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An individual has the following utility, U = In X + 2 In Y. What do we know about the Marshallian and Hicksian demand elasticities of good x with respect to the price of x? O a. Marshallian elasticity ep. will be more negative than Hicksian elasticity ep. O b. Marshallian elasticity ex.P. will be less negative than Hicksian elasticity ef.p, O c. Marshallian elasticity ex.p, will be the same as Hicksian elasticity e.p. O d. Marshallian elasticity and Hicksian elasticity will have opposite signs. Clear my choice

An individual has the following utility, U = In X + 2 In Y. What do we know about the Marshallian and Hicksian demand elasticities of good x with respect to the price of x? O a. Marshallian elasticity ep. will be more negative than Hicksian elasticity ep. O b. Marshallian elasticity ex.P. will be less negative than Hicksian elasticity ef.p, O c. Marshallian elasticity ex.p, will be the same as Hicksian elasticity e.p. O d. Marshallian elasticity and Hicksian elasticity will have opposite signs. Clear my choice

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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### Understanding Marshallian and Hicksian Elasticities #### Question 1: An individual has the following utility function, \( U = \ln X + 2 \ln Y \). What do we know about the Marshallian and Hicksian demand elasticities of good \( x \) with respect to the price of \( x \)? - **a. Marshallian elasticity \( \varepsilon_{x, p_x} \) will be more negative than Hicksian elasticity \( \varepsilon^c_{x, p_x} \).** - b. Marshallian elasticity \( \varepsilon_{x, p_x} \) will be less negative than Hicksian elasticity \( \varepsilon^c_{x, p_x} \). - c. Marshallian elasticity \( \varepsilon_{x, p_x} \) will be the same as Hicksian elasticity \( \varepsilon^c_{x, p_x} \). - d. Marshallian elasticity and Hicksian elasticity will have opposite signs. *Selected answer: a* #### Explanation: Marshallian (or uncompensated) and Hicksian (or compensated) elasticities measure the responsiveness of demand to price changes. The Marshallian demand elasticity \( \varepsilon_{x, p_x} \) usually accounts for both income and substitution effects, while the Hicksian demand elasticity \( \varepsilon^c_{x, p_x} \) considers only the substitution effect. Given the income effect is typically negative, the Marshallian elasticity is often more negative than the Hicksian elasticity. --- ### Demand and Elasticity in Utility Functions #### Question 2: An individual has the utility function \( U(X, Y) = X^{1/3}Y^{2/3} \). Which of the following is true? - **a. Demand for \( X \) and \( Y \) have constant expenditure shares \( s_X \) and \( s_Y \).** - b. The income effect for both goods is 0. - c. \( X \) and \( Y \) are net complements. - d. The own-price substitution effect of \( x \) ( \( \partial h_x / \partial p_x \) ) is 0. *Selected answer: a* #### Explanation: The given utility function \( U(X, Y) = X^{1/3}Y^{2/3} \) is a Cobb-Douglas utility function. For such functions,
Transcribed Image Text:### Understanding Marshallian and Hicksian Elasticities #### Question 1: An individual has the following utility function, \( U = \ln X + 2 \ln Y \). What do we know about the Marshallian and Hicksian demand elasticities of good \( x \) with respect to the price of \( x \)? - **a. Marshallian elasticity \( \varepsilon_{x, p_x} \) will be more negative than Hicksian elasticity \( \varepsilon^c_{x, p_x} \).** - b. Marshallian elasticity \( \varepsilon_{x, p_x} \) will be less negative than Hicksian elasticity \( \varepsilon^c_{x, p_x} \). - c. Marshallian elasticity \( \varepsilon_{x, p_x} \) will be the same as Hicksian elasticity \( \varepsilon^c_{x, p_x} \). - d. Marshallian elasticity and Hicksian elasticity will have opposite signs. *Selected answer: a* #### Explanation: Marshallian (or uncompensated) and Hicksian (or compensated) elasticities measure the responsiveness of demand to price changes. The Marshallian demand elasticity \( \varepsilon_{x, p_x} \) usually accounts for both income and substitution effects, while the Hicksian demand elasticity \( \varepsilon^c_{x, p_x} \) considers only the substitution effect. Given the income effect is typically negative, the Marshallian elasticity is often more negative than the Hicksian elasticity. --- ### Demand and Elasticity in Utility Functions #### Question 2: An individual has the utility function \( U(X, Y) = X^{1/3}Y^{2/3} \). Which of the following is true? - **a. Demand for \( X \) and \( Y \) have constant expenditure shares \( s_X \) and \( s_Y \).** - b. The income effect for both goods is 0. - c. \( X \) and \( Y \) are net complements. - d. The own-price substitution effect of \( x \) ( \( \partial h_x / \partial p_x \) ) is 0. *Selected answer: a* #### Explanation: The given utility function \( U(X, Y) = X^{1/3}Y^{2/3} \) is a Cobb-Douglas utility function. For such functions,
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