$D(p) = 50 - p$
$S(p) = p/20$
The p* of this problem is $47.61$, however, when I add a .1 proportional tax I get an answer of $43.29$ which does not make sense because that price is lower than the previous equilibrium price.
I am using the equations:
$D(p) = 50 - (p + .1p) = (p + .1p)/20 = S(p)$
Am I dividing wrong? I suspect that I am getting a percentage change that is correct, it is just negative instead of positive. Any help would be appreciated.