# problem of maximizing the utility function

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Consider the problem of maximizing the utility function u = f(c) + g(s) subject to the budget constraint pc + s=y where c is consumption and s is savings. derive and interpret the Slutsky equations and explain what happens if g double prime (s) = 0

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##### Solution Summary

Slutsky's equation is expained.

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Please see the attached file.

| u1,1u1,2 -p1 | | ∂x1/∂p1 | | λ |

| u2,1u2,2 -p1 | | ∂x2/∂p1 | = | 0 |

| -p1-p2 0 | | ∂λ/∂p1 | = | 0 |

where ui,j is ∂2u/∂xj∂xi

If we denote the 3x3 matrix on the left-hand side as H and create a vector X = (x1, x2, ...

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