How is the equilibrium modified if there is a continuum of

Question

(Bewley 1981) Imagine a world with 2 consumers and 2 potential jurisdictions. Each of the consumers has one unit of labor to supply and preferences described by

where Gi is the quantity of public good provided in the jurisdiction i of residence. Denote labor supply in jurisdiction i by Lⁱ; the public good is produced from labor with production function Gⁱ = Lⁱ: The regions both levy a tax on labor income to finance provision of their public good supply.

a. Assuming that consumers take taxes and public good provision as given when choosing their location, construct an ancient equilibrium for this economy.

b. Discuss the inconsistency of consumer beliefs in this equilibrium.

c. How is the equilibrium modified if there is a continuum of consumers, each of whom is ‘‘small'' relative to the economy?