# Maximise utility given marginal utilities and utility function watch

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1. Hello. I have a specific homework question that I have attempted to solve, but haven't had any success yet. The question deals with marginal substitution and utility maximising bundles. I am given the following problem:

Utility function is U(c,w,b)=2*c^2 * w - 4*b^2, where a unit of "c" costs is €2, a unit of "w" is €4, and a unit of "b" is €1. Income is €300/week. Utility function implies that margin utility of "c" is 4cw, marginal utility of 2C^2, and marginal utility of "b" is -8B.

I'm required to find the utility maximising bundle of the three goods, with a hint of "look at the utility function and consider the marginal utility of each good" but I am at a complete loss as to where to turn.

I considered using the relationship: MU of c / price of c = MU of w / price of w = ... etc. but I don't know if that would work.

Can anyone help me? I am certainly struggling with this question.

Thank you!
2. Find when the marginal utilities of each are equal?
3. Have you done Lagrangian multipliers yet? You might be able to solve this setting up a Lagrangian.

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Updated: September 29, 2011
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