Marshallian demand functions
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Consider the problem of maximizing u = (x1x2)2 subject to p1x1 + p2x2 = y. Derive the Marshallian demand functions and the indirect utility function; and confirm that Roy's identity holds.
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Solution Summary
Marshallian demand Functions and indirect utility functions are noted. Maximizing problems are examined.
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please refer to the attachment.
Consider the problem of maximizing u = (x1x2)2 subject to p1x1 + p2x2 = y. Derive the Marshallian demand functions and the indirect utility function; and confirm that Roy's identity holds.
Since we want to max U=(x1x2)2 subject to p1x1 + p2x2 = y
We can write the Lagrangian Function as:
L = (x1x2)2 - m (p1x1 + p2x2 - y)
Where m >= 0 to be determined
Then take the first order condition:
DL/dX1 = 2X1 X22 - mp1 = 0 or ...
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