The function used is:
g(x)=[e^(Uo/A)][e^(-x^2)/(2A)]
where x is a quantity of a good, Uo is a constant that represents utility, and A is a positive constant.
We have to prove that the graph of g(x) is concave down for x < √(A) and concave up for x > √(A).
How do we verify this?
Please help me with this question.
Thank you everyone in advance!
I have to admit that I wondered what an "inferior good question" would be. If it's a "good question", how can it be "inferior"?
You need to differentiate with respect to x, not or A! What you have is essentially
where , a constant.
By the chain rule, the first derivative is and the second derivative is .
You say A and Uo is a constant. For simplicity, let's assume they are both one.
e is nothing more than just a number so it is a constant.
Any constant multiplied by a constant or raised to a constant is always a constant.
Instead of saying , we can call it C or K or M or N or anything you want to.
Also, Halls told you what C is already.