Suppose that there is a credit market imperfection due to asymmetric information. In the economy, 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 (1 – b)a consumers are good borrowers who each receive an endowment of 0 units in the current period and y units in the future period. Finally, a fraction (1–b)(1–a) of consumers are bad borrowers who receive 0 units of endowment in the current and future periods. Banks cannot distinguish between good and bad borrowers. The government sets G = G' = 0, 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.

(a) Write down the government's budget constraint, making sure to take account of who is able to pay their taxes and who does not.

(b) Suppose that the government decreases t and increases 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? Show with the aid of diagrams.

(c) Does Ricardian equivalence hold in this economy? Explain why or why not.