The market for coal has the following demand and supply curves:

$Q_D=100-P$

$Q_S=-40+P$

The usage of coal increases pollution, generating a marginal external cost $($negative externality$)$

MEC$=8$

Find the perfectly competitive equilibrium.

a$)$ Price $(P_c)$

b$)$ Quantity $($Qc$)$

Note: In which firms do not internalize the negative externality

c$)$ Consumer Surplus

d$)$ Producer surplus and

e$)$ The Total Surplus

Note : $($do not forget to subtract the negative externality when calculating total surplus$)$

Assume that now the government imposes a tax of $$8$ per unit of coal produced to eliminate

market inefficiencies. Find :

f$)$ The socially optimal equilibrium Price $(P_{\text{S}\text{o}\text{c}})$

g$)$ Quantity $($Qsoc