How to Make Social Entrepreneurship Sustainable? A Diagnosis and a Few Elements of a Response

Abstract

Social entrepreneurship is a precarious activity that must always strike a delicate balance between commercial principles and social concerns. There is no shortage of discussion concerning the possible solutions that could help to maintain this balance, and social entrepreneurs are striving to reconcile conflicting aims on a daily basis, but the economic roots of this precariousness remain. Based on an analysis of these root causes, we propose a new radical approach to this precariousness, “radical” in the etymological sense of the term “root”. We start by identifying what determines the dilemma that lies at the heart of the precariousness of social entrepreneurship in present-day economic institutions. This enables us to identify the institutional conditions that might allow us to overcome it. The first condition is linked to the conservation of money in individual trade, which might be alleviated. To determine the second condition, we introduce the notion of the endogeneity of the institutional solutions to the dilemma. The lesser the involvement of the actors concerned by its formulation, the less endogenous is the solution. On this basis, we suggest institutional reforms that could prompt entrepreneurs to organize themselves in support of the actions of the most socially oriented entrepreneurs, thus safeguarding their sustainability.

Appendices

Appendix 1

This model of the virtuous cycle is based on an imaginary population of 1000 companies whose initial levels of social concern are distributed normally. Let s_i,t=j be the degree of social concern of the ith entrepreneur at the time t = j, and R_i,t=j its share of the common fund C according to the redistribution rule R_t=j. $C = \sum\nolimits_{i = 1}^{1000} {R_{i,t = j} }$. At the outset, the companies decide that rewards should simply be proportional to s_i,t=0: this is the R₁ redistribution. R_i1 = a₁·s_i,t=0, with $a_{1} = \frac{C}{{\mathop \sum \nolimits_{i = 1}^{1000} s_{i,t = 0} }}$. This form of redistribution encourages the least socially minded companies to progress at the time t = 1 (it can be considered that the most socially minded companies have attained an unsurpassable level—s_max1). Consequently, all of them move nearer to s_max1. The least socially inclined company will progress from level s_min,t=0 (s_min1 = 0) to level s_min,t=1 (s_min2) and will consequently receive a higher level of remuneration. A transition is made to R₂. R_i2 = a₂·s_i,t=1, with $a_{2} = \frac{C}{{\mathop \sum \nolimits_{i = 1}^{1000} s_{i,t = 1} }}$. Because s_i,t=1 > s_i,t=0 (the degree of social concern increases), we have a₂ < a₁: the remuneration of the most socially inclined company diminishes and what is gained by the least socially advanced companies is lost by their more advanced counterparts. This is illustrated in Fig. 6, which shows the transition from R₁ to R₂ for a dozen companies.

Fig. 6

Transition from R₁ to R₂

The firms that lose out form coalitions in order to re-establish a rule of redistribution that enables them to approach the level of their previous remunerations, or, for the most socially advanced companies, to achieve that level again—this is R₃. R₃ is defined as restoring the original share of the most socially minded entrepreneur while conserving the shared fund C. Therefore, R_i3 = a₃·s_i,t=1 + b₃, with a₃ and b₃ solutions of the following equations system:

$$\left\{ {\begin{array}{*{20}l} {a_{3} \cdot \mathop \sum \nolimits_{i = 1}^{1000} s_{i,t = 1} + 1000 \cdot b_{3} = C} \hfill \\ {a_{3} \cdot s_{\hbox{max} } + b_{3} = R_{1} \left( {s_{\hbox{max} } } \right) = a_{1} \cdot s_{\hbox{max} } } \hfill \\ \end{array} } \right.$$

The least socially inclined companies are encouraged to progress at the time t = 2, leading to R₄: R_i4 = a₃·s_i,t=2 + b₃. R₄ once again reduces the remunerations of the most socially minded firms, which form new coalitions to defend their interests, introducing a new rule R₅. Once again R₅ is defined as restoring the original share of the most socially minded entrepreneur while conserving the shared fund C. Therefore, R_i5 = a₅·s_i,t=2 + b₅, with a₅ and b₅ solutions of the following equations system:

$$\left\{ {\begin{array}{*{20}l} {a_{5} \cdot \mathop \sum \nolimits_{i = 1}^{1000} s_{i,t = 2} + 1000 \cdot b_{5} = C} \hfill \\ {a_{5} \cdot s_{\hbox{max} } + b_{5} = R_{1} \left( {s_{\hbox{max} } } \right) = a_{1} \cdot s_{\hbox{max} } } \hfill \\ \end{array} } \right.$$

Appendix 2

The graph below shows the possible consequences of the introduction of power struggles into all of the 1000 companies used in our simulation (Fig. 7).

Fig. 7

Modelization of the virtuous circle without inequalities (first three stages, on the top) and with inequalities (last three stages, at the bottom)

The first three thumbnail illustrations show the first three stages in the development of the distribution rule, previously presented in Fig. 4 and “Appendix 1”, assuming that the companies have identical economic clout. At the moment of renegotiation, the most socially oriented companies—whose degree of social concern is above the threshold s_s—unite against the least socially oriented in order to decide on a new rule R₃ that could benefit them.

