Suppose a monopoly market has only two types of consumers: low $($L$)$ and high $($H$).$ The low$-$type

consumers have the combined demand function:

P $=2002$Q

and the high$-$types have

P $=300$ Q

If the monopoly can tell which consumers are high$-$types and which are low$-$types, then how much

will the they supply to the high$-$types and how much to the low$-$types? The monopoly$$s cost function

is:

C$($Q$)=$ Q

$2$

$4.$ Find $($all$)$ the Nash equilibrium of the above game. Is it unique?