Appendix 1 - Growth collapse with rent-seeking

Summary

The model below is closely based on Murshed (2010: chap. 2). The innovative feature of the model is that the macroeconomic collapse that comes from a reduction of the capital stock, hence productivity, has microfoundations in rent- seeking contests. We begin with a competitive game of rent-seeking in the spirit of Tullock (1967). In this framework, several agents compete for a prize equivalent to a pot of rents in each period that resource revenues are available. The competition to capture this prize, which is akin to a tournament, entails a cost, be that bribery, lobbying expenditure, or whatever. Let P represent the winner-take-all prize that each rent-seeking agent is attempting to seize. This prize corresponds to the contestable or appropriable revenue from resource rents. This does not preclude collusive group behaviour, as long as groups compete with each other. Each agent’s probability of success will depend on his own rent-seeking expenditure relative to all others. The expected utility (E) of an agent (i) in a symmetrical setting can take the form

where π is the probability of winning, based upon the contest success function, and c represents lobbying costs or expenditures. The contest success function is given by

In this example above there are only two agents, i = 1, 2. The crucial parameter s represents the “efficiency or productivity” of lobbying expenditure or bribery; if s > 1, there are increasing returns to scale in such expenditure. If that is so, under weak institutions of governance, when the law is honoured more in the breach than in the keeping, lobbying expenditure is even more productive as far as rent-seekers are concerned. In many ways, s can be characterized to be negatively related to good governance and institutional quality, with s > 1 being a sign of a very poor institutional environment. Wick and Bulte (2006) also incorporate increasing returns to scale in connection with resource rents when the agent’s choice is between rent-seeking and conflict. My set-up is different: the increasing returns to scale emanate from poor institutional quality and not the mere “pointiness” (concentrated) or capturability of resources.