$4.(12$ marks$)$ Consider a manufactured good whose production process generates pollution. The annualdemand for the good is given by Qd $=100-3$P$.$ The annual market supply is given by Qs $=$ P$.$ For everyunit of output produced, the industry emits one unit of pollution. The marginal damage from each unit of pollution is given by $2$Q$.$a$.$ Draw a diagram that depicts the industry described above. Find the equilibrium price and quantity in a market with no government intervention. Depict the equilibrium price and quantity on your diagram.b$.$ What is the efficient level of output in this industry? Depict the efficient level of output on your diagram above.c$.$ Shade the areas that correspond to CS$,$ PS and DWL in the absence of government regulation.d$.$ Now draw a new diagram with the information in $($a$)$ and $($b$)$ incorporated, but this time shade the areas that correspond to CS$,$ PS and DWL if the efficient output were produced.e$.$ Will there still be some pollution at the efficient level of output? Explain.