Consider a product market with three consumers X, Y and Z with demand function P_X = 6 - Q_X, P_Y = 12 - Q_Y and P_Z = 18 - Q_Z respectively, where P is the price in dollars and Q_X, Q_Y and Q_Z are 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) $3, (b) $9 and (c) $21.