• University of California, Berkeley

• ECON 119

Econ 119, Fall 2015
Prof: Dan Acland
Problem Set #4
Page 1
Problem Set #4.
Due in lecture, Tuesday, October 27, 2015.
Solutions
Problem 1. Nigel and Sophie live for three periods, t = 0; 1; 2, and have to make
some decisions about saving, borrowing, and consumption. (They make all their decisions
separately.) All consumption happens in periods 1 and 2. Period 0 is just a decision-making
period. Both Nigel and Sophie have instantaneous utility function u(ct) = ct where ct is the
amount they consume in period t. In addition, they both have present-biased preferences
with β = 12 and δ = 1. However, Nigel is a naif (β^ = 1), whereas Sophie is a sophisticate
(β^ = β).
Nigel and Sophie each start off with a wealth of $20 at t = 0, and earn additional income of
$20 per period at t = 1 and t = 2. At t = 0 each of them can keep his or her initial wealth
in a checking account, in which case it earns no interest, but is available for consumption in
either period 1 or period 2. Alternatively, they can choose to put part or all of their initial
wealth in a savings account