Jack makes his consumption and saving decisions two months at a time. His income this month is 1000 and he knows that he will get a raise next month making his income 1050. The current interest rate (at which he is free to borrow and lend) is 5 per cent. This means that if Jack saves one dollar today, he will get 1.05 dollars tomorrow. Also, if he borrows 1 dolalr today, he needs to pay back 1.05 dollars tomorrow.
a) How much can Jack consume this month, if he consumes his whole income from this month, and borrows against the whole income next month? Similarly, what is most that Jack can consume next month?
b) What is the equation for Jackís budget line? Denoting this monthís consumption by x and next monthís by y, for each of the following utility functions, state whether Jack would choose to borrow, lend or do neither in the first month.
c) U(x; y) = (x^2)y;
d) U(x; y) = x(y^2)
e) U(x; y) = min(x; 2y)
f ) U(x; y) = 2x + 5y