-1
$\begingroup$

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?

$\endgroup$
2
  • $\begingroup$ 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 '21 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 '21 at 9:11
2
$\begingroup$

The solution to question

  1. Your Solution is correct.

  2. To get the total differential use the following formula

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.