In the consumption savings model, suppose that we have a representative consumer and his utility is given by U(c, c') = min {c, βc'} The budget constraint for the consumer is c + s = y - t second period budget constraint is c'= y' - t' + (1 + r)s Suppose the government finances expenditures G and G' by lump-sum taxes (t > 0 and t' > 0) and borrowing B.
a) Find the consumer's consumption the first and second period
b) Now assume that the government decides to keep the expenditure the same but sets t = 0 to finance G and G'. Keeping interest rate constant, find the amount by which tomorrow's tax will have to change in order to have the government's budget constraint hold.
c) Show that the consumer's optimal consumption choice is still the same as before after the tax change in b)
d) Find the amount of consumer savings before and after the tax change in b). Does savings go up or down after the change?