Suppose u(c, c') = ln c+β ln c' , there exists N consumers and each consumer lives for 2 periods. In each period they receive an endowment y, y' and are taxed t, t' . There also exists a government which spends G and G' . Finally there exist one period bonds B which exist in a frictionless market and for which both consumers and government have access to.

a. Derive the lifetime budget constraint for both the consumer and government

b. Define equilibrium of this economy

c. Solve for the equilibrium objects