Answer Happy

u Question (50 points). Consider a two-period endowment economy. There are N consumers and a government in this economy. Consumers have preferences for current and future consumption given by: « (c,c) = Inc+ B Inc, 0<BS1 Note that B is the weight in the future consumption, or the discount rate. B measures how the consumer discounts future utility. When B is low, the consumers are impatient. When ß is high, the consumers are patient. The government operates in both periods, it must finance expenditures G and G'. To do so the government can tax consumers in a lump sum fashion, so taxes on each consumer are t, t'. The government can also borrow and save issuing debt B (when debt is negative it is savings). (a) Carefully define an equilibrium for this economy. (6) Write down the first-order conditions that characterize the consumer's problem. Interpret the first-order conditions. (c) Find the optimal choices of current and future consumption for the consumers given y, y',t,t',r, B (d) Find the equilibrium real interest rate r as a function of exogenous y, y',G,G',N,B. (e) What is the effect of an increase in B on the equilibrium real interest rate r? Interpret B to explain your results.