Entrepreneurship and the Legal Form of Businesses: The Role of Differences in Beliefs

Oscar Gutiérrez; Pedro Ortín-Ángel

doi:10.1515/rle-2014-0027

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Entrepreneurship and the Legal Form of Businesses: The Role of Differences in Beliefs

Oscar Gutiérrez und Pedro Ortín-Ángel

Veröffentlicht/Copyright: 13. Februar 2016

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Abstract

Entrepreneurship has been considered a way to implement interpersonal authority, i. e., to convince other persons to use their resources in an alternative way to the optimal one in accordance with their beliefs. This paper presents a theoretical model that relates the above assumption with the following two questions: (i) how and why financial constraints can prevent the implementation of entrepreneurial projects; and (ii) how creditors’ priorities provided by the different legal forms of the business can reduce the financial requirements for implementing the firm. The attractiveness of such an explanation lies in its capacity to justify a wide array of features of firms (entrepreneur origin, property rights, authority, financial constraints and creditor priorities) from a single basic assumption: agents have different beliefs about how production should be organized.

Keywords: entrepreneurship; beliefs; credit constraints; creditors’ priorities; legal form

JEL: D23; L21; L22

Funding source: Ministerio de Economía y Competitividad

Award Identifier / Grant number: ECO2013-48496-C4

Funding statement: Ministerio de Economía y Competitividad, (Grant/Award Number: ‘ECO2013-48496-C4’ subprojects 3-R and 4-R).

Appendix A: Financial market equilibrium and utility assumptions

We have assumed that at Period 0 the financial market is in a situation of equilibrium in the sense that persons have no interest to perform (more) lending/borrowing transactions. Let us characterize this equilibrium by a minimum return required for the production activities r_M and the decisions on goods consumption and production assets at Period 0:

Production assets (li0). The assets dedicated to production by Person i in Period 0.

Consumption (m_i =A_i – li0). Non-production assets or goods, those dedicated to consumption by Person i in Period 0.

Our focus is about decisions on the use of production assets. The distribution of the output generated by production activities at Period 1 implies a monetary income to Person i of w_i. Persons value the different production activities according to w_i – l_i, where li= (1+r_M) li0, and the changes that they will imply in the equilibrium situation described above.

An easy way to grasp all of these assumptions is through the following inter-temporal utility function of the agents (uit is the utility at period t):

Ui=ui01+rM+ui1=(Ai−li0+rBbi−rLki)1+rM+wi−bi1+r+ki1+r.

The variable b_i ≥ 0 indicates that Person i is borrowing at interest rate r. The increase of one euro in consumption increases its utility at Period 0 by r_B. The variable k_i ≥0 indicates that Person i is lending at interest rate r. The decrease of one euro in consumption decreases his/her utility by r_L. When b_i>0, then k_i=0 and vice versa. The market equilibrium implies that r_B <1< r_L.

Then, we assume that whatever the price of the financial transaction is, r, there is a social cost R= (r_L – r_B) (1+r_M)>0 associated with the fact that one Person i lends one euro to another –i, k_i=b_–i =1. This is justified in terms of market equilibrium deviance (r_L – r_B>0). We assume that all of these costs are assumed by the lender (r_B= (1+r) /(1+r_M)). Then utility Ui can be written as:

Ui=Ai1+rM+ui=Ai1+rM+wi−li−Rki.

As we have assumed that A_i and r_M are exogenously given, the different production activities can be compared by Person i in terms of u_i=w_i – l_i – Rk_i, the utility function proposed in the paper.

Appendix B: Risk aversion and differences in beliefs

The general framework

Following Van den Steen (2010a), actions (in our case, L=a_E, a_W) can be expressed as random variables (lotteries) with two possible realizations, V and v, with V>v; p_i,L represents the probability associated with V, which can vary depending on the person (i=E,W) who values the action. For the sake of simplicity and without loss of generality, we normalize U_i(V) =1 and U_i(v)=0 for both persons, where U_i(·) represents the utility associated with Person i.

The values associated with different actions

According to Person i, the value (measured in terms of the certain equivalent CE) of a random variable, L, can be expressed as: CE _i,L=U_i^–1 (p_i,L). Then, in the case of differences in beliefs (p_E,L≠ p_W,L) and risk neutrality we can establish that:

CEE,aE=pE,aEV+(1−pE,aE)v=q^E,CEW,aE=pW,aEV+(1−pW,aE)v=q^W(aE),CEE,aW=pE,aWV+(1−pE,aW)v=q^E(aW),andCEW,aW=pW,aWV+(1−pW,aW)v=q^W

But different values of the lotteries (qˆE,qˆW (a_E), qˆE (a_W) and qˆW) can also be obtained when there are no differences in beliefs, p_E,L= p_W,L=p_L, but rather there are differences in the utility function of the agents:

qˆE=CEE,aE=UE−1paE,qˆWaE=CEW,aE=UW−1paE,qˆEaW=CEE,aW=UE−1paW andqˆW=CEW,aW=UW−1paW.

The difference: Disagreement in the social welfare.

