  The quotient of random variables with normal distributions is examined and
proven to have have power law decay, with density $f\left( x\right) \simeq
f_{0}x^{-2}$, with the coefficient depending on the means and variances of the
numerator and denominator and their correlation. We also obtain the conditional
probability densities for each of the four quadrants given by the signs of the
numerator and denominator for arbitrary correlation $\rho \in\lbrack-1,1).$ For
$\rho=-1$ we obtain a particularly simple closed form solution for all $x\in$
$\mathbb{R}$. The results are applied to a basic issue in economics and
finance, namely the density of relative price changes. Classical finance
stipulates a normal distribution of relative price changes, though empirical
studies suggest a power law at the tail end. By considering the supply and
demand in a basic price change model, we prove that the relative price change
has density that decays with an $x^{-2}$ power law. Various parameter limits
are established.
