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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.

Question
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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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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Since we are entitled to answer up to 3 sub-parts, we’ll answer the first 3 as you have not mentioned the subparts you need help with. Please resubmit the question and specify the other subparts you’d like to get answered.

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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