Consider a product market with three consumers X, Y and Z with demand function Q_X = 6 - P_X, Q_Y = 3 - P_Y and Q_Z = 12 - P_Z respectively, where P is the price in dollars and Q_X, Q_Y and Q_Zare the quantities demanded by Consumer X, Y and Z respectively.

If the product is public good, obtain the marginal social benefit function and draw the diagram.

Determine the optimal quantity of the product in the market if the marginal cost of the product is constant at (a) $4, (b) $9 and (c) $16.