1

Entrepreneurial Behavior and the development of Trading

Institutions: An Analytical Approach

byKaren A. Campbell∗

October 2008

This paper makes explicit the role of the entrepreneur in a consumer-producer econ-omy. Entrepreneurial behavior changes the status quo by altering existing compar-ative advantages. A positive feedback effect with trading institutions ensues. Thismodel shows how the entrepreneur can, when successful, create economic growthbut if unsuccessful, can contribute to an economic contraction. Using our theo-retical approach, propositions are generated that explain empirical observations ofentrepreneurship. This framework offers a tool for future analytical and empiricalinvestigations into entrepreneurship in a systematic way. (JEL: D 01, D 49, D 61,D 81, 0 12)

“Entrepreneurship innovation and capitalism will make it into the eco-nomics classrooms only with the arrival of ‘abstract, formal’ treatments.When those arrive, economics — and capitalism — will receive a huge boost.”

- Phelps [2005] p. 30

1 Motivation

Entrepreneurship – this single word conjures up different, often conflicting, connota-tions.1 Schumpeter [1934] recognized the entrepreneurial contribution as creating

∗This paper is based on Chapter 1 of my doctoral dissertation, “Towards a General Theoryof Entrepreneurship,” submitted to Temple University in May 2008. I thank Dimitrios Dia-mantaras of Temple University for his many comments and especially his encouragement. Ithank, also, an anonymous referee for extremely useful and constructive suggestions. I am alsograteful for the helpful comments of Mohsen Fardmanesh of Temple University, Rob Gillesof Virginia Tech, students in a graduate seminar at Temple University and participants atthe 2007 USF-Silicon Valley Global Entrepreneurship Research Conference. All errors are,however, my own.

1The term was first introduced into economics in 1755 by Richard Cantillion and popularized bySay in the early 1800’s (Casson, 1982).

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change and ultimately growth potential in an economy’s structure. Hayek [1945] sawthe role of the entrepreneur as using idiosyncratic knowledge and Kirzner [1973] furtherargued that it is the “alertness” of the entrepreneur in acting on a profit opportunitythat affects growth. If, as Lazear [2005] states, “the entrepreneur is the single mostimportant player in a modern economy,” a rigorous analytical framework based on mod-ern microeconomic theory would be a useful aid in understanding the economic role ofthe entrepreneur.

There is some controversy as to whether a mathematical framework is an appropriatetool for the study of entrepreneurship (see Shane and Venkataraman, 2000). Thispaper shows that the economic behavior of the entrepreneur lends itself to an analyticalinvestigation. The decision problem of the entrepreneur involves changing the statusquo. When the entrepreneur chooses to do this, and what effect it has on the econ-omy are questions not answered by standard neoclassical microeconomic theory. Yet theneoclassical analysis has proved to be a powerful tool that has given economists pre-cise arguments for such things as competitive markets, welfare comparisons and policyanalysis. Therefore, rather than separate entrepreneurs from this microeconomic model,we should introduce the entrepreneur into the model, creating a more unified microframework. As Holcombe [1998] summarizes, “the incorporation of entrepreneurshipinto the framework of economic growth not only fills in the institutional details to helpmake the growth process more understandable, but also points toward more promisingeconomic policy recommendations for fostering economic growth” (p. 60). By using thistype of analysis, this paper seeks to contribute a first step towards a unified ‘ground-up’theory of entrepreneurship, consumers, producers and the development of the institu-tions (firms, legal systems, etc.) in which they operate. This is done by demonstrating apositive feedback between entrepreneurship, institutions and market structures. Wittand Zellner [2006] assert that there is “an incessant sequence of institutional adap-tations to changing production technologies which, in turn, influence the incentives insociety to drive the development of technology further” (p. 1).

The model introduced in this paper builds on the mathematical formulation of in-framarginal models pioneered by such researchers as Yang and Yao [2001], Ng andYang [1997], Wen [1998], Sun [2002] and others. Inframarginal, also known as newclassical, analysis is defined in Yang [2003] as “a total benefit-cost analysis across cor-ner and interior solutions, in addition to marginal analysis of each corner and interiorsolution” (p. 9). New classical theorists assume individuals are initially both consumersand producers. This literature asserts that each individual will not just optimize withingiven institutions or market structures, but will evaluate different institutions and seekto specialize and trade if higher utility is achievable. Much of this literature has beenconcerned with an ambitious research agenda: proving the existence of equilibria of themost general models, proving analogues to the classical first and second welfare theo-rems and pursuing many applications. Analysis for this type of model focuses mainlyon trade-offs between transaction efficiency and economies of specialization,2 in which

2A main assumption of this literature follows in the tradition of Young [1928], that there areincreasing returns to scale in production.

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endogenous changes are driven by exogenous improvements in transaction efficiency.However, Yang [2003] does allude to a role for the entrepreneur to act as a middlemanthat improves transaction efficiency.

This paper takes a different approach with inframarginal analysis. Rather thanassume economies of specialization through increasing returns to labor, we show how anentrepreneur’s decision creates economies of specialization indirectly by attempting toimplement a potential venture idea. This attempt alters the status quo and hence createsa comparative advantage. When an altered configuration of comparative advantagesis anticipated, individuals evaluate possible trading institutions and find economies ofspecialization by exploiting classical Ricardian gains from trade.

