1. Business
  2. Economics
  3. only part d...

Question: only part d...

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ONLY PART d.

2 Utility Functions (2 Points) Consider the utility function u(c) where c denotes consumption of some arbitrary good and ơ (the Greek letter sigma) is known as the curvature parameter because its value governs how curved the utility function is and is treated as a constant. In the following, restrict your attention to the region c > 0 (because negative consumption is an ill-defined concept) a. (0.50 Points) Plot the utility function for σ 0, Does this utility function display diminishing marginal utility? Is marginal utility ever negative for this utility function? b. (0.50 Points) Plot the utility function for ơ 1/2 Does this utility function display diminishing marginal utility? Is marginal utility ever negative for this utility function? c. (0.50 Points) Consider instead the natural-log utility function u(c) - In(c). Does this utility function display diminishing marginal utility? Is marginal utility ever negative for this utility function? d. (0.50 Points) Determine the value of σ (if any value exists at all) that makes the general utility function presented above collapse to the natural-log utility function in part c (Hint: Examine the derivatives of the two functions)

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