Question

Jack makes his consumption and saving decisions two months at atime. His
income this month is 1000 and he knows that he will get a raisenext month
making his income 1050. The current interest rate (at which he isfree to borrow
and lend) is 5 per cent. This means that if Jack saves one dollartoday, he will
get 1.05 dollars tomorrow. Also, if he borrows 1 dolalr today, heneeds to pay
back 1.05 dollars tomorrow.
a) How much can Jack consume this month, if he consumes his wholeincome
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, foreach of
the following utility functions, state whether Jack would choose toborrow, 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