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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.
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