider the equilibrium. Equilibrium is defined as the goods and factor
markets clearing (i.e., supply equals demand) at a given level of e . The goods market clearing
condition isqi   pi  G  1Y ,

(7)

and the factor market clearing condition isL  n  ncqi  ,(8)which means that the population ( L ) needs to match the amount of entrepreneurs and workers;
i.e., all those not entrepreneurs must be fully employed as workers.
The equilibrium for a given fixed share of entrepreneurs can be obtained by solving Eqs.
(7) and (8) simultaneously, after substituting Eqs. (2) through (6). We then haveq i  

1 e
ec

(9)

as the equilibrium output of each firm. Thus, having fewer entrepreneurs (and therefore fewer
firms), implies that the output (or size) of each firm is larger. Substituting Eq. (9) into Eq. (6)gives the equilibrium profit:


1 e
.
e  1

(10)

Result 1. When the share of entrepreneurs ( e ) within the population is fixed, the profit of eachfirm (  ) can take any positive value depending on e and the elasticity of substitution between
any two varieties (  ) according to the following relationship: the lower e and/or the lower  ,the higher  .

Result 1 can be interpreted intuitively as follows. Imagine that only a smaller fraction of
the population is allowed to be entrepreneurs. Then, other things being equal, each firm becomeslarger (as shown in Eq. 9) and correspondingly each firm’s profit becomes larger (as shown in Eq.
6). Continuing this leads to considering a tiny e close to 0: as e  0 ,    . Also, imagine thatthe consumers’ love of variety becomes stronger and the firms produce less similar or lesssubstitutable varieties. Other things being equal, as shown in Eq. (3), this implies a higher markup and higher prices, leading to higher profits (as shown in Eq. 6). Continuing this leads toconsidering a low  very close to 1: as   1 ,    .

5Here, in the equilibrium for a fixed share of entrepreneurs, each entrepreneur earns  ,while each worker earns 1. Since both entrepreneurs and workers face the same prices, adifference in their earnings implies a difference in their utilities. (The indirect utilities for theentrepreneurs and the workers are  G and 1 G , respectively.)   1 (   1 ) means that theentrepreneurs’ utilities are higher (lower) than those of the workers. Since there is no upper limiton  , in theory, inequality can increase infinitely.
There is growing interest throughout the world regarding inequality. Result 1 indicatesthat there are both supply side and demand side reasons for inequality: Restriction to entry intobusiness, for example, implies a lower e and increases inequality. At the same time, weaker loveof variety, i.e., smaller  , will also increase inequality.

3. Free entry equilibrium
This section considers free entry where the share of entrepreneurs ( e ) is no longer fixed, meaningthat the population can choose occupations. Given the level of  , the workers now consider
whether they also want to become entrepreneurs. Workers have incentives to do so if   1 , thatis, when existing entrepreneurs earn more than what the workers do. On the other hand, if   1 ,meaning that the entrepreneurs earn less than the workers, the entrepreneurs shut down theirfirms and become workers. In any case, entry or exit occur until   1 . (Entry means the workers
becoming entrepreneurs; exit means the entrepreneurs becoming workers.) Substituting   1 into
Eq. (10) and solving for e , we havee 1  .

(11)

Result 2. In the free entry equilibrium, the share of entrepreneurs within the population ( e ) only
depends on the elasticity of substitution between any two varieties (  ), and e is the reciprocal of.

1  is the optimal share of entrepreneurs in this model economy.  , as defined in theoutset, reflects the love of variety: stronger (weaker) love of variety implies lower (higher)  .
Result 2 can then be interpreted that when peoples’ love of variety is strong (i.e.,  is low), more
people in the population will become entrepreneurs, and therefore the economy will have more

6

firms and varieties. It is only the demand parameter  that determines the share of entrepreneurs
within the population in the free entry equilibrium.

