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$$U_1 = 1 - \frac{1}{x_1} - \frac{3}{y_1}$$ $$U_2 = 1 - \frac{3}{x_2} - \frac{1}{y_2}$$

How would one go about deriving the MRS for such utility functions and what would their indifference curves look like?

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closed as off-topic by Herr K., HRSE, optimal control, Giskard, BKay Mar 1 '16 at 18:03

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question does not meet the standards for homework questions as spelled out in the relevant meta posts. For more information, see our policy on homework question and the general FAQ." – Herr K., HRSE, optimal control, Giskard, BKay

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Although you are new here, it is much appreciated if you looked at our guidelines for asking questions, particularly ones that look like homework questions. Generally, we ask that people show some reasonable semblance of effort into trying the question, and to talk about which part of the question they are struggling with. We're not homework doing machines.

As such, I can only give a rough guideline for how to approach the question.

Any cursory Google search will show you that the marginal rate of substitution is marginal utilities of each good $(x, y)$ divided by each other.

$$\text{MRS}_{xy, i} = \frac{\frac{\partial U_i}{\partial x_i}}{\frac{\partial U_i}{\partial y_i}}$$

Where $i$ is person 1 or 2.

To find the indifference curves, simply solve for $y$ in terms of $x$ and $U$, where $U$ is treated as a constant level of utility.

Now try the question for yourself.

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