(10 points) If P

1

= $

4, P

2

= $2,

and I = $2

0, and my utility is given by u(x

1

, x

2

) =

4x

1

+ 3x

2

, find

x

2

*. (Note: I'm asking for optimal consumption of

Good 2

). (Hint: This is linear utility).

3.

(20 points)

Jack's utility is given by u(x

1

, x

2

) = x

1

3

x

2

3

. If I = $160, P

1

= $20 and

P

2

= $4, how many units of x

1

will Jack

consume to maximize his utility?

(Hint: This is Cobb

-

Douglas utility. You can use the 5 step method to solve this problem, or the appropriate demand

function derived in class).