4. Conflict of interest between incumbent entrepreneurs and potential entrants
When the economy reaches the free entry equilibrium, both the entrepreneurs and the workers
earn 1, and equality is achieved. It is important to note, however, that the free entry equilibrium(compared to the initial equilibrium for a fixed share of entrepreneurs) does not necessarily raise
the utility of all. Suppose that initially   1 and entry occurs, i.e., the workers set up new firms
and start their own businesses. How will this affect the welfare of the existing entrepreneurs?
Since  decreases to 1 in the free entry equilibrium, the existing entrepreneurs’ utility changes
from  GS to 1 GL , where G S is the price index in the equilibrium with fixed share ofentrepreneurs and G L is the price index in the free entry equilibrium. For the existing
entrepreneurs to enjoy increased utility, therefore, it is necessary that  GS  1 GL . That is, using
Eqs. (4), (10), and (11),11  e  GS    e 1  .


e


1
G



L 

  

(12)

However, as shown below, it turns out that (12) does not always hold. Differentiating the leftand the right-hand sides of (12) with respect to e , we obtain

1
1 e


e
e  1 e 2   1

(13)

and


G S G L  e 1

.
e
 1

(14)

Inspecting Eqs. (13) and (14), recalling that by assumption 0  e  1 and   1 , we can confirm
that  e  0 and GS GL  e  0 . These imply that both  and GS GL are always decreasingin e . In addition, evaluating Eqs. (13) and (14) at e  1  , we have2at e  1 

e
 1

(15)

G S G L at e  1  .
e
 1

(16)

and

7

Comparing Eqs. (15) and (16), since   1 ,
 2


 1  1

which implies that the slope of  is steeper than that of GS GL at e  1  . We have, therefore,  GS GL , i.e.,  GS  1 GL , at least in the neighborhood of the free entry equilibrium (i.e.,e  1  ). These results are jointly illustrated in Figure 1.

Result 3. If   1 , then as the economy approaches the free entry equilibrium (i.e.,   1 ande  1  ), the existing entrepreneurs’ utility decreases.

Result 3 can be interpreted as follows. On the one hand, entry improves the utility of all
because the new firms provide new varieties, reflected as a fall in the price index, G . On theother hand, however, entry also means tougher competition for the existing entrepreneurs, soeach firm’s output falls and correspondingly profit falls. As the economy approaches the freeentry equilibrium, in which, as I have already shown, there are an increasing number ofentrepreneurs and rival firms, the latter effect outweighs the former; gains from the increase invariety cannot compensate individual entrepreneurs for their loss in profits relative to the starting
situation.
Importantly, Result 3 means that a conflict of interest exists between the incumbent
entrepreneurs and potential entrants. The incumbents are unlikely to accept new entry given that
their economic welfare deteriorates, and therefore self-interested incumbents have an incentive todeter entry.

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

1 e
e  11GS e 1
GL

1

1


e

Figure 1: The free entry equilibrium

5. Entry deterrence by voting and inequality
I assume that entry regulation exists, which can be influenced by the population. The entry
regulation functions in such a way that entry requires the consent of the population. Specifically,
I examine a simple case in which entry is decided by majority voting, and therefore entry requires‘permission’ by the majority of the population.2 The voting is assumed to be costless.
Based on the above assumptions, given Result 2, blocking entry by majority voting canonly be successful when 1   1 / 2 , i.e.,   2 .3 If   2 , then the incumbent entrepreneurs neverconstitute a majority of the population, and majority voting against entry cannot be successful.

Result 4. Entry can only be blocked in industries in which firms are producing sufficiently
dissimilar goods or goods with sufficiently low elasticities of substitution, i.e., when   2 .
2

I am abstracting from the real-world political process of indirect policy making.
Examples of traded goods that satisfies   2 from the Broda and Weinstein (2006) study are motor cars and othermotor vehicles, thermionic, cold cathode, photocathode valves, etc., footwear, silver, platinum and other platinumgroup metals for the period 1972-1988, and thermionic, cold cathode, photocathode valves, etc., telecommunications
equipment n.e.s. and parts, n.e.s. for the period 1990-2001.
3

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The equilibrium under majority voting depends on the initial state. Suppose initially theshare of entrepreneurs ( e ) is less than 1 2 . Then, even though entry lowers the welfare of theincumbents and they will be against entry, entry will continue because they do not yet constitutea majority of the population. However, when e reaches 1 2 , further entry now gets blocked bymajority voting. The equilibrium e is therefore 1 2 in this case. If the initial e is greater than orequal to 1 2 , then the incumbents already constitute a majority and therefore voting does notallow any further entry. That is, in this case, the equilibrium e is equal to the initial e .

