# 3. A canonical utility function. Consider the utility function u(c) 1-σ where c denotes consumption of some arbitrary good and ơ (Greek lowercase letter sigma") is known as the "curvature parameter" because its value governs how curved the utility function is. In the following, restrict your attention to the region c> (because "negative consumption" is an ill-defined concept). The parameter σ is treated as a constant. Plot the utility function for ơ-0. Does this utility function display diminishing marginal utility? Is marginal utility ever negative for this utility function? Plot the utility function for ơ marginal utility? Is marginal utility ever negative for this utility function? Consider instead the natural-log utility function u(c)=In(c). Does this utility function display diminishing marginal utility? Is marginal utility for this utility function? 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.) a. b. 2. Does this utility function display diminishing c. ever negative d.

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We have, the given canonical utility function in equation (1)

Where, σ = curvature parameter (constant)

And, c = consumption level of some arbitrary good (c>0)

a)We have the utility function in equation (1),

Putting σ = 0 in equation (1), we get equation (2)

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