
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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Transcribed Image Text: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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- Q.7 A consumer's utility function is given by the expression: U = (0.6A"' + 0.47'"s} Determine the marginal utility functions for each commodity. Does marginal utility decrease when consumption increases? Assuming that the price of good X is Rs 15 and the price of Y is Rs 6, write the equation of the budget line and plot it when income is Rs 450. What is its slope? What does it indicate? Calculate the marginal rate of substitution of Y for X and interpret its economic meaning. Write the equation showing consumer's equilibrium condition. Obtain the equilibrium values of X and Y. Find the expressions for change in MUx due to increase in Y and change in MUy due to increase in X.arrow_forwardhurry up its urgentarrow_forwardWhen diminishing returns are present in consumption, the relationship between total utility and marginal utility is as follows: O Total utility increases at a decreasing rate while marginal utility decreases Total utility increases at an increasing rate while marginal utility increases Total utility increases at an increasing rate while marginal utility decreases Total utility decreases at a decreasing rate while marginal utility increasesarrow_forward
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