Result 5. Let e S and e L be the initial and equilibrium shares, respectively, of entrepreneurs
under majority voting. Assuming that 1)   2 and 2) entry permission is subject to costlessmajority voting by the population, if eS  1 2 , then eL  1 2 . Otherwise, if 1 2  eS  1  , thene L  eS .

I illustrate in Figure 2 the case of   1.5 . For this value of  , Result 2 gives the freeentry equilibrium e as 2 3 . When 0  e  1 / 3 , there is no conflict of interest, because   GS GL ,which means that entry is welfare improving for the incumbents. When e  1 3 , then entry
reduces the welfare of the incumbents. This is when self-interested incumbents vote to block
entry. However, when 1 3  e  1 2 , the incumbents do not constitute a majority of the population.
Therefore, blocking entry cannot be legalized as a result of majority voting. The votes forblocking entry constitutes a majority when e  1 2 . Then, depending on the initial level of e , theequilibrium e will be 1 2 or in between 1 2 and 2 3 .
If entry deterrence occurs as presented in Result 5, inequality between the entrepreneurs
and the workers is not eliminated (i.e.,   1 ) and the entrepreneurial participation rate does notreach the free entry equilibrium level found in Result 2 (i.e., e  1  ).

10



1 e
e  11GS e 1GL

1votingequilibrium

1
3

0

no conflict of interest

G
 S
GL

1
2

free entry equilibrium(no voting)2  1 
3  

e

conflict of interest



GS
GL

Figure 2: Example of blocked entry with   1.5

6. Summary and conclusion
This paper analyzed an entrepreneurial model of monopolistic competition distinguishing
between the equilibrium for a fixed share of entrepreneurs and that under free entry. When theshare of entrepreneurs is fixed, inequality exists in general (Result 1), which induces new entry.
Free entry leads to the share of entrepreneurs within the population being 1  (Result 2), at which
point inequality has been eliminated. Inspecting the welfare changes of the incumbent andpotential entrepreneurs, however, it is found that a conflict of interest exists because theincumbents do not necessarily gain from new entrepreneurs joining their industry. (Result 3).
This implies that the incumbents may have an incentive for deterring entry. If there is a proceduresuch as majority voting to permit/deter entry, entry deterrence can be successful when   2 , thatis, when the firms are producing sufficiently dissimilar goods or goods with sufficiently low
elasticities of substitution (Result 4). The consequence of a successful entry deterrence will be

11that the (no voting) free entry equilibrium given in Result 2 is not achieved (Result 5), andtherefore a low e (i.e., low entrepreneurial participation rate) and inequality persist.
In contrast to the studies in the strategic entry deterrence literature, this paper showed that
non-strategic entry deterrence can occur in a general equilibrium model of monopolisticcompetition in which firms are atomistic and do not conduct strategic actions. The kind of entry
deterrence presented in this paper may be relevant not only to entrepreneurs in general but also toentry regulations seen in a number of professions.

Acknowledgement
I appreciate the financial support of a Grant-in-Aid for Scientific Research (16H06548) from theJapan Society for the Promotion of Science.

References
Baldwin, Richard, Rikard Forslid, Philippe Martin, Gianmarco Ottaviano and Frederic RobertNicoud (2003) Economic Geography and Public Policy, Princeton University Press: Princeton
and Oxford.
Broda, Christian and David E. Weinstein (2006) “Globalization and the gains from variety”
Quarterly Journal of Economics 121, 541-585.
Clemens, Christiane (2006) “Monopolistic competition and entrepreneurial risk-taking”
Economics Letters 93, 68–74.
Clemens, Christiane (2008) “Imperfect Competition and Growth with Entrepreneurial Risk”
German Economic Review 9, 180–206.
Dixit, Avinash K. and Joseph E. Stiglitz (1977) “Monopolistic competition and optimum productdiversity” American Economic Review 67, 297-308.
Forslid, Rikard and Gianmarco I.P. Ottaviano (2003) “An analytically solvable core-peripherymodel” Journal of Economic Geography 3, 229-240.
Frank, Jeff (1990) “Monopolistic Competition, Risk Aversion, and Equilibrium Recessions”
Quarterly Journal of Economics 105, 921-938.
Wilson, Robert (1992) “Strategic Models of entry Deterrence” in Robert J. Aumann and Sergiu
Hart eds. Handbook of Game Theory Chapter 10 Amsterdam: North-Holland/Elsevier Science
Publishers.

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