An umbrella-manufacturer in a perfectly competitive market [price-taker} faces an inverse demand curve given by PG?) 2 10 Q. The cost-function of the rm is given by C0?) = 2Q + EQZ. Suppose that producing an umbrella is a very polluting process, and the marginal external damage cost of every umbrella is estimated to be 4 dollars, so that the total health cost of producing Q umbrellas is C9 (Q) = 40. A} Find the marginal {private} cost function of the umbrella manufacturer. B} Add the marginal external damage cost to the marginal private cost function C] to obtain the marginal social cost function, which tells us the total cost (private + external} of producing one more umbrella, in terms of the number of umbrellas already produced. Acknowledging the fact that the supply function of the umbrella- manufacturer will coincide with its marginal cost function and that market forces lead to the equalization of supply and demand, nd the equilibrium number of umbrellas, Q", and the equilibrium price, P\". D} Given the quantity and price you found in C}, nd the consumer surplus, CS, E} F] private producer surplus, P3P, total health cost, C9, social producer surplus, P53, and social welfare W3. Feel free to use the graph at the end of this assignment to aid yourself in guring out the calculations you must do to nd these numbers. Now, suppose the umbrella-manufacturer is socially-conscious and takes into account (internalizes) the cost that its production of umbrellas induces on the health of the community. This means it acts as if its marginal cost function (and consequently, its supply function} were the marginal social cost function you found in B}. Find the equilibrium quantity, G, and price, F, that would be observed in the market if this were the case. Find again the quantities you calculated in part D}, but this time using the quantity and price you found in E}. Also calculate the deadweight-loss, DWL, induced by the pollution externality. As before, feel free to consult the graph at the end of this assignment to gure out the required calculations