There are two main reasons the consumer-producer paradigm (i.e, new classical anal-ysis) is conducive for the study of entrepreneurship. First, there is evidence that theentrepreneur sees an opportunity because he himself is a user or consumer. That is, theconstraint he wants to change binds him personally. For example, von Hippel [2001]alludes to the entrepreneur being both a consumer and producer by calling this per-son a User (defined there as someone who appropriates technology for his own personalproductivity and possibly sells it to a manufacturer.)3

Second, given the individuals’ relevant constraints, the entrepreneur may choose thecorner solution, namely, not to use entrepreneurial effort. Shane and Venkataraman[2000] point out, “Not only must there be a discovery of opportunity but [entrepreneurs]must choose to act on it. We can only empirically look at when people choose to act. Butit is when they choose not to that is also important both theoretically and for policy.”Therefore analytical models must be able to handle inframarginal decisions.

We can use this analysis to trace how market institutions might evolve throughrational, mutually beneficial decisions when the entrepreneur attempts to create a com-parative advantage. One insight from this model is that trade has a more subtle benefitthan the usual gains from trade. In this way, comparative advantage and trade, longseen as an engine of growth, can be traced to entrepreneurial decisions.

The paper is organized as follows. Section 2 details the entrepreneurial economymodel. Section 3 proceeds to investigate conditions for entrepreneurial action when theentrepreneur acts alone (that is, with no market available for specialization and trade) asthe benchmark case. Section 4 studies entrepreneurship in the context of a competitivemarket when a venture idea is production specific. Section 5 concludes.

The entrepreneurship literature makes a distinction between product and process en-trepreneurs. The model below analyzes a production process entrepreneur, which is anindividual who has an idea about improving the technology that produces a specific con-sumption good. The framework, though, can also be interpreted and analyzed from theperspective of a product quality improvement. The venture idea (defined below) wouldyield higher utility of the consumption good rather than a technological improvementthat yields more of the consumption good.

3The inframarginal approach eliminates the false dichotomy between demand and supply and there-fore makes explicit how one’s demand is intimately linked to the individual’s productive capabilities.The separation between demand and supply in a modern economy is due to ever increasing division oflabor driven, as argued here, by entrepreneurs.

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Many of the formal definitions found in the paper are due to ideas conceptualized inEckhardt and Shane [2003] and Davidsson [2002] who built on the theoretical foun-dation laid by Casson [1982], Venkataraman [1997] and Shane and Venkatara-man [2000]. For instance, these authors refined the definition of entrepreneurial oppor-tunity. However, due to recurring confusion and debate in the literature over the precisemeaning of “opportunity”, Davidsson [2003] argues persuasively for the term “ventureideas.”

2 An Entrepreneurial Economy

Let M be a finite set in R++ in which a typical element m specifies the productioncoefficient (technology). Denote the current, status quo, production process for a con-sumption good as m0. Define the set of technologies K = {k ∈ M|k ≤ m0} as the setof known technologies and the set U = {m1 ∈ M|m1 > m0} as the set of (currently)untried or unimplemented technologies. Hence the space of all relationships or ideas,M, is partitioned into two sets where the status quo technology is the highest element,m0, in K. A Venture Idea is an element of the set U .4

There are two consumption goods x ∈ R+ and y ∈ R+. Let lx and ly denote labortime allocated to the production of x and y respectively and le denote an entrepreneurialinvestment of time implementing one’s venture idea.

A Potential Entrepreneur is an individual who has a venture idea, m1 ∈ U . Apotential entrepreneur becomes an Entrepreneur by choosing positive entrepreneurialeffort le > 0.

There are two individuals i ∈ {E,P}. E denotes a potential entrepreneur (mE1 ∈ U)

and P denotes a [potential] trading partner who is not a potential entrepreneur.5 Bothindividuals are endowed with one unit of labor (Li = 1).6 Therefore the time constraintsfor each individual i ∈ I are:

1 ≥ lix + liy + lie,(1)

0 ≤ lij ≤ 1, j ∈ {x, y, e}.(2)

Each individual has a utility function7:

U i(xi, yi) = xiyi.(3)

4This paper does not investigate how the entrepreneur becomes aware of or creates the venture idea.For work being done in this area see, for example, Rigotti [2006], Minniti [2004] or Dekel, et. al.1998.

5This is a simplification for the analysis. Extensions of this model could have both individuals aspotential entrepreneurs.

6Normalizing this to 1 does not change the analysis.7This functional form is used to make each individual sensitive to possible entrepreneurial failure by

making both goods necessary for each individual. Also, the entrepreneur receives no direct utility fromentrepreneurial effort. In this way we can study more subtle economic reasons for entrepreneurshiprather than by assuming some intrinsic personal value. Future papers will consider other functionalforms. Different functional forms can be tailored to specific case studies as well.

