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


  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?

  • $\begingroup$ 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. $\endgroup$
    – Community Bot
    Nov 26, 2021 at 1:18
  • $\begingroup$ 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 $G_2$? $\endgroup$
    – Macosso
    Nov 26, 2021 at 9:11

1 Answer 1


The solution to question

  1. Your Solution is correct.

  2. To get the total differential use the following formula

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


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