Private-gift equilibria in the private provision of public goods

This dissertation examines the Nash equilibrium in giving by private individuals when the gifts are used to produce a pure public good which benefits everyone. A new approach to proving the existence of equilibrium is developed that relaxes the conditions of Bergstrom et al., 1986 by requiring only the private good (instead of both private and public goods) to be normal. The equilibrium level of provision is shown to be unique still. This alternative approach also makes possible a more straightforward way to determine the equilibrium level of provision of the public good and to identity the contributors versus the free riders. The approach is extended to cover a commonly used type of quasi-linear utility functions as well as the case when the public good's production function is concave and not necessarily linear. The dissertation also analyzes equilibrium when the public good requires a start-up cost to be covered before positive quantities of it can be produced. Examples are presented to show the following in this latter case: (a) Non-provision of the public good is possible in equilibrium. (b) There may be multiple equilibrium levels of provision of the public good. (c) Government may be able to effect a Pareto improvement by levying a tax and using the revenues to cover the start-up cost, in the process inducing agents to "give" more. This contrasts sharply with the common result in the literature that public spending crowds out private giving to public goods. (d) Moreover, it is shown that equilibrium does not necessarily exist in this case.