1. Julian has $15 to spend this week on orange juice and muffins. Juice costs $.50 per bottle, and muffins cost $2.00 each.

a) Express Julian's budget constraint algebraically.

b) Graph Julian's budget constraint.

c) Graph the budget constraint when the price of juice increases to $1.00 per bottle. d) Graph the budget constraint when Julian's allocation of money to juice and muffins falls to $10 this week (at the original prices).

e) Suppose that additionally, Julian faces the constraint that he cannot consume more than 20 bottles of juice per week. Graph his feasible set (at the original income and prices from here forward - unless otherwise specified).

f) Suppose instead that Julian can get a bottle of juice for free after every ten bottles of juice purchased. Graph his feasible set.

g) Suppose instead that if Julian purchases at least 4 muffins he only pays $1 for the

h) additional muffin. Graph his feasible set.

i) Suppose instead that if Julian purchases at least 4 muffins, all his muffins cost only $1 each. Graph his feasible set.

j) Suppose instead that Julian gets one free bottle of juice with each muffin purchased. Graph his feasible set.

Suppose instead that Julian gets five free bottles of juice each week, regardless of how many muffins he purchases. Graph his feasible set.

PREFERENCES

2. Mimi's preferences for soda (x1) and french fries (x2) are monotonic; ie, more is better. One of Mimi;s indifference curves is: x2 = 20/ x1

1. a) Graph the indifference curve.

2. b) Compare the following bundles using one of the following symbols: >,

1

3. Richard Runner gets twice the amount of pain relief from Aspirin as from Tylenol, but does not experience any side effects from either.

1. a.) SketchRichard'sindifferencemap.

2. b.) What types of preferences does Richard have?

3. c.) What is Richard's marginal rate of substitution of Aspirin for Tylenol? What is Richard's marginal rate of substitution of Tylenol for Aspirin?

4. d.) Write down a utility function consistent with Richard's preferences.

4. Martha's preferences for apples (x1) and bananas (x2) can be expressed as U(x1, x2)= x1 2 x2

a.) What kinds of preferences does Martha have?

b.) Compute the expression for the indifference curve through the point (2,4).
c.) Compute the formula for the marginal rate of substitution of apples for banana along this indifference curve. Compute the value of the MRS at (2,4) and at (1,16),

d.) Compute the formula for a marginal utility of a banana, and the marginal utility of an apple.

e.) Compute the marginal rate of substitution of apples for bananas using the marginal utilities. Compute the value of the MRS at (2,4) and at (1, 16).

CHOICE

5. Mimi's preferences over hot dogs (x1) and hot dog buns (x2) can be described by the utility function:

U(x1,x1) = min(x1, 2x2)

1. a.) What kind of preferences does Mimi have?

2. b.) Sketch two of Mimi's indifference curves

3. c.) Suppose that hotdogs cost $2 each, and hotdog buns cost $3each, and Mimihas $15 to spend. Solve for Mimi's optimal choice of hot dogs and buns.

6 Suppose Martha's preference for Fantastic (X1) and Pine Sol (X2) can be described by the utility function:

U(x1, x2) = x1 + 3x2

1. What kind of preferences does Martha have?

2. Sketch two of Martha's indifference curves

3. Suppose that Fantastic costs $2 per bottle, and Pine Sol costs $3 per bottle, and Martha has $15 to spend. Solve for Martha's optimal choice of Fantastic and Pine Sol.

7. Suppose instead that Martha's preferences were described by the utility function: U(x1, x2) = x12+ 2x2

2

1. What kind of preferences does Martha have?

2. Sketch two of Martha's indifference curves.

3. Given the same budget constraint, solve for Martha's optimal choice of Fantastic and Pine Sol.

8. Al's preference over meals (x1) and wine (x2) can be described by the utility function:

U(x1, x2) = x1x23

1. What kind of preferences does Al have?

2. Suppose that meals and wine each cost $5 per unit, and Al has $60 to spend.

   Solve for Al's optimal choice.

3. Derive the expression for the indifference curve through Al's optimal choice.

4. Suppose that, additionally, Al is given 24 free meals.

   1. Graph his budget constraint

   2. Compute his optimal choice.

   3. Compute the MRS at Al's optimal choice

   4. Compute Al's utility at his optimal choice

5. Suppose that instead of the 24 free meals, Al were given the cash value of those meals.

   1. Graph his budget constraint

   2. Compute his optimal choice.

   3. Compute the MRS at Al's optimal choice

   4. Compute Al's utility at his optimal choice