# How do I determine PED from price consumption curve with slope of zero?

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?