<p>The MRS represents the rate of exchange between goods x and y that would leave the agent indifferent to trading the two. It is the slope of the indifference curve for a given value of utility U.</p>

<p>To derive the indifference map (the set of indifference curves), take U constant in the utility function, and solve for y in terms of x. You can check if your MRS calculation is correct by taking the first derivative of your indifference map function.</p>

CC BY-SA 4.0
2019-09-19T14:41:51.023Z
2019-09-19T15:42:20.033Z
2019-09-19T15:42:20.033Z
heh
<p>1) <strong>To draw indifference curves.</strong>
Assume some value of U on the LHS, assume some values of x and calculate corresponding values of y. for e.g. assume U=10.</p>

<pre><code>assuming
x=0,0.01, 0.04, 0.09, 0.16, 0.25, 0.36, 0.49, 0.64, 0.81, 1 you get
y=2, 1.8, 1.6 ,  1.4,  1.2, 1,    0.8,  0.6,  0.4,  0.2,  0.
</code></pre>

<p>Join these (x,y) coordinates to get indifference curve for U=10. Repeat for other values of U. What does this curve mean? It means any (x,y) on this curve gives you the same utility U=10. Therefore you are <strong>indifferent</strong> between all points (x,y) on this curve.</p>

<p>2) <strong>MRS</strong></p>

<p>What you did is right mathematically.</p>

<p>The MRS is the slope of the indifference curve. It is the rate at which you must substitute y for x to remain on the same utility curve. i.e. suppose you are currently consuming a bundle (1,0) . You now want to consume some y, how much x must you substitute out to get to consume 1 unit of y <em>at this point</em>? That's  the question the MRS answers.</p>

CC BY-SA 4.0
2019-09-20T14:57:49.947Z
2019-09-22T07:41:08.067Z
2019-09-22T07:41:08.067Z
Vaidyanathan Viswanathan Sauna
<p>Given a utility function <span class="math-container">$U= {10x^{0.5}} + 5y$</span>, calculate the MRS and explain its economic meaning.</p>

<p>The MRS I calculated is <span class="math-container">$\frac{1}{\sqrt{x_1}}$</span>, but I can't really understand it's economic meaning or how to derive its indifference curve. Some help please?</p>

<microeconomics>
Utility function is given as U(x1, x2) = 10x 0.5 1 + 5x2
Federico Raspanti
# Utility function is given as U(x1, x2) = 10x 0.5 1 + 5x2

(Asked by: username_0 on 2019-09-19)

Given a utility function $U= {10x^{0.5}} + 5y$, calculate the MRS and explain its economic meaning.

The MRS I calculated is $\frac{1}{\sqrt{x\_1}}$, but I can't really understand it's economic meaning or how to derive its indifference curve. Some help please?

**Tags:** microeconomics


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## 2 answers

### Answer by username_1 on 2019-09-19. Score: 3

The MRS represents the rate of exchange between goods x and y that would leave the agent indifferent to trading the two. It is the slope of the indifference curve for a given value of utility U.

To derive the indifference map (the set of indifference curves), take U constant in the utility function, and solve for y in terms of x. You can check if your MRS calculation is correct by taking the first derivative of your indifference map function.


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### Answer by username_2 on 2019-09-20. Score: 1

1) **To draw indifference curves.**
Assume some value of U on the LHS, assume some values of x and calculate corresponding values of y. for e.g. assume U=10.

```
assuming
x=0,0.01, 0.04, 0.09, 0.16, 0.25, 0.36, 0.49, 0.64, 0.81, 1 you get
y=2, 1.8, 1.6 ,  1.4,  1.2, 1,    0.8,  0.6,  0.4,  0.2,  0.

```

Join these (x,y) coordinates to get indifference curve for U=10. Repeat for other values of U. What does this curve mean? It means any (x,y) on this curve gives you the same utility U=10. Therefore you are **indifferent** between all points (x,y) on this curve.

2) **MRS**

What you did is right mathematically.

The MRS is the slope of the indifference curve. It is the rate at which you must substitute y for x to remain on the same utility curve. i.e. suppose you are currently consuming a bundle (1,0) . You now want to consume some y, how much x must you substitute out to get to consume 1 unit of y *at this point*? That's the question the MRS answers.


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