Hi,I need some help with a math question. Probably it's a silly question but today math and I are not friends...To give you economic intuition I'm interested into the sign of the elasticity of two prices with respect the same underlying variable. The two prices are associate to assets with different maturity.Mathematically, I want to just characterize the sign of:[$]\partial_z (H(z,T1) - H(z,T2))\quad \forall T2>T1>0[$]where[$]H(z,T) = \frac{\int_0^T m(\tau) e^{g(\tau, T) + m(\tau) z} d\tau}{\int_0^T e^{g(\tau, T) + m(\tau) z} d\tau}[$]we know that [$]m(\tau)[$] is positive and either monotone increasing or monotone decreasing.I know that [$] (H(z,T1) - H(z,T2)) [$] is positive for [$]m(\tau)[$] monotone decreasing and negative for [$]m(\tau)[$] monotone increasing.I'm not sure what happens when I take the derivative with respect to z.Thanks a lot in advance

If you have a probability distribution over a random variate x, then E((f(x) - fbar)^2) = E[f(x)^2] - E[f(x)]^2 > 0.Doing your derivative directly seems to me to produce the middle expression in that last relation with x = tau and suitable pdf = p(tau); hence positive.