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May 9th, 2017, 04:51 AM   #1
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Micro-economics

Hello

Can you please help me about the following exercise:

The straight graph y = Y0 > 0 cuts all the equivalent curves. Prove that the marginal rate of substitution decreases when moving from one cutting point to a second cutting point (from left to right).

My answer:
We have y = Y0 > 0 which is parallel to the axis of x, so that from one cutting point to a second cutting point we can see that the amount of x units increases during that the amount of y units doesn't change, it means that the producer doesn't give up on y units during that the amount of x units increases, that's why the marginal rate of substitution decreases when moving from one cutting point to a second cutting point (from left to right).

Am i right?

Thanks a lot!
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May 10th, 2017, 12:40 PM   #2
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what do you mean by all equivalent curves? I guess this doesnot apply if the graph is concave up
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May 10th, 2017, 01:48 PM   #3
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Quote:
Originally Posted by dthiaw View Post
what do you mean by all equivalent curves? I guess this doesnot apply if the graph is concave up
I meant: https://en.wikipedia.org/wiki/Indifference_curve
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May 11th, 2017, 11:08 AM   #4
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Quote:
Originally Posted by IlanSherer View Post
Quote:
Originally Posted by IlanSherer View Post
Hello

Can you please help me about the following exercise:

The straight graph y = Y0 > 0 cuts all the equivalent curves. Prove that the marginal rate of substitution decreases when moving from one cutting point to a second cutting point (from left to right).

My answer:
We have y = Y0 > 0 which is parallel to the axis of x, so that from one cutting point to a second cutting point we can see that the amount of x units increases during that the amount of y units doesn't change, it means that the producer doesn't give up on y units during that the amount of x units increases, that's why the marginal rate of substitution decreases when moving from one cutting point to a second cutting point (from left to right).

Am i right?

Thanks a lot!
your answers sounds perfect but I am not sure if it satisfies a math proof though
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May 11th, 2017, 11:39 AM   #5
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Quote:
Originally Posted by dthiaw View Post
your answers sounds perfect but I am not sure if it satisfies a math proof though
Yes, I'm not sure too.
I tried to prove it with formula of https://en.wikipedia.org/wiki/Margin...f_substitution, but the value of marginal rate of substitution will be always 0 because y is constant (if I'm not mistaken).
I don't know... do you have an idea?
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May 11th, 2017, 12:20 PM   #6
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A point to the right on the next indifference curve is always better because the consumer gets more of product x and the same amount of product y. Because of the law of diminishing marginal utility, the consumer would be willing to give up less of product y to obtain an additional unit of product x at the second cutting point. Therefore, this implies that the MRS has decreases at the second cutting point.

Cheers. This is enough of a proof without math
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May 22nd, 2017, 08:09 AM   #7
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Informal proof...

Since for all indifference curves

$\displaystyle \frac{dy}{dx} < 0$,

then

$\displaystyle \frac{\Delta y}{\Delta x} < 0$.

Consider two coordinates $\displaystyle (x_1, y_1)$ and $\displaystyle (x_2, y_2)$ which represent points on a single indifference curve where the line $\displaystyle y = y_1$ and $\displaystyle y = y_2$ cut the curve.

Consequently,

$\displaystyle \frac{y_2 - y_1}{x_2 - x_1} < 0$

Since the second curve has $\displaystyle x_2 > x_1$, the condition above is only satisfied if $\displaystyle y_2 < y_1$.
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