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 May 9th, 2017, 04:51 AM #1 Member   Joined: Mar 2017 From: Israel Posts: 72 Thanks: 2 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!
 May 10th, 2017, 12:40 PM #2 Member   Joined: Jan 2017 From: California Posts: 80 Thanks: 8 what do you mean by all equivalent curves? I guess this doesnot apply if the graph is concave up
May 10th, 2017, 01:48 PM   #3
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Quote:
 Originally Posted by dthiaw 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

May 11th, 2017, 11:08 AM   #4
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Quote:
 Originally Posted by IlanSherer
Quote:
 Originally Posted by IlanSherer 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

May 11th, 2017, 11:39 AM   #5
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Quote:
 Originally Posted by dthiaw 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?

 May 11th, 2017, 12:20 PM #6 Member   Joined: Jan 2017 From: California Posts: 80 Thanks: 8 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 Thanks from IlanSherer
 May 22nd, 2017, 08:09 AM #7 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 2,133 Thanks: 719 Math Focus: Physics, mathematical modelling, numerical and computational solutions 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 $\displaystyle y_2 < y_1$. Thanks from IlanSherer

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