Chapter 3 Utility: End of Chapter Exercises

#1: In regard to their consumption of cookies and coffee, Mark and Sharon face the same prices and both believe they are in equilibrium. As a consequence we can conclude

• a. Mark and Sharon have the same marginal utility for cookies

• b. Mark and Sharon have the same marginal utility for coffee

• c. Mark and Sharon have the MRS of cookies for coffee

• d. All of these are true

#2: If I truly believe that Coke & Pepsi are interchangeable, where x = Coke and y=Pepsi, my preferences can be best represented by which of the following:

• a. U(x,y)=2x + 2y

• b. U(x,y) = min{x, y}

• c. U(x,y) = xy

• d. We cannot know without a budget constraint

• e. None of these

Short Answer:

#1: Suppose Mark insists on consuming 3 spoonfuls of Cocoa Puffs (good x) with exactly 2 spoonfuls of Honeynut Cheerios (good y). Write down Mark's utility function.

#2: True or False: The utility function u(x,y) = 5ln(x) + 2ln(y) represents Cobb-Douglas preferences.

Sketch of Solutions:

1. C, same MRS of cookies for coffee

2. A, interchangeable implies we’re willing to trade one for the other at some constant rate. Of the utility functions provided only (a) represents substitutes preferences.

Short Answer

1. Mark has perfect complements preferences: U(x, y) = min{2x, 3y}. We get this from first inspecting bundles that Mark is sure to approve of e.g. x=3 and y=2 and then x=6 and y=4. We can recognize the relationship between x and y as y=(2/3)x which provides the equation for the ray emanating from the origin that must go through all the corners of the indifference curves. Expanding we write 3y=2x and replacing the equals sign with a comma we obtain the utility function: min{2x, 3y}

2. True, this is a monotonic transformation of u(x,y) = (x^5) (y^2)