Widgets are supplied by a perfectly competitive market. The marginal internal cost function is given MCI(Q) = (1/2)Q. Unfortunately, production of widgets also produces pollution, which has a marginal damage to society given by MCX(Q) = Q, where Q denotes the total number of widgets produced. Aggregate demand in the widget market is given by Qd(p) = 100-p.

a. find out the socially efficient level of widget sales.

b. find out the competitive equilibrium output of widgets.

c. find out the tax (or subsidy) that the government should impose per widget to obtain the socially efficient production at the resulting competitive equilibrium.

d. Suppose that the widget makers all merge, so the above supply function also represents the marginal cost function for the new widget monopolist. Is social welfare higher under competition (your solution in (b)) or under monopoly? describe.