Engine standards. Let inverse demand for new vehicles be given by P $=40,0000\mathrm{.}05$Q and inverse

supply is initially given by P$0=8,000+0\mathrm{.}03$Q$.$ Suppose new engine standards require costly technology

adoption, shifting the supply for new vehicles up to P$1=10,000+0\mathrm{.}05$Q$.$ Prior to the engine standards,

new vehicles generate $$1200$ of damages per year and used vehicles generated $$2100$ of damages per

year. Following the engine standards, new vehicles generate $$900$ of damages per year.

$($a$)$ What was the pre$-$standard quantity of new vehicles sold and post$-$standard quantity of new

vehicles sold