# Q1 Derive the Marshallian demand and indirect utility funct.pdf

A

Q1. Derive the Marshallian demand and indirect utility function for u(x,y)=(0.3x+0.7y)2. Q2. Derive the Hicksian demand and the expenditure function for u(x,y)=(0.3x+0.7y)2 Q3. Suppose that the indirect utility is v(p,I)=27px2py4I3. (a) Use the Roy's identity to derive the Marshallian demand. (b) Use the relationship between the indirect utility and expenditure function to derive the expenditure function. (c) Use the Shephard's lemma to obtain the Hicksian demand from the expenditure function. (d) Use the relationship between Marshallian and Hicksian demand and obtain the Hicksian demand directly from the Marshallian demand by plugging in the expenditure function. Compare your answer to (c), it should be the same..

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### Q1 Derive the Marshallian demand and indirect utility funct.pdf

• 1. Q1. Derive the Marshallian demand and indirect utility function for u(x,y)=(0.3x+0.7y)2. Q2. Derive the Hicksian demand and the expenditure function for u(x,y)=(0.3x+0.7y)2 Q3. Suppose that the indirect utility is v(p,I)=27px2py4I3. (a) Use the Roy's identity to derive the Marshallian demand. (b) Use the relationship between the indirect utility and expenditure function to derive the expenditure function. (c) Use the Shephard's lemma to obtain the Hicksian demand from the expenditure function. (d) Use the relationship between Marshallian and Hicksian demand and obtain the Hicksian demand directly from the Marshallian demand by plugging in the expenditure function. Compare your answer to (c), it should be the same.
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