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Production exhibits constant returns to scale in the one input (labor). As mentioned,most of the inframarginal literature assumes increasing returns. Extensions of this workwill also consider increasing returns. However, the assumption of constant returns toscale is used in order to handicap the entrepreneur. This way, we can discover whetherthere are fundamental motivations for entrepreneurial effort rather than exploiting in-creasing returns. The marginal product of labor for good y is 1 for simplicity. Good xcan be produced with the status quo technology in which the marginal product of laboris m0 or some labor effort can be used to try and change this technology. Thus thecurrent production functions can be written as:

yi = liy,(4)

xi = m0lix.(5)

A potential entrepreneur faces a two-stage decision. In the first stage, he decideswhether or not to use entrepreneurial effort by weighing the two possible second stagestates that might arise if he becomes an entrepreneur. These two possible states aresuccess or failure. An entrepreneur’s probability of success is a function of his en-trepreneurial investment time le. Let the function γ̂ : [0, 1] → (0, 1], translate en-trepreneurial investment, le into a (subjective) probability of success. Thus if an in-dividual chooses to implement his venture idea (lie > 0) either with probability γ̂i(le),mi

1 will be realized and can be used, or with probability 1 − γ̂i(le), m0 (i.e., the sta-tus quo technology) will be used. The ex-post state that obtains is random8, but theentrepreneur can improve his probability of success with greater entrepreneurial effort,because we assume γ̂′(le) > 0.9

For this paper we assume a linear functional form for the probability of successfunction10:

(6) γ̂i = γilie 0 < γi ≤ 1.

The entrepreneurial investment process gives the entrepreneur an expectation of suc-cess. This expectation is an individual (subjective) perception, although it may be ashared perception (as we assume in the trade case below). This formulation capturesthe intuition that one’s entrepreneurial effort positively affects one’s perception of theirprobability of success but there are other (random) factors that may play a role suchthat success is not guaranteed.

Entrepreneurial efficiency can be described by the parameter γ. This can be in-terpreted in a number of ways for specific case analysis and/or calibrated for specificempirical studies. For example, this parameter could capture how conducive an eco-nomic environment is for entrepreneurial activity. Is it very difficult to be a successful

8See Campbell [2008d] for an ex-post analysis of this framework using a computational approach.9This captures the empirical finding discussed by Parker [2005] that entrepreneurs work more hours

for less return because an entrepreneur attempts to increase his expected value through the part of hissuccess he can control.

10Note, if a greater than 1 time allotment is assumed an off-setting restriction on γ would be neededto insure that the probability of success remains less than or equal to 1.

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Figure 1

Entrepreneur’s Autarky Decision

l*e> 0 l*

e = 0

γl*e

1 – γl*e

USuccess UFail

USQ

E

entrepreneur due to bureaucratic restrictions? Is the economy populated by a numberof potential entrepreneurs that may help increase probability of success or are thererelatively few individuals with venture ideas that lead to a perception of greater iner-tia? This parameter could also be used to capture more individual characteristics. Forexample, has this entrepreneur been successful in the past?

If the discovery process is a success, the entrepreneur can produce:

xE = mE1 lEe .(7)

otherwise he must produce, xE according to the current (or status quo) technology(equation 5) above.

3 Case 1: No Trade

In this section, we drop the entrepreneur’s superscript since there is no possibility ofconfusion. As mentioned above, the economic environment creates a two-stage problemfor the entrepreneur. In the first stage, given his (perceived) entrepreneurial efficiency (γ)and venture idea (m1), he evaluates what level of entrepreneurial effort would maximizehis expected utility by forecasting his possible second stage outcomes. That is, in thesecond stage, if he chooses to act on his idea, he will either succeed or fail. Let USuccess

and UFail denote his respective maximum utility in each of these ex-post states. If hedetermines that he will not use entrepreneurial effort, then his utility remains what ithas been. We will denote this status quo utility as USQ 11. Thus in choosing whetherto act or not, he compares his expected utility from his idea with the maximum utilityhe is receiving with the status quo technology. To better visualize the entrepreneur’sproblem a decision tree may be helpful.12

11Note that is also the [potential] trading partner’s utility in autarky since the two individuals areex-ante identical.

12To be technically the precise, the entrepreneur faces an infinite number of choices of le > 0 in thecontinuum (0,1]. The entrepreneur chooses the le > 0 that gives him the most expected utility. Forconcision and simplicity we show this as l∗e .

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The following propositions follow from the framework. Many of the proofs are omit-ted for brevity but are available upon request.13 Some proofs are included to demonstratethe technique.

Proposition 1 Given the above model, a potential entrepreneur in autarky, who allo-cates no time to entrepreneurial effort, has maximal status quo utility of USQ = m0

4.

The proof is an immediate consequence of maximizing (3) subject to equations (1)and (4-6).

Proposition 2 Given the above model, an entrepreneur in autarky, if successful, hasa maximum utility of USuccess = m1(

12− 1

2l∗e)

2, which is a function of the chosen level ofentrepreneurial effort.

Proposition 3 Given the above model, an entrepreneur in autarky, if unsuccessful,has maximal utility of UFail = m0(

12− 1

2l∗e)

2, which is a function of the chosen level ofentrepreneurial effort.

Given the above model and propositions 1, 2 and 3, an entrepreneur in autarkychooses his optimal entrepreneurial effort, l∗e , in order to solve the problemmaxle {USQ, (γ̂USuccess + (1 − γ̂)UFail)} subject to 0 ≤ le ≤ 1 and γ̂ = γle. Thenext proposition makes clear exactly when a potential entrepreneur will choose each ofthese solutions. Let EA ⊂ (0, 1] × U be the set of pairs (γ,m1) such that the potentialentrepreneur chooses le > 0.

