$(8$ points$)$ Let the supply and demand functions for sugar be given by

$p=S(q)=1\mathrm{.}5q-0\mathrm{.}8$ and $p=D(q)=-1\mathrm{.}7q+3\mathrm{.}2$

where $p$ is the price per pound and $q$ is the quantity in thousands of pounds.

$QD$

$($a$)$ Find the equilibrium quantity and the equilibrium price.$*$

$-1\mathrm{.}7q+3\mathrm{.}2=1\mathrm{.}5q-0\mathrm{.}8$

$1\mathrm{.}5q-1\mathrm{.}5q$

$3\mathrm{.}2q+3\mathrm{.}2=-0\mathrm{.}8$

$-3\mathrm{.}2-3\mathrm{.}2$

$\frac{3\mathrm{.}2q}{3\mathrm{.}2}=\frac{4}{3\mathrm{.}2}$

$q=1\mathrm{.}25$

Th equilibrium price aprox $$1\mathrm{.}75$

$q=1\mathrm{.}25$

Cequilibrium Quanity is

aprox. $1250$ pounds

$($b$)$ If the price of sugar is $$1\mathrm{.}20,$ will there be a shortage or a surplus of this product? Explain.$*$