Convex Concave and MRS

2 Qs

1.) The example in the book is of a convex curve as seen from the origin. But it depends how you look at it? It’s a bit like this:

Depends how you look at her, she could be spinning either right or left same with convex or concave claim. Is it something you just need to remember and that’s it or is there some other way of understanding convex vs concave.

A lens is simple to understand:

No Ambiguity there. Just confused in the case of economics.

2.) Is there a good way to remember MRS questions? i.e. MRSxy (rate at which consumer is willing to give up y for x) vs MRSyx (rate at which consumer is willing to give up x for y). Again, it kinda depends on the way you label the axis.

Convex opens upwards - simple as that.

I didn’t want to rote learn it, but I think I figured it out, if you’re looking at the curve from the origin as per the text, then it’s definitely bulging out at you. If you’re looking at it from the opposite side, then it’s like a cave hence concave.

When placed horizontally :

Convex shape looks like a smile - you can connect the lines from one end the other without touching the middle point.

Concave shape looks like a frown - you can not connect the lines from one end to the other without touching the middle point.

Hope this helps…

An interesting point to add…

Presumably, you know what the price / yield relationship looks like. (Like the lower half of the letter C right?)

This relationship is convex. If you read about bonds with embedded options, like mortgages, there is a characteristic described as “negative convexity” which refers to the left side of the price yield relationship strating to curve downwards…like th top half of a backwards C…

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