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Given a budget for two goods $x_1$ and $x_2$, a fixed price for good 2 and three prices for good 1 with the corresponding optimal amount of good 1 ($x_1$), I like to calculate the PED for good 1.

By looking at the three given points, I know that the price consumption curve for good 1 is a horizontal curve, i.e. the slope of the price consumption curve seems to be zero (connecting the three points).

Since I know the price ratio, I also know the MRS for the three given points.

So I have to find $x_1(p_1, p_2, m)$, where $p_2$ and $m$ are known constants, in order to determine $\partial x_1(...)/\partial p_1$.

What is the correct approach to this problem?

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Since you have discrete datapoints and want to calculate PED, you will have to make assumptions, like "the data represents the general behavior of the consumption function". (You can also get more data or throw your hands up in despair.)

If you know that price has no effect on the quantity demanded, you can apply the PED formula, and get a very specific number for PED.

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