# 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 Preview

Please see the attached file.

| u1,1u1,2 -p1 | | âˆ‚x1/âˆ‚p1 | | Î» |

| u2,1u2,2 -p1 | | âˆ‚x2/âˆ‚p1 | = | 0 |

| -p1-p2 0 | | âˆ‚Î»/âˆ‚p1 | = | 0 |

where ui,j is âˆ‚2u/âˆ‚xjâˆ‚xi

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

#### Solution Summary

Slutsky's equation is expained.

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