Question 1
Fred has the following utility function characterizing his preferences over leisure time and
disposable income:
. He is also constrained to be on his potential income
constraint:
where w is the wage rate, T is total available hours, YN is nonla

Midterm 1 Review Problems
1. Tom, Dick, and Harry, the only three people on a desert island with two consumption goods,
apples and bananas, have utility functions UT, UD, and UH, respectively, where:
UT=(xa,xb)=6xa+9xb
UD=(xa,xb)=8xa+12xb
UH=(xa,xb)=xaxb2

Some extra practice with derivatives.
Solve for the partial derivative with respect to x and y for the following functions. Note that
letters other than x and y are constants.
= square root (xy)
Answers