Assume a consumer who has current-period income y=200, future period income y’=150, current taxes t = 40, and future taxes t’= 50, and faces a market interest rate of r=5 percent or .05. The consumer would like to consume such that c’=c*(1+r) if possible. However, this consumer is faced with a credit market imperfection, in that no borrowing is allowed. That is s must be greater or equal to zero.
Show the consumer’s lifetime budget constraint and indifference curves in a diagram
Calculate the optimal c and c’ for this consumer and show this in your diagram.
Suppose that everything stays the same except that t = 20 and t’ = 71. Calculate the effects on c, c’, and s. Show this in your diagram.
Now, suppose that y = 100. Repeat the previous 3 parts and explain any differences.