Increasing returns, entrepreneurship and imperfect competition (Q852322)

The aim of this paper is to investigate a simple bilateral oligopoly model in which economic agents, initially endowed with capital, decide sequentially (1) whether they want to act as producers (Entrepreneurs), or as capital lenders (Rentiers), and then, (2) which quantity of the consumption good they would like to produce in the former case, and which quantity of capital they would like to lend in the latter case, through exchange of capital against the produced good. The production takes place under increasing returns to scale. The proposed mathematical framework supports Knight's conjecture about the role of wealth differences in explaining firms' creation: it is likely to be better to become entrepreneur when one holds a capital endowment above some critical level. The authors prove the existence of a ``natural equilibrium'' at which every economic agent who has chosen to be an entrepreneur is wealthier than every agent choosing to be a rentier. However, there may exist simultaneously one or several ``non-natural'' equilibria at which this property is not satisfied, but these non-natural equilibria are shown to be destroyed when the number of agents is sufficiently large. In informal terms, the analysis is translated as equilibria of the following two-stage game. In the first stage, the agents decide whether to be a rentier or an entrepreneur. In the second stage, taken as given the resulting partition of \(N = \{1, 2, \dots, n\}\) set of agents into the sets \(E\) (Entrepreneurs) and \(R\) (Rentiers), the agents in \(R\) decide about the amount of capital they lend, whereas agents in \(E\) decide about the amount of the consumption good produced they sell. In this second stage of the game, all agents take into account the incidence of their individual decisions on a certain price \(p\) and, accordingly, on the resulting amounts of consumption good they obtain as payoffs. Now, again in the first stage, in which each agent has two strategies, viz. to be a rentier or entrepreneur, an equilibrium is defined as a partition on \(N\) into the non-empty sets \(E\) and \(R\), such that no entrepreneur in \(E\) wishes to become a rentier, and no rentier in \(R\) wishes to become an entrepreneur. Due to its simplicity, the proposed model has the advantage of allowing a very simple Pareto-ranking of possible outcomes: the larger the number of entrepreneurs, the smaller the resulting welfare. The study of equilibria efficiency shows that a too small number of entrepreneurs, which is a good feature in terms of efficiency, may not be an equilibrium since the low price of capital is likely to induce more people to become entrepreneur. Conversely, a too large number of entrepreneurs may not be an equilibrium since the resulting high price of capital may induce some of them to become rentiers. At equilibrium, these two forces balance each other: the price of capital is sufficiently low to discourage entrepreneurs to become rentiers and sufficiently high to discourage rentiers to become entrepreneurs. This market balance could possibly require a large number of entrepreneurs, at the expense of efficiency, a topic that deserves to be investigated in-depth.