Hi,
I am trying to work out how a derivative (sensitivity of x to variable y) is affected by the change in a variable g and variable k.
if dx/dy = (g - k)/(k*(y-g)^2)
I know this is negative for K>g
The derivative of dx/dy with respect to k is:
d (dx/dy) / dk = -g/(k^2*(y-g)^2)
This is negative. What does the negative sign mean? That sensitivity to y is lower if k is higher (or the opposite)?
The derivative of dx/dy with with respect to g is more difficult. I think it is (correct me if I'm wrong):
d (dx/dy) / dg = [1 / (k*(y-g)^2)]*[1-2(k-g)/(y-g)]
I think this is negative if:
(k-g) / (y - g) > 0.5
Again, if it is negative, what does that mean exactly for sensitivity of x to y if g is higher?
Many thanks for any help on this!
I am trying to work out how a derivative (sensitivity of x to variable y) is affected by the change in a variable g and variable k.
if dx/dy = (g - k)/(k*(y-g)^2)
I know this is negative for K>g
The derivative of dx/dy with respect to k is:
d (dx/dy) / dk = -g/(k^2*(y-g)^2)
This is negative. What does the negative sign mean? That sensitivity to y is lower if k is higher (or the opposite)?
The derivative of dx/dy with with respect to g is more difficult. I think it is (correct me if I'm wrong):
d (dx/dy) / dg = [1 / (k*(y-g)^2)]*[1-2(k-g)/(y-g)]
I think this is negative if:
(k-g) / (y - g) > 0.5
Again, if it is negative, what does that mean exactly for sensitivity of x to y if g is higher?
Many thanks for any help on this!