# Utility Function Challenge

A utility function is given for two goods

Good 1 and Good 2 $$U=f({G_1},{G_2})=45{{G_1}^{0.7}}{{G_2}^{0.3}}$$

1. Did I get this right? the marginal utility functions with respect to G1 and G2 will be following:

$$\frac{\partial{U}}{\partial{G_1}}$$ $$\implies$$ $$MU$$ of Good 1

$$\frac{\partial{U}}{\partial{G_2}}$$ $$\implies$$ $$MU$$ of Good 2

$$U=f({G_1},{G_2})=45{{G_1}^{0.7}}{{G_2}^{0.3}}$$

1. Total differential of this utility function should be:

$$d{U} = d{f}= f{G_1}({G_1},{G_2})d{G_1} + f{G_2}({G_1},{G_2})d{G_2}$$

Are these workings right?

• Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
– Community Bot
Nov 26, 2021 at 1:18
• can you please check again the Utility function? is it $U=f({G_1},{G_2})=45{{G_1}^{0.7}}{{G_2}^{0.3}}$ because you have , which does not make sense unless it is a general function. And also what do you want to achieve? do you want to have a Marginal utility with respect to $G_1$ and Marginal utility with respect to $G_2$? Nov 26, 2021 at 9:11

$$d{U} = d{f}= \frac{\partial{U}}{\partial{G_1}}d{G_1} + \frac{\partial{U}}{\partial{G_2}}d{G_2}$$