# Marshallian demand functions

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 Preview

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 ...

#### Solution Summary

Marshallian demand Functions and indirect utility functions are noted. Maximizing problems are examined.