Imagine the market for Good X has a demand function of QDX = 100 – 2PX – 4PY + .05M + .1AX and a supply function of ...

To find the equilibrium quantity of good X we have to equate the supply and demand of good X because the equilibrium quantity is determined where demand equals the supply of a good.

$\begin{array}{rcl}\mathrm{QDX}& =& 100–2\mathrm{PX}–4\mathrm{PY}+.05\mathrm{M}+.1\mathrm{AX}\\ \mathrm{QSX}& =& 4\mathrm{PX}–10\\ \mathrm{PY}& =& \$3\\ \mathrm{M}& =& \$24,000\\ \mathrm{AX}& =& \$500\\ \mathrm{Put} \mathrm{QSX}& =& \mathrm{QDX}\\ 4\mathrm{PX}–10& =& 100–2\mathrm{PX}–4\mathrm{PY}+.05\mathrm{M}+.1\mathrm{AX}\\ 4\mathrm{PX}–10& =& 100–2\mathrm{PX}–(4\times 3)+(0.05\times 24,000)+(0.1\times 500)\\ 4\mathrm{PX}–10& =& 100–2\mathrm{PX}–12+1,200+50\\ 4\mathrm{PX}+2\mathrm{PX}& =& 100–12+1,200+50+10\\ 6\mathrm{PX}& =& 88+1,200+50+10\\ 6\mathrm{PX}& =& 1,288+50+10\\ 6\mathrm{PX}& =& 1,338+10\\ 6\mathrm{PX}& =& 1,348\\ \mathrm{PX}& =& \frac{1,348}{6}\\ \mathrm{PX}& =& 224.67\\ \mathrm{Put} \mathrm{PX}& =& 224.67 \mathrm{in} \mathrm{supply} \mathrm{equation} \mathrm{to} \mathrm{find} \mathrm{equilibrium} \mathrm{quantity}.\\ \mathrm{QSX}& =& 4\mathrm{PX}–10\\ \mathrm{QSX}& =& 4\times 224.67–10\\ \mathrm{QSX}& =& 898.68–10\\ \mathrm{QSX}& =& 888.68\\ \mathrm{The} \mathrm{equilibrium} \mathrm{quantity} \mathrm{of} \mathrm{good} \mathrm{X}& =& 888.68\end{array}$

Therefore, the equilibrium quantity of good X is 888.68 units.