Q$5(20$ points$)$

Suppose that the inverse market demand curve for cloth is $p=150-2Q,$ the private marginal cost $($unregulated competitive market supply$)$ is $=75+Q,$ and the private marginal damage from pollution is $=2Q.$

a$.(8$ points$)$ What is the unregulated competitive equilibrium quantity and price?

b$.(6$ points$)$ What is the social marginal cost of production and social equilibrium quantity and price?

c$.(6$ points$)$ What specific tax $t($per unit$)$ would result in the social optimum?