3.10 Cobb–Douglas utility Example 3.3 shows that the MRS for the Cobb–Douglas function U xð Þ¼ , y xayb is given by MRS ¼ a b

y x

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a. Does this result depend on whether a þ b ¼ 1? Does this sum have any relevance to the theory of choice?

b. For commodity bundles for which y ¼ x, how does the MRS depend on the values of a and b? Develop an intuitive explanation of why, if a >

b, MRS > 1. Illustrate your argument with a graph.

c. Suppose an individual obtains utility only from amounts of x and y that exceed minimal subsistence levels given by x0, y0.

In this case, U xð Þ¼ , y ð Þ x % x0 að Þ y % y0 b Is this function homothetic? (For a further discussion, see the Extensions to Chapter 4.)