Proposition 4 Given the above autarky model, EA = {(γ,m1) ∈ (0, 1]×U| 127

(γm1+(1−γ)m0)3

(γ(m1−m0))2>

m0

4}.

Proof The proof proceeds by solving the entrepreneur’s decision problem. Fromproposition 1 we know the value of the first element in the entrepreneur’s decision set,USQ = m0

4. Turning to the second element, we must first solve the entrepreneur’s

optimization problem.

E[UA] = γ̂USuccess + (1− γ̂)UFail.

From Proposition 2 and 3 we know

(8) maxle

γle

(m1

(1

2− 1

2le

)2)

+ (1− γle)

(m0

(1

2− 1

2le

)2).

Setting the first derivative equal to zero and solving yields either

(9) le = 1 or l∗e =1

3− 2

3

1

γ

m0

m1 −m0

.

13The proofs can also be found on the author’s website at astro.temple.edu\~karen3.

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The first solution is the minimum; spending all one’s time on entrepreneurial effortleaves no time to produce the goods that bring utility. The second solution achievesthe maximum. By substituting this positive maximal entrepreneurial effort, l∗e into theentrepreneur’s expected utility equation above, we have:

(10) E[UA] =1

3(γm1 + (1− γ)m0)

(1

3+

1

3

1

γ

m0

m1 −m0

)2

=1

27

(γm1 + (1− γ)m0)3

(γ(m1 −m0))2.

Utility maximization requires entrepreneurial effort to be positive when this expectedutility, equation 10, overcomes the entrepreneur’s certain status quo utility. Thereforethe entrepreneur’s effort will jump from le = 0 to le = 1

3− 2

31γ

m0

m1−m0only when:

1

27

(γm1 + (1− γ)m0)3

(γ(m1 −m0))2>m0

4.

Q.E.D.

The model predicts that the potential entrepreneur jumps from a corner solution(decision not to be entrepreneurial) to a positive solution when he believes doing sowill yield higher utility than he is currently receiving. This jump in effort is intuitive.Entrepreneurs often express it in words such as “I took the plunge” or “I saw theopportunity and decided to go for it.” When potential entrepreneurs choose the cornersolution, le = 0, they expect the opportunity to yield them less than or equal to what theyare currently receiving in utility. This is expressed by many potential entrepreneurs withphrases such as, “I once had an idea for ... but never acted on it.” For each entrepreneur,the effort level will be different given the size of his venture idea (or opportunity) andhis evaluation of how successful he will be if he puts forth positive effort.

The optimal level of effort is negative at low potential ideas and is exactly equal tozero when the potential idea yields the same expected utility as the status quo. Potentialideas greater than this zero level, will be those for which entrepreneurship is empiricallyobserved.

For policy purposes, it is interesting to look at some comparative statics on en-trepreneurial effort in terms of what influence has the greatest effect on entrepreneurialbehavior.

Corollary 1 Assuming the above model and proposition 4, if le > 0, then assuming allelse equal, entrepreneurial effort will (1) decrease if the status quo technology increases(2) increase if the size of the venture idea increases and (3) increase if entrepreneurialefficiency, γ increases.

The proof is found by taking the appropriate partial derivatives of the optimal interiorentrepreneurial effort.

This corollary has interesting implications for empirical work as well. In cases wherethe model’s assumptions hold, this corollary may help explain why we see technologyplateaus. That is, initially there is high entrepreneurial effort in an industry. As this

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higher level becomes the new status quo, less entrepreneurial effort may result perhapsbecause individuals might become more complacent in discovering new technologies, orperhaps because the additional benefits from getting more of the same good are falling.

Note that these results obtain even though:

1. There are no explicit increasing returns to new technology.

2. The entrepreneur is not relatively more risk-loving than the general population.

3. The entrepreneur gets no direct, intrinsic utility from entrepreneurial effort or hisventure idea.

4 Case 2: With Trade

Next we would like to determine how a market institution might affect the entrepreneur’sbehavior. By modifying the above model to account for trade and comparing the re-sults to the autarky case, we can ask such questions as: What effect does trade haveon entrepreneurial effort and productivity improvement? Why do we see some evidencethat there may be more business failures in a more developed market economy versusin less developed market economies? Why do we see evidence that large firms oftenmake smaller incremental improvements while small firms make larger incremental im-provements?14 Why might we observe relative price changes for a good without anyobservable change in production technology?15

To account for trade, we modify the above model by defining a market price for thetwo goods and adding a budget constraint to each individual’s behavior decision. Firstdefine prices for x and y as px and py respectively. Then define the relative price asp = px/py. As before xi and yi denote the amount of each good produced by individuali. Let xis and xid denote the amount of good x supplied and demanded respectively byindividual i and define yis, yid analogously. Then an individual’s budget constraint is

yid + pxid ≤ yis + pxis(11)

Each individual is still assumed to have the same preferences for the two consumptiongoods x and y. However the utility function can be written to show the consumption ofeach good coming from trade. Precisely:

U i = (xi + xid − xis)(yi + yid − yis).(12)

Each individual’s time endowment is still normalized to 1 unit of time that can bespent producing x, y or on entrepreneurial effort. The current (status quo) production

14In the literature this is usually distinguished by the terms innovations versus inventions. The formerare the smaller incremental improvements made on inventions.

