1. Suppose that there is a credit market imperfection because of asymmetric information. In the economy, there are N consumers. A fraction b of consumers consists of lenders, who each receive an endowment of y units of the consumption good in the current period and 0 units in the future period. A fraction of borrowers are good borrowers, who each receive an endowment of 0 units in the current period and y units in the future period. Finally, the left consumers are bad borrowers, who receive 0 units of endowment in both periods. Banks cannot distinguish between good and bad borrowers. The government sets G and G' as government spending, and each consumer is asked to pay a lump-sum tax of t in the current period and t' in the future period. The government also cannot distinguish between good and bad borrowers, but as with banks can observe endowments. The lending rate is r.
a. Write down the government's budget constraint.
b. Find out the budget constraints of good borrowers, bad borrowers, and lenders respectively.
c. Suppose that the government decrease t and increase t' in such a way that the government budget constraint holds. Does this have any effect on each consumer's decisions about how much to consume in each period and how much to save? Explain.
d. Does Ricardian equivalence hold in the economy? Explain why or why not?