This article demonstrates one way to write complex equations using <a href="https://latex-project.org/intro.html">LaTeX on your WordPress blog.

Why blog with LaTeX? At least two reasons:

1. WordPress and other text editors don't support complex mathematical notation out-of-the-box.
2. Writing in LaTeX is a standard skill in research. So you can blog and be pro at the same time.

The instructions here allow the use of a subset of LaTeX. Specifically, everything gets dumped into a LaTeX \\math environment. Basically, this approach will suit your needs for writing equations, but not for creating whole papers or documents.

Steps:

• Install the Jetpack plugin for WordPress.
• Activate the Beautiful Math with LaTeX module in Jetpack.
• Review the documentation, linked above, and start writing your equations in LaTeX!
  • You may also want to play around some with an online LaTeX editor. Like this one.
  • You can click here to download a text document containing an example of how to use Beautiful Math. The example contains the same text used to render the text below this bulleted list.
  • That text is also the solution to a question found on the Advanced Macro I – Ramirez Final Edition exam!
  • Thanks to Brian, Ennio, and Josh for showing me how to solve the related problem.

Given:

$latex Y = C(Y-T) + I(i-\pi^e, Y_{-1}) + \bar{G} + X(
ho, Y, Y*) \\\\ \frac{M}{P} = L(i, Y-T) \\\\ BOP = X(
ho, Y, Y*) + \sigma(i - i*) + K $

We must write the total derivative in matrix form. The result will have a column of endogenous variables $latex dY, di,$ and $latex d
ho$.

Solving for $latex dY$:

$latex Y = C(Y-T) + I(i-\pi^e, Y_{-1}) + \bar{G} + X(
ho, Y, Y*) \\\\ dY = \frac{dC}{dY}(dY - dT) + \frac{dI}{dr}(di - d\pi^e)

• \frac{dI}{dY}dY_{-1} + d\bar{G} + \frac{dX}{d
  ho}d
  ho + \frac{dX}{dY}dY + \frac{dX}{dY^}dY^ \\\\ dY - dY\frac{dC}{dY} - dY\frac{dX}{dY} - di\frac{dI}{dr} - d
  ho\frac{dX}{d
  ho} = -\frac{dC}{dY}dT - \frac{dI}{dr}d\pi^e + \frac{dI}{dY}dY + d\bar{G} + \frac{dX}{dY*}dY* \\\\ dY(1 - \frac{dC}{dY} - \frac{dX}{dY}) - di\frac{dI}{dr} - d
  ho\frac{dX}{d
  ho} = -\frac{dC}{dY}dT - \frac{dI}{dr}d\pi^e + \frac{dI}{dY}dY + d\bar{G} + \frac{dX}{dY*}dY* \\\\ $

Solving for $latex dL$:

$latex \frac{M}{P} = L(i, Y-T) \\\\ d\frac{M}{P} = \frac{dL}{di}di + \frac{dL}{dY}(dY - dT) \\\\ d\frac{M}{P} = \frac{dL}{di}di + \frac{dL}{dY}dY - \frac{dL}{dY}dT \\\\ \frac{dL}{dY}dY + \frac{dL}{di}di = d\frac{M}{P} - \frac{dL}{dY}dT \\\\ $

Solving for $latex d
ho$ from the BOP function:

$latex BOP = 0 = X(
ho, Y, Y*) + \sigma(i - i*) + K \\\\ 0 = \frac{dX}{d
ho}d
ho + \frac{dX}{dY}dY + \frac{dX}{dY^}dY^ + \frac{d\sigma}{dr}i - \frac{d\sigma}{dr}i^* + dK \\\\ \frac{dX}{dY}dY + \frac{d\sigma}{dr}i + \frac{dX}{d
ho}d
ho = \frac{d\sigma}{dr}i^* + \frac{dX}{dY^}dY^ + dK \\\\ $

Expressing the system of equations for $latex dY, di,$ and $latex d
ho$ in matrix form:

$latex dY(1 - \frac{dC}{dY} - \frac{dX}{dY}) - di\frac{dI}{dr} - d
ho\frac{dX}{d
ho} = -\frac{dC}{dY}dT - \frac{dI}{dr}d\pi^e + \frac{dI}{dY}dY + d\bar{G} + \frac{dX}{dY*}dY* \\\\ \frac{dL}{dY}dY + \frac{dL}{di}di = d\frac{M}{P} - \frac{dL}{dY}dT \\\\ \frac{dX}{dY}dY + \frac{d\sigma}{dr}i + \frac{dX}{d
ho}d
ho = \frac{d\sigma}{dr}i^* + \frac{dX}{dY^}dY^ + dK \\\\ \\\\ \implies \begin{bmatrix} F_1 & \frac{dI}{dr} & -X_
ho\\ L_Y & \frac{dX}{d
ho} & 0\\ X_Y & \sigma_r & X_
ho \end{bmatrix} \begin{bmatrix} dY\\ di\\ d
ho \end{bmatrix}

\begin{bmatrix} F_2\\ d\frac{M}{P} - \frac{dL}{dY}dT\\ F_3 \end{bmatrix} \\\\ \\\\ F_1 = 1 - \frac{dC}{dY} - \frac{dX}{dY} \\\\ F_2 = -\frac{dC}{dY}dT - \frac{dI}{dr}d\pi^e + \frac{dI}{dY}dY + d\bar{G} + \frac{dX}{dY*}dY* \\\\ F_3 = \frac{d\sigma}{dr}i^* + \frac{dX}{dY^}dY^ + dK $