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Question Three
 
Consider an individual with the utility function, U(x , x ) (x  
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x1 and x2 and his income are px 1  0, p x2  0 , and I > 0.
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. The prices of
x )
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i. Show that this utility function satisfies diminishing marginal rate of substitution.
(4marks)
ii. Derive his Marshallian (uncompensated) demand functions for x1 and x2
(4marks)
iii. Derive his indirect utility function.
(4marks)
iv. Determine the Roy’s identity
(4marks)
v. Without solving his dual problem (i.e., minimizing expenditure subject to a given
utility), derive his expenditure function.
(4marks)
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