$(2021$ Summer Final Q$53-56)$ A perfectly competitive market is initially in a long run equilibrium, with $\backslash ($ n $\backslash )$ identical firms $(\backslash ($ n $\backslash )$ can take non$-$integer values$).$ The demand curve and the shortPage $14$ it supply curve are given as follows.

Supply: $\backslash ($ Q$=2$ P$-1\backslash )$ thousand units

Demand: $\backslash ($ Q$=2100-4$ P $\backslash )$ thousand units

$($a$)$ The equilibrium price is dollars per unit and the equilibrium quantity is thousand units.

$($b$)$ Suppose there is an increase in demand such that each consumer's willingness to pay increases by $100$ dollars, and suppose this is a constant cost industry. Then, the quantity traded in the market is thousand units when the market reaches a long run equilibrium again.

$($c$)$ Continue with the previous question. Suppose the new entrants and the incumbent firms are all identical. After the increase in demand, $10$ new firms eventually enter the market so that a new long run equilibrium is reached. The average cost curve of an individual firm is minimized at $\backslash ($ q$=\backslash )$ thousand units.

$($d$)$ The average cost at this quantity is dollars per unit.