I have a function,
$V(D) = (1-\tau_E) (1-\tau_C) \int_0^{100} (R-D) dF(R) + (1-\tau_D) \int_D^{100} D dF(R) + (1-\tau_D)(1-b) \int_0^D RdF(R)$
Where R is a random variable $R \in [0,100]$ with distribution $F(R)$. $D \in [0,100]$. I need to find $V'(D)$ and $V''(D)$, ultimately to find an interior optimal $D^*$.
I have the expression for $V'(D)= (1-F(D)) \cdot [\overline{1-\tau_D}-(1-\tau_E)(1-\tau_C) ] - Df(D)(1-\tau_D) + D(1-\tau_D)(1-b)$
Is this correct?
I have to specify then that R follows Uniform Distribution in $[0,100]$ to find $D^*$. But, when I am doing this, all my Ds are getting cancelled.
Thank you!