15For example, industries that experience price increases may also report higher profits. This wouldseem to contradict the neoclassical theory that price is a reflection of marginal cost. Indeed, higherprices combined with higher profits often triggers regulators to investigate claims of price-gouging orcollusion. Although this paper does not attempt to answer specific cases, it gives regulators anotheranalysis tool that could potentially be applied to these cases.

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functions are also the same for both individuals: yi = liy and xi = m0lix, as is the

entrepreneurial investment process γ̂i = γilie (γi ∈ (0, 1]). Therefore the entrepreneuris successful with probability γ̂ and thus has a comparative advantage in producing x.That is:

xE = mE1 lEx(13)

where, recall, mE1 > m0.

For this section we also assume the following.

Assumption 1 Property rights to a new venture idea are respected by the trading part-ner. That is, if an entrepreneur successfully implements a new technology, the tradingpartner will not steal this technology to use in her own production.

This condition is arguably strong (unless the entrepreneur can effectively keep the tech-nology a secret). We use it here to analyze one type of equilibrium. 16

Assumption 2 When individuals trade, the Walrasian equilibrium results.

This condition may seem implausible given that we are talking about entrepreneurshipand a new technology (and given that there are only two traders). Indeed almost allthe literature studying entrepreneurship makes the assumption that the market is eithermonopolistic or oligopolistic. Therefore either explicitly or implicitly much of the mo-tivation for entrepreneurial effort comes from a priori monopoly profit. By assumingcompetitive markets and letting the entrepreneur try to create economic gains, we re-veal more subtle entrepreneurial motivations. In a sense, the model here stacks the deckagainst the entrepreneur. Assuming a competitive market and identical individuals atthe status quo, there is no gain to be had at the status quo equilibrium (Proposition5 below). Hence if the entrepreneur wants to gain, he must find a way to change thestatus quo. It is in this way we can trace economic growth through the entrepreneur’sactions.

Assumption 3 Individuals agree to specialize and trade prior to knowing whether theentrepreneur will be successful or not. Once they agree, this contract is fully enforceable.

In the consumer-producer framework Diamantaras and Gilles [2004] (buildingon the work of Wen, 1998) prove a theorem that individuals do at least as well if notbetter by completely specializing in production (in other words they don’t buy and sellthe same good). They prove this assuming only two weak regularity conditions on thetransaction efficiency and the utility function, which are satisfied in the set-up of thismodel.

16Campbell [2008c] relaxes this assumption and analyzes what equilibria may arise if the tradingpartner could in fact observe and implement the entrepreneur’s new venture idea into her own produc-tion.

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Figure 2

Entrepreneur’s Decision With Trade

l*e>0

l*e = 0

γl*e 1 - γl*

e

USuccess UFail

USQl*e>0

l*e = 0

γl*e 1 - γl*

e

UM

Success UM

Fail

USQ

E

TradeAutarky

Theorem 1 (Diamantaras and Gilles) If in any configuration the individual buys andsells the same good, then there is a configuration in which the individual does not buyand sell the same good and in which the individual is at least as well off.

For this reason we assume here, when individuals trade, both completely specialize inthe production of the good for which they have an expected comparative advantage. Herethe entrepreneur will expect to change his production technology for good x. Therefore,if there is trade, the entrepreneur will produce and sell x while the trading partner willproduce and sell y.

A decision tree may again be helpful in visualizing the entrepreneur’s decision whentrade is possible.

As in the previous section we proceed with proposing the pay-offs to the entrepreneurat each of the possible terminal nodes. The proofs are immediate substitutions of thechosen functional forms.

Proposition 5 Given the two-person trade model and assumption 2, if the entrepreneurchooses lEe = 0, both individuals are indifferent between trade and autarky and have autility of USQ = m0

4.

Proposition 6 Given the two-person trade model and assumptions 1, 2, and 3 anentrepreneur with a trading opportunity, if successful, has a utility of USuccess

M = (m1(1−le)− xs)pxs which is a function of the chosen level of entrepreneurial effort, the amountof x supplied and the relative price of x.

Proposition 7 Given the two person trade model and assumptions 1, 2, and 3 anentrepreneur who trades and is unsuccessful has a utility of UFail

M = (m0(1− le)−xs)pxswhich is a function of the chosen level of entrepreneurial effort, good x supplied and therelative price of x.

The resulting entrepreneurial behavior can be compared to the entrepreneur’s behaviorin the no trade case.

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Proposition 8 Given the two person trade model and assumptions 1, 2, and 3 anentrepreneur in autarky with no trading opportunity has a lower positive amount ofentrepreneurial effort than when there is a trading opportunity.

Proof The proof involves solving the entrepreneur’s decision problem when tradeis possible and comparing it to optimal entrepreneurial effort given in Proposition 4(lAe = 1

3− 2

31γ

m0

m1−m0).

The entrepreneur’s ex-ante expected utility is a weighted average of his utility fromsuccess and failure. Since his probability of success is γ̂ = γle, the problem becomes:

maxle,xs

EUM = γleUSuccessM + (1− γle)UFail

M .

From Propositions 6 and 7 above we have:

maxle,xs

E[UM ] = γle[(m1(1− le)− xs)pxs] + (1− γle)[(m0(1− le)− xs)pxs].(14)

Setting the derivatives, ∂EUM

∂leand ∂EUM

∂xs equal to zero, gives two equations with twounknowns.