In the case where there are no differences in beliefs, p_E,L= p_W,L=p_L, but there are differences in the utility functions, W agrees with E in the social welfare generated by the actions (L=a_E, a_W). For example, in the case that lottery a_E is played by Person E, both agree that the social welfare will be:

qˆE=CEE,aE=UE−1paE,

but this will not be the case when there are differences in beliefs and risk neutrality.

Analogously, when lottery a_E is played by Person E:

Social welfare for W will be equal to pW,aE V+(1– pW,aE)v=qˆW(aE)≠pE,aEV+(1−pE,aE)v=qˆE=social welfare according to E.

Similar arguments can be replicated by changing the action and/or the person.

So, what we assume is that persons disagree about the welfare generated by a certain action made by a certain person.

Typology of situations

No differences in beliefs: CEE,aE≥CEE,aW and CEW,aE≥CEW,aWor CEE,aE≤CEE,aW and CEW,aE≤CEW,aW

In this case, both persons have the same preferences about actions. So, in a certain way, the output of the firm can be modeled as is usual in agency theory: a single lottery. There can be risk-neutral agents (CE_{E,a_E}=CEW,aE and CEE,aW=CEW,aW) or those without differences in terms of risk preferences (CEE,aE ≠ CEW,aE).

Differences in beliefs: The remaining cases.
Optimism. ^[8] CEE,aE>CEW,aE and CEE,aW>CEW,aW or
CEE,aE<CEW,aE and CEE,aW<CEW,aW
Differences in confidence: ^[9] CEE,aE>CEW,aW or CEE,aE<CEW,aW
No differences in confidence: CEE,aE=CEW,aW.

Beliefs about beliefs

Furthermore, Van den Steen (2010a) assumes that the firms have been established before beliefs are known by the persons and that beliefs are private information. So before taking some decisions it must be known the joint distribution of probabilities about the beliefs each person has, whether each player has different beliefs about the distributions of such probabilities. At this point the assumptions of the model are:

There are no differences in beliefs concerning the joint distribution of beliefs. So both players share the same joint distribution.
Those distributions are independent. The beliefs of one person do not reveal about the beliefs of the other.
Initially, the distribution of probabilities concerning the beliefs that each person has is identical.

With these assumptions, the only possible cases are (a) identical beliefs with risk-neutral agents or (b) differences in beliefs with no differences in confidence.

At a second step, Assumption iii) is modified, so at this point the possible cases are (a) equal beliefs with different degrees of risk aversion or (b) differences in beliefs with differences in confidence.

Appendix C: Why not betting contracts?

We argue that, although workers and entrepreneurs can establish a framework of compromises, the actions may be unverifiable by third parties. Usually, workers and entrepreneurs have better information about the situation of the firm than do third parties before output is finally obtained. When actions are not verifiable, betting contracts favor poor collaboration or even “sabotage” actions (like a fixed boxing match).

Let us extend our basic model to incorporate such arguments. If a firm is created, the timing is as follows:

Agreement:
Market solution.
Firm:
i Entrepreneur	Observable actions:	Information:	Sabotage actions:	Final output is obtained:
–i Worker	a_i where i= E or W	I=qˆi or I=qˆ−i (a_i)	g_–i=1 or g_–i=0	q=I –g_–i (qˆ−i (a_i))
1	2	3	4	5 Stages

Before obtaining the final output q (Stage 5), entrepreneurs and workers have private, and consequently, non-contractible information (Stage 3) about how things are. They know whether the firm works in accordance with the entrepreneur’s beliefs, I=qˆE, or workers’ beliefs, I= q^−i (a_i). Given this information, the worker can decide (Stage 4) to collaborate more or less actively with the team; in other words, perform actions to reduce production (g_–i=1) or not (g_–i=0). Those actions are not verifiable by third parties and, consequently, not contractible. The cost of such actions is practically null and the losses caused to the firm are equal to qˆi– qˆ_–i (a_i). These five stages are fairly close to those used by Gibbons (2005, Sec. 4) to compare four theories of the firm. As can be checked, the key differences among the cited models are the assumptions about beliefs. The rest of the assumptions have been made before in other models.

In such a situation, a (betting) contract where the entrepreneur pays L if q=qˆi and H>L if q=qˆ_–i (a_i) will never be offered by the entrepreneur because, if I=qˆi in Step 4, the worker would have incentives to perform sabotage actions, so the output obtained is q=qˆ_–i (a_i) and the final wage is H. Thus, in Stage 1 betting contracts can be improved by fixed wages equal to H, because output can be either q=qˆi or q=qˆ_–i (a_i). So the solution coincides with the solution of a simplified model with the following three steps (imposing now that betting contracts are ruled out, so there are no incentives for sabotage, g_–i=0; this is what we do in the main text of the paper):

Agreement:
Market solution.
Firm:
i Entrepreneur	Observable actions:	Final output is obtained:
–i Worker	a_i where i=E or W	q=qˆi or q=qˆ−i (a_i)
1	2	3 Stages

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Published Online: 2016-2-13

Published in Print: 2016-3-1

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entrepreneurship; beliefs; credit constraints; creditors’ priorities; legal form