Jack makes his consumption and saving decisions two months at a time. His income
ID: 1252753 • Letter: J
Question
Jack makes his consumption and saving decisions two months at a time. Hisincome 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
Explanation / Answer
a. If he consumes all this month, he can consume 1000 + 1050/1.05 = 2000. If he chooses to delay it all until next month, he could consume 1000*(1.05) + 1050 = 2100 next month. b. Next period's consumption = (2000 - this month's consumption) * 1.05 c. This favors current consumption, so he would borrow. d. This favors future consumption, so he would save. e. This requires fixed proportions: he needs twice as much current consumption as future. He would have to borrow. f. Future consumption is a perfect substitute, except that it is 2.5 times more effective at providing utility. He would save.
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