The solutions of these equations are:

lMe =1

2− 1

2

1

γ

m0

m1 −m0

and(15a)

xs =1

2[(1− le)(γle(m1 −m0) +m0)].(15b)

Substituting appropriately and simplifying yields:

lM∗e =1

2− 1

2

1

γ

m0

m1 −m0

,(16a)

xs∗ =1

8

(γm1 + (2− γ)m0 +

1

γ

m20

m1 −m0

).(16b)

Again recalling from the proof of proposition 4 the interior optimal level of entrepreneurialeffort in autarky, it is true that

1

3− 2

3

1

γ

m0

m1 −m0

<1

2− 1

2

1

γ

m0

m1 −m0

or equiv. − 1

6

1

γ

m0

m1 −m0

<1

6.(17)

Q.E.D.

Baumol [2005] and others make a case for market based reforms as a way of fosteringentrepreneurship with empirical studies showing significant positive correlation betweenthe two. Proposition 8 demonstrates a possible theory behind this statistical link: whenthere is a market for goods, greater entrepreneurial effort (investment) can occur. Thefollowing corollary and proof give further insight into this link between markets andentrepreneurship. The first lends theoretical support for observing more incremental

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Figure 3

Threshold values of venture ideas for various entrepreneurial efficiencies

technological improvements in market economies; the second gives theoretical credenceto the critique that greater openness to trade may result in higher volatility in output.

When there is a market opportunity, define EM ⊂ (0, 1]×U as the set of pairs (γ,m1)such that the individual chooses to become an entrepreneur, le > 0.

Proposition 9 Under assumptions 1, 2 and 3, EA ⊂ EM .

This proof is in the appendix but demonstrated here by the following four graphs infigure 3 where γ = .25, .5, .75, 1.0 respectively.

Proposition 9 may help explain empirical evidence suggesting that large firms makesmaller relative improvements while small firms implement greater relative improve-ments.17 There is a trade-off between the size of the improvement and entrepreneurialefficiency. The more incremental the improvement (venture ideas closer to the statusquo), the higher the γ needs to be to induce entrepreneurial effort. Arguably, largefirms may have greater entrepreneurial efficiencies18 due to such things as greater accessto financial and other capital resources and greater specialization within firms givingindividuals more time to invest.19 If this is true, then large firms would, in general,have higher γ′s than small firms. Thus using this model, we would predict that moreincremental improvements would come from large firms while small firms would havebigger relative improvements over the status quo. Because small firms attempt ven-ture ideas further from the status quo, they may also give a perception of being moreentrepreneurial than large firms.

5 Further Implications of the Framework

This paper has developed an analytical tool for studying the entrepreneur. The propo-sitions thus far have shown the framework is useful for explaining some of our intuitive

17C.f. Ace and Audretsch [2005], CHI Research Inc. [2003] and Detienne [2001]18Entrepreneurs in large firms are usually referred to as intrapreneurs.19Some researchers have pointed out that small business entrepreneurs often need to be ”jack of

all trades.” This may be more a consequence of the institutional form in which the entrepreneur isoperating rather than a feature of entrepreneurship.

14

and empirical understanding of entrepreneurs. The following propositions use the toolto gain insight into a phenomenon that is perhaps not as well understood or explained;namely, how does the positive feedback channel between entrepreneurship and marketinstitutions work?

The first proposition explains the incentives entrepreneurs have for seeking marketopportunities. Traditional Ricardian gains from trade analysis begins with an exogenouscomparative advantage. Here an exogenous comparative advantage is one for whichthe individual-entrepreneur can produce x with technology m1 without exerting anyentrepreneurial effort, while the trading partner produces x with technology m0. Wefind that, given the assumption of a competitive market, although the entire economyexperiences traditional Ricardian gains from trade, the individual-entrepreneur with anexogenous comparative advantage20 does not strictly benefit from trade. Interestingly,though, the entrepreneur who creates a comparative advantage through entrepreneurialeffort does expect to strictly benefit from trade.

Proposition 10 Given the two person trade model and assumptions 1, 2 and 3, anindividual with an exogenous comparative advantage is indifferent between autarky anda market. In contrast, an entrepreneur who creates a comparative advantage expectsgreater utility in a market than in autarky.

The proof is omitted but one can verify that when comparative advantages are exoge-nous and the market price is the competitive price, the individual with a comparativeadvantage in x production gets the same utility whether he trades or operates in au-tarky. The lower technology trading partner does strictly better in the presence of anexogenous comparative advantage. In contrast, the table below demonstrates the addi-tional gains an entrepreneur expects from having a trade opportunity when his expectedcomparative advantage in x is endogenous. In the table the status quo technology, m0, isnormalized to 1 and entrepreneurial efficiency in the economy is γ = 0.6. The followingtable calculates some expected utilities for different venture ideas.

From Table 1 we see that the entrepreneur in the endogenous case would choose le > 0in the range of approximately 2.7 ≤ m1 ≤ 4.3 when a trade is possible, but does not doso in autarky. In this range, not only does a market produce above ‘normal’ expectedgains from trade, but having a market makes the difference for entrepreneurship to occur.Thus the model gives theoretical insight into a phenomenon that would be difficult if notimpossible to observe empirically. It reveals ranges for which potential entrepreneurschoose not to act due to undeveloped market opportunities. This underdevelopmenthinders one’s ability to specialize and therefore limits ones time to invest. The timeconstraint combined with the inherent uncertainty constraint leads to less individualschoosing to be entrepreneurial.

