Question

Hello Friends,
I am quite confused about the interpretation of decreasing concave up function. For example, A country's economy is slowing down (first derivative < 0, so decreasing fucntion) for last 10 years now, but for last 2 years now the rate of slow down has increased (it's slowing down faster than it'd been earlier- perhaps due to a natural disaster). So can we say that the function is decreasing concave up? Similarly, if the rate of slow down is decreasing (it's slowing down yet the rate of slow down has decreased - perhaps due to a economic stimulus) can we say that it's decreasing c

Answer 1

Alright, I think I can explain it now. In terms of economics, a decreasing concave up function would indicate that while the economy has been getting worse, it is getting worse a slower rate as time goes on. A decreasing concave down function would mean that as time was going, the decline in the economy it getting worse.

Answer 2

*economy would be getting worse.

Answer 3

I'm not sure if I understand this question. Convex (concave up) and concave (concave down) can be defined without any reference to an economy.

However, let's say you have a graph with years on the x-axis and GNP on the y-axis.

Your GNP could actually be falling so the graph would "start" high and go lower.

Or the GNP could be going up but at a lower rate in each year and the graph would "start" low and go higher.

Answer 4

Between first and second year
y2 = 10 (first year GDP)
y1 = 10.5 (second year GDP)

f' -.5 -> f' < 0

between second and third year

y2=9.4 (third year GDP)
y1=10

f' = -.6 f' < 0

f" between first and third year interval [1,3]

f" -.1 -> f" < 0 concave down - economy is getting worse.

But if
between second and third year

y2=9.7 (third year GDP)
y1=10

f' = -.3 < 0

f" between first and third year interval [1,3]

f" = +.2 f" > 0
So concave up - though economy is still sliding down its downward ternd has been arrested a little.

Answer 5

Could you please confirm if my inference is correct?

Answer 6

Yes, this is why you specify an appropriate interval because a graph may exhibit different behaviors over different intervals.

Answer 7

Thank You Everyone for the help.

Answer 8

You're welcome.