4.3. Julie has preferences for food F and clothing C described by a utility function U(F, C) ! FC. Her marginal utilities are MUF ! C and MUC ! F. Suppose that food costs $1 a unit and that clothing costs $2 a unit. Julie has

$12 to spend on food and clothing.

a) On a graph draw indifference curves corresponding to u ! 12, u ! 18, and u ! 24. Using the graph (and no algebra), find the optimal (utility-maximizing) choice of food and clothing. Let the amount of food be on the horizontal axis and the amount of clothing be on the vertical axis.

b) Using algebra (the tangency condition and the budget line), find the optimal choice of food and clothing.

c) What is the marginal rate of substitution of food for clothing at her optimal basket? Show this graphically and algebraically.

d) Suppose Julie decides to buy 4 units of food and 4 units of clothing with her $12 budget (instead of the optimal basket). Would her marginal utility per dollar spent on food be greater than or less than her marginal utility per dollar spent on clothing? What does this tell you about how she should substitute food for clothing if she wanted to increase her utility without spending any more money?