Proposition 10 is interesting for a number of reasons. The most notable is thepresence of expected gains from having a market, even when the expected price is equal

20If the comparative advantage is exogenous, then the individual is not technically an entrepreneur bythe definition given above. However, for comparison with the endogenous entrepreneur, the individualwith the exogenous comparative advantage in x will be referred to as the individual-entrepreneur.

15

Table 1

Entrepreneur’s Expected Trade Gains from Endogenous Specialization

γ m1 lMe lAe E[UM ] E[UA] Endogenous Trade Gain0.6 2.666 0.000 0.000 0.250 0.250 0.0000.6 4 0.222 0.000 0.272 0.250 0.0220.6 4.33 0.250 0.000 0.281 0.250 0.0310.6 6 0.333 0.111 0.333 0.263 0.0700.6 7 0.361 0.148 0.367 0.278 0.0890.6 8 0.381 0.175 0.402 0.295 0.1070.6 9 0.396 0.194 0.438 0.314 0.124

to the expected marginal cost. This offers a theoretical link between societies populatedwith potential entrepreneurs and the development of market institutions. That is, wewould expect individuals, given the opportunity to create comparative advantages, wouldseek to create markets in which to trade. It is not the competitiveness, per se, of amarket that is the driving factor but rather the openness or availability of a market thatis important.21

Besides the investment time advantage, the presence of the market benefits the en-trepreneur in another way. By specializing, the entrepreneur does not produce y andtherefore the production of good y is not disrupted by his failure. Had he not been ableto trade, he would have reduced some of his time producing y in order to pursue hisventure idea. In the event of failure, in autarky, he would not only lose some of x buthe also loses some y. In a market, on the other hand, y production is not diminished.Given our competitive market assumption and the enforceability of contracts, the en-trepreneur is able to consume the same amount of y as he would at the status quo (andboth consume either more or less x depending on whether the entrepreneur succeedsor fails). Given that the trading partner now also faces decreased consumption if theentrepreneur fails, one might suspect that trade agreements or market institutions maybe trickier to implement than the assumptions of this paper.22 By relaxing assumption3 one could study, for example, how institutions of risk-sharing might arise.

By incorporating entrepreneurs into the economy, a more dynamic micro economyemerges where the maximized amount of consumption goods can increase or decrease.That is, if the entrepreneur chooses to act rationally on his idea, then he ex-ante effi-ciently allocates his time resource. If he subsequently realizes a failure, the maximizedamount produced given his failure is an efficient amount. In other words, it is not thesuccess or failure of the entrepreneur that determines whether entrepreneurial effort isefficient. Although failure constitutes an economic loss, consumption below that of theprevious status quo level, the entrepreneur would not have attempted to implement

21Note neither is receiving the expected marginal cost a hindrance.22Campbell [2008c] studies the question of trading partner incentives and intellectual property

protection mechanisms.

16

his idea if he did not rationally expect a gain. The risk of failure helps to temperentrepreneurial effort such that there is not too much economic upheaval. (Withoutsome risk of failure new ideas would be implemented as soon as they were thought. Al-though change is good, too much change may negate some of the productivity benefitsof learning by doing, etc. as well as being very disruptive, in general, for society.)

Lastly the framework can be used to study the way market prices transmit infor-mation regarding entrepreneurial activity. Competitive market prices transmit signalsregarding the relative states of demand and supply; the final utility of each individual isindirectly dependent on the price of the goods. As entrepreneurial efficiency rises, theexpected marginal cost of producing, in this case, x falls; or, in other terms, the expectedamount of good x rises and therefore its price relative to that of y falls. Therefore themore successful the entrepreneur, the more the trading partner could receive while theentrepreneur can only get what the trading partner is willing and able to supply of y.The following proposition makes this explicit.

Proposition 11 If there is positive entrepreneurial activity, the expected price of x interms of y is decreasing in both γ and m1.

The proof is omitted for brevity but is found by a comparative statics analysis of theprice found in the proof of proposition 9 (in the appendix). Entrepreneurial success candrive the relative price of other goods higher and therefore the entrepreneur can actuallybecome hindered by his own success. This “winner’s curse” type phenomenon may helpexplain such things as technology sharing.23.

Proposition 11 shows how entrepreneurial activity in one industry can have rippleeffects in other industries. This has empirical implications. At the micro level, we maywant to investigate the dynamics that could occur between industries due to the presenceof entrepreneurial activity. For example, can we investigate industries that have seen rel-ative price increases and determine whether they have experienced more entrepreneurialfailures or whether other industries have experienced more entrepreneurial successes?Do these price changes encourage more productive activity in those industries? Howdoes entrepreneurial behavior in various industries respond to these price signals?

Whether successful or unsuccessful, entrepreneurial effort, le > 0, alters the relativeprices in a market economy. While some might view this as instability of the marketsystem, this increased volatility is a sign of economic growth. Although sometimes thatgrowth is negative, the historical trend of economic growth in market based economiesis overwhelmingly positive Baumol [2002].

