Allin Cottrell Wake Forest University Department of Economics November 16, 2001

This is a trivial SGML document that illustrates the use of the alt element for math. Here is a little bit of inline math: $C = \alpha + \beta Y^{\gamma} + \epsilon$ . It is embedded in the text. New paragraph. Here is a bit of displayed math \[F_{2,T-k}=\frac{(ESS_r-ESS_u)/2}{ESS_u/(T-k)}\] Note that for this sort of display you get excessive vertical spacing if you bracket the math with double dollar signs, $$. The spacing is better if you use \[ and \] instead. Now here is a slightly more complex piece of displayed math, for which we adjust the spacing using \renewcommand{\arraystretch}{1.3} \setlength{\arraycolsep}{.05in} within the alt element: \renewcommand{\arraystretch}{1.3} \setlength{\arraycolsep}{.05in} \[ \left[ \begin{array}{c} \dot{L} \\ \dot{C} \end{array} \right] = \frac{1}{-\alpha} \left[ \begin{array}{cc} af & bfh \\ 1 & b(fh-k) \end{array} \right] \left[ \begin{array}{c} L \\ C \end{array} \right] -\frac{1}{\alpha} \left[ \begin{array}{cc} afh & 0 \\ h & \alpha \end{array} \right] \left[ \begin{array}{c} \dot{m} \\ r_w \end{array} \right] \] Finally we try using the formal <equation> tag with a title: \[ \hat{\beta} = \frac{\sum_{t=1}^n x_t y_t - \bar{y} \sum_{t=1}^n x_t} {\sum_{t=1}^n x^2_t - \bar{x}\sum_{t=1}^n x_t} \]