The marginal cost (MC) of supplying a material used in the construction of a government project is MC = Q/100 where Q is the quantity. The private (inverse) demand curve for the good is P = (6 4Q)/100. The government will need 50 added units of Q at every price P.

a)Derive the expression for the new (inverse) demand curve that includes the government's demand.

b)Calculate the pre- and post-government equilibrium quantity and price.

c)By how much did total output increase as a result of the government's demand for the material? By how much did the private sector's quantity demanded fall as a result of the increase in price?

d)Determine the total social cost of the extra units produced to meet the government's needs.