A good example is Y = 1/X and Y = 2/X.

The curve do not cross (because 1 does not equal 2), but they are not parallel.

[NEAS: Correct; one can make up dozens of examples.]

Y1 = x^2 +5

Y2 = -(x^2)

Y1 - Y2 = 2*x^2 +5

 

Example let x=2.  Y1 = 9 and Y2 = -4

Y1-Y2 = 13

"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."

if you set up the domain for such function, I partly agree w/ you. By that, I mean, they won't cross in the domain, and won't be parallel of course. but if we change the domain of function to [0, 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."

I completely disagree w/ this example, you said those 2 function aren't parallel? B/C I believe any X makes Y1-Y2=5. Can you find any x false that? If you cant, that mean 2 functions are parallel to each other, aren't they?

Chances favor the prepared mind...

"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]

Question 3.1: Indifference Curves

All but which of the following are true regarding indifference curves?

An indifference curve is a locus of points that are equally desirable to the consumer.

Indifference curves for a single consumer cannot cross.

Indifference curves for a single consumer are always parallel.

A single consumer has an infinite number of indifference curves.

Indifference curves for two goods are downward sloping.



Answer 3.1: C

Know the four attributes of indifference curves in A, B, D, and E, and know that indifference curves are not necessarily parallel.

About this question, I felt that all choice statement are true.

Considering the truth that all curves should never cross each other, it does mean that all curves should be parallel all the time, otherwise, there exist some points in the plane which 2 of curves cross each other.

Why C is false?

Chances favor the prepared mind...