PLEASE BREAK EVERYTHING DOWN SO I CAN SEE EXACTLY HOW YOU GOT THE ANSWER, I NEED THE ANSWERS TO SEE HOW TO DO FUTURE ONES. $1.$ Suppose that firms in a perfectly competitive industry produce a product in amount Q$.$ The demand curve for the product is given by

QD $=8002$P$,$ where P is the price. The supply curve is given by

Q S $=12$ P $.$

$($a$)$ Derive expressions for the marginal willingness to pay $($MWTP$)$ and marginal

cost $($MC$)$ curves.

$($b$)$ Find the equilibrium price and quantity of the good.

$($c$)$ At the equiibrium level of production, compute the following:

i$.$ the consumers$$ surplus;

ii$.$ the total value $($total willingness to pay$)$ of all the units sold to the con$-$ sumers;

iii. the producers$$ surplus;

iv$.$ the net total social benefit.

$2.$ Suppose, now, that the production process in the previous question results in marginal external damage with costs given by MEC $=2$Q$.$

$($a$)$ Derive an expression for the social marginal cost $($SMC$)$ curve. $[$Remember$,$

you are adding costs, not quantities.$]$

$($b$)$ Find the socially efficient level of production and consumption.

$($c$)$ Explain in words why the socially efficient level is lower than the market equi$-$ librium found in the previous question.

$($d$)$ Compute each of the following when moving from the market equilibrium to the socially efficient outcome:

i$.$ the loss in market surplus;

ii$.$ the value of the reduction in external damage.

$($e$)$ Compute the value of the social gain in moving from the market equilibrium to the socially efficent level of Q$.$II