1.          Each week, three rational, utility-maximizing individuals (Bill, Mary, and Jane) select quantities of two goods, X and Y, to consume that will make them as happy as they can while staying within their budgets.  Each also spends      his/her entire income on these two goods each week.

a.          Bill’s choices are represented by the following table:

Did Bill’s utility increase or decrease between Week One & Week Two?          Between Week One and Week Three?  Explain using a graph in your answer. Can revealed preference arguments help here?  Why or why not?

b.          Mary’s choices are represented by the following table:

Did Mary’s utility increase or decrease between Week One and Week Three? Does Mary consider both goods to be normal?  Why or why not?  Explain.

c.          Jane’s choices are represented by the following table:

Plot Jane’s three chosen bundles on a well-labeled graph.  What can be said    about Jane’s preferences in this case?  Provide an expression for Jane’s utility function in this case.  Document the magnitude and direction of the                   substitution and income effects that result from a drop in the price of X from $2 / unit to  $1 / unit.

2.          Sam & Barb derive utility from leisure (N) , in hours, and the amount of the   composite good ( G ) they consume.  In order to maximize utility, they need   to allocate the 24 hours of their days between taking leisure and working for an hourly wage rate ( w ).  They have NO non-wage income.  Assume the         price of the composite good is  $1 / unit of G .  The following table                     summarizes their choices under different wage rates:

w (in $ / hour )                         Sam’s N (in hours)                   Barb’s N (in hours)

8                                                    16                                                 14

9                                                    15                                                 14

10                                                 14                                                 15

11                                                 14                                                 16

On well-labeled indifference curve diagrams, show each person’s optimal       choices.  Assume each has strictly monotonic and strictly convex preferences for leisure and the composite good.  Further assume they both view both        goods as normal.  Comment on the relative magnitudes of the substitution     and income effects of each wage change for each person.

Now, construct a labor supply curve for each person (separate diagrams of course).  Does each person’s labor supply curve have a perfectly inelastic    portion here?  Why?  Explain.  Does each person’s labor supply curve have both an upward sloping and a downward-sloping portion here?  Why?         Explain.

3.          Return to our Fisher model of consumption today/consumption tomorrow. If we continue to assume individuals have strictly convex preferences for    those two goods and face the same interest rate for borrowing and lending, draw diagrams for each of the situations below:

a.          A consumer who is optimizing by borrowing today responds to an increase in the interest rate by becoming a lender today.

b.          A consumer who is optimizing by lending today responds to an increase in the interest rate by choosing the Polonius Point.

c.          A consumer who is optimizing by borrowing today responds to an increase in the interest rate by choosing the Polonius Point.

Do any of these situations violate revealed preference theory?  If so, why?  If not, why not?  Explain.