"Considering the truth that all curves should never cross each other, it does mean that all curves should be parallel all the time"
I'll attempt to answer this. Hopefully NEAS will intervene if my discussion goes awry (wrong).
Curves not crossing is NOT the definition of parallel. Note that parallel lines keep the same vertical distance between two points with the same x-coordinate. For example, consider the lines
y=5x+2 and y=5x+17
For any given x, the difference in y values is 17-2=15 units.
Now consider the functions
y= (1/x) and y=1/(x^2) on the domain from x=2 to x= infinity.
These curves never cross, but they are not parallel. In fact the distance between the curves approaches 0 as x approaches infinity.
As another example, consider the functions
y=(x^2) + 5 and y= - (x^2) for any domain.
Again these functions never cross and are definitely not parallel.
The book tends to draw examples of indeifference curves that look parallel. However, the only requirements of these curves is that they fill the first quadrant of the plane, they are convex, and they cannot cross. This can be accomplished without requiring parallelism.
[NEAS: Correct]
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