Question

Julie has preferences for food, f, and clothing, c, described by a Cobb-Douglas utility function u(f, c) = f · c. 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. Sketch Julie’s indifference curves corresponding to utility levels U¯ = 12, U¯ = 18, and U¯ = 24. Using the graph (no algebra yet!), show the optimal/utility-maximizing choice of food and clothing. Please put food on the x-axis and clothing on the y-axis.

b. What is the mathematical expression for sJulie’s MRS in terms of f and c?

c. If Julie had 2 units of food and 9 pieces of clothing, what value would her MRS be (ie, how willing is she to substitute clothing for food at that bundle)?

d. Using algebra (HINT: the tangency condition and the budget line), find her optimal choice of food and clothing.

e. What is the value of her MRS at the optimal bundle? How does that relate to the prices she faces at the store? f. Suppose Julie decides to buy 4 units of food and 4 units of clothing with her $12 budget (instead of her optimal bundle). Would her marginal utility per dollar spent on food be greater than or less than her marginal utility per dollar 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?

Answer 1

Thanks!