6 Conclusion

This paper takes the new classical consumer-producer paradigm and makes explicitthe role of the entrepreneur. The model demonstrates a positive feedback betweenentrepreneurial behavior, increasing returns to specialization and markets. Withoutassuming increasing returns to specialization directly, we show how entrepreneurs, by

23The question of more general type technologies that can be shared is explored in Campbell [2008b]

17

attempting to change the status quo, alter the comparative advantages in an economy.This opens a window for trade and specialization. Ricardian gains from trade are fur-ther reinforced by an indirect return to specialization due to the entrepreneur devotingmore time to implement an idea and therefore increasing his (and the trading partner’s)expected utility.

Without assuming that entrepreneurial behavior is driven by a monopoly profit incen-tive, we show how even a competitive market gives a potential entrepreneur an incentiveto be an entrepreneur. Most studies of entrepreneurship assume some type of oligopolyor monopoly environment for the entrepreneur. This, though, is more an ex-post conse-quence of entrepreneurial activity (and/or a consequence of intellectual property laws).Note too that the model can easily incorporate monopolistic or oligopolistic elementsand future studies (especially applied) may find this reasonable. However, we contendthat entrepreneurs act from a competitive environment. It is their act of trying to creategains that make them entrepreneurs and this is why, from an economic perspective, westudy them as a resource.

We also do not need to assume the entrepreneur receives intrinsic benefit from en-trepreneurial activity as an inducement to be entrepreneurial. Nor do we assume en-trepreneurship is embodied in any particular institutional form (e.g., a firm). In short,we do not have to assume the individual is any different from another individual apartfrom the fact that he or she has an idea for an improvement.

The fact that we can analytically model entrepreneurship in a familiar microeco-nomic framework, will help us systematically investigate the role of entrepreneurs in aneconomy. This model is intended as a building block to begin a ground-up understand-ing of an entrepreneurial economy. Future studies can build more complexity into theeconomy and assumptions can be altered to study such questions as what the economiceffects of the entrepreneur are, how institutions affect the entrepreneur and what thewelfare distributional effects of an entrepreneurial economy are. This framework can alsohelp inform empirical investigation and policy. Lastly, we can bring this tool into theclassroom to help explain entrepreneurship, innovation and capitalism within a unifiedmicro-theoretical framework.

Appendix: Proof of Proposition 9

Proof To prove this proposition we continue solving the problem in the proof ofProposition 8 by using the optimal lM∗e and xs∗ values as follows.

An entrepreneur who chooses positive entrepreneurial effort expects to produce:

x =1

4

(γm1 + (2− γ)m0 +

1

γ

m20

m1 −m0

),

and therefore plans to consume:

xc ≡ x− xs∗ =1

8

(γm1 + (2− γ)m0 +

1

γ

m20

m1 −m0

).

18

Remembering the budget constraint, yd = pxs, the entrepreneur’s expected utilityis:

(A1) E[UM ] = (xc)(pxs) = p

(1

64

(γm1 + (2− γ)m0 +

1

γ

m20

m1 −m0

)2).

By assumption 2, we can find the Walrasian price that clears the market. For this, wemust also solve the trading partner’s decision problem.

Recall that by assumption 1, the trading partner operates according to the statusquo technology and by theorem 1 will produce and sell y. Her problem then is:

maxxd

U = xd(y − ys) s.t.; 1 = ly, y = ly, pxd ≤ ys.

The maximizing solution is: 1− 2pxd = 0 =⇒ xd = 12

1p. Substituting this solution

back into the constraints yields the following values: y = 1, ys = 12, and therefore the

trading partner’s utility is UT = 1p

14.

For a Walrasian equilibrium, all markets clear which implies that ys = yd = pxs.Substituting the trading partner’s optimal ys found above and the entrepreneur’s

optimal xs found above yields the market clearing equation:

1

2= p

(1

8(γm1 + (2− γ)m0 +

1

γ

m20

m1 −m0

).

This implies that the expected market price is:

(A2) p =4

γm1 + (2− γ)m0 + 1γ

m20

m1−m0

.

Denoting the utility achievable from a market for the entrepreneur as UM we have24:

E[UM ] =1

16

(γm1 + (2− γ)m0 +

1

γ

m20

m1 −m0

)(A3)

Next hold γ constant and define a market idea threshold mM1 and an autarky idea

threshold mA1 as:

E[UM ] = 116

(γmM

1 + (2− γ)m0 + 1γ

m20

mM1 −m0

)=m0

4(A4)

E[UA] = 127

(γmA1 +(1−γ)m0)3

(γ(mA1 −m0))2

=m0

4(A5)

The second equation is the entrepreneur’s expected utility in autarky. It can bechecked that for any (γ,m1) pair in the range for which le ≥ 0 for both equations, it istrue that E[UM ] > E[UA]. Therefore in order for equations (A4) and (A5) above to beequal (when γ is constant), it must be true that mM

1 < mA1 . Q.E.D.

24Because of the assumption of a competitive equilibrium, with the same preferences for the goods,the individuals equally share all expected gains and hence the trading partner has the same expectedutility.

19

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Karen A. Campbell, Ph.D.Center for Data AnalysisThe Heritage Foundation214 Massachusetts Ave NEWashington D.C.United StatesE-mail:karen.campbell@heritage.org