The three thumbnail illustrations below show the development of the distribution rule on the assumption that the 30 least socially oriented companies have as much power as the 970 others. Initially, an identical redistribution R₁ to that envisaged with a homogeneous population is considered (it could be imagined that the initial redistribution is proposed by the public authority and that even the most powerful companies can see that there are sufficient tax concessions in it to deter them from opposing it). It is then considered that the companies respond in the same manner to the incentive thus created, which leads to R₂. The situation changes at the moment of the renegotiation of the redistribution rule. The 501 most socially oriented companies are not sufficiently powerful to determine the new rule. They need form a coalition with 469 other companies in order to counter the power of the 30 most powerful companies. This consequently determines a new threshold $s_{s}^{{\prime }}$ above which the companies concerned benefit from the new rule $R_{3}^{{\prime }}$. The coalition decides to define $R_{3}^{{\prime }} = R_{3} /3$ for $s < s_{s}^{{\prime }}$. For $s \ge s_{s}^{{\prime }}$, $R_{3}^{{\prime }}$ is defined as restoring the original share corresponding to $s_{s}^{{\prime }}$ while conserving the part of the fund which is not granted to the 30 least socially minded entrepreneurs $(C - \sum_{i = 1}^{30} R_{i3}^{{\prime }} )$. Therefore, $R_{3}^{{\prime }} = a_{3}^{{\prime }} \cdot s_{3} + b_{3}^{{\prime }}$ for $s \ge s_{s}^{{\prime }}$ and with $a_{3}^{{\prime }}$ and $b_{3}^{{\prime }}$ solutions of the following equations system:

$$\left\{ {\begin{array}{*{20}l} {a'_{3} \cdot \mathop \sum \nolimits_{i = 31}^{1000} s_{i,t = 1} + 970 \cdot b'_{3} = C - \mathop \sum \nolimits_{i = 1}^{30} R'_{i3} } \hfill \\ {a'_{3} \cdot s'_{s} + b'_{3} = R_{2} \left( {s'_{s} } \right) = a_{2} \cdot s'_{s} } \hfill \\ \end{array} } \right.$$

The new $R_{3}^{{\prime }}$ rule is certainly less attractive than R₃. Indeed, the 501 most virtuous companies must share their rewards with the 469 least socially oriented companies in order to counter the 30 most powerful companies. However, it can be observed that this redistribution remains incentivizing.

Appendix 3

Let us suppose that the price function P(Q) is linear, decreasing with Q, zero when Q = q_max (The company’s production is maximum if its production is free), and its maximum is P₁ (only one customer agrees to pay P₁, and no customer accepts to pay more). Then we have:

$$P\left( Q \right) = P_{1} - \frac{{P_{1} }}{{q_{\hbox{max} } }}Q$$

(1)

Then, the total revenue function is:

$${\text{TR}}\left( Q \right) = QP\left( Q \right) = P_{1} Q - \frac{{P_{1} }}{{q_{\hbox{max} } }}Q^{2}$$

(2)

Let us suppose that the redistributive function R(Q) is linear and equal to zero at the origin (the less a social enterprise produces, the less it produces positive externalities, the less it receives a redistributed share of the pot). Then we have:

$$R\left( Q \right) = aQ$$

(3)

To calculate a, let us suppose that the market is price segmented, that each social enterprise is specialized in one segment, and that the contribution of each company to the shared funds corresponds to a fraction β of their total revenues. Therefore:

$$\mathop \int \limits_{0}^{{q_{\hbox{max} } }} R\left( Q \right){\text{d}}Q = \beta \mathop \smallint \limits_{0}^{{q_{\hbox{max} } }} {\text{TR}}\left( Q \right){\text{d}}Q$$

(4)

From (4), we find

$$a = \frac{{\beta P_{1} }}{3}$$

(5)

At the end, each enterprise receives a net total revenue which is the total revenue minus the contribution to the shared funds plus the redistributed share of the pot. With (2), (3) and (5), we have:

$${\text{TR}}_{\text{net}} \left( Q \right) = \left( {1 - \beta } \right)\left[ {P_{1} Q - \frac{{P_{1} }}{{q_{\hbox{max} } }}Q^{2} } \right] + \frac{{\beta P_{1} }}{3}Q$$

(6)

The market incentives encourage the social enterprises to maximize their total net revenue. The production q* corresponding to this maximum is the solution to the following equation:

$$\frac{{\partial TR_{\text{net}} \left( Q \right)}}{\partial Q} = \left( {1 - \beta } \right)\left[ {P_{1} - \frac{{2P_{1} }}{{q_{\hbox{max} } }}Q} \right] + \frac{{\beta P_{1} }}{3} = 0$$

(7)

From (7) we have:

$$q^{*} = \frac{{\left( {1 - \beta } \right) + \beta /3}}{{2\left( {1 - \beta } \right)}}q_{ \hbox{max} }$$

(8)

Let us suppose that the optimal production level is q_max (q̌ = q_max). The production level q* encouraged by the market incentives needs to be equal to the optimal production level in order to avoid the trade-off between revenue and positive externalities: q* = q_max. From (8) we then get:

$$\beta = \frac{3}{4}$$

(9)

To avoid the trade-off, the contribution of each enterprise to the redistributed pot would need to be 75% of its total revenue. A more complex polynomial model (rather than this linear one) provides a more reasonable estimation of the percentage of revenue that must be pooled to fully address the issue, around 30%, thus potentially narrowing the gap and potentially further reducing the reliance on exogenous elements. Nonetheless which of these models better reflects the real world is something yet to be empirically determined.