Jim Whitney Economics 102
 Illustrating the Social Gains from Trade: A Free Market Equilibrium
  (1) Demand:      Qd = 24 - 2P
                       (=> Pb = 12 - (1/2)Q)
 (2) Supply:      Qs = -6 + 3P
                       (=> Ps = 2 + (1/3)Q)
 (3) Equilibrium: Qd = Qs

To find the equilibrium P:
      Qd = Qs
 24 - 2P = -6 + 3P
      30 = 5P
       P = 6
 Q = 24 - 2(6) = -6 + 3(6) = 12
 

1. Equilibrium: Social welfare if output = 12
     Consumer surplus (CS) = 1/2 x (12 - 6) x 12 = $______ million
     Producer surplus (PS) = 1/2 x  (6 - 2) x 12 = $______ million
     Society's welfare gains from trade in wine  = $______ million

2. Underproduction: How much social welfare is lost if output stops at 9?
     In the diagram, the lost social welfare = A + B
     A. To find the area of A, we have to determine how high the demand
        curve is at Q = 9:
          From equation (1):  Pb = 12 - (1/2)Q = 12 - (1/2)9 = ______
          So A = 1/2 x (______ - 6) x (12 - 9) = $______ million loss
     B. To find the area of B, we have to determine how high the supply
        curve is a at Q = 9:
          From equation (2):  Ps = 2 + (1/3)Q = 2 + (1/3)9 = ______
          So B = 1/2 x (6 - ______) x (12 - 9) = $______ million loss
     So A + B = $______ million + $______ million = $______ million
     Society's gains from trade fall to $60 - $______ = $______ million.

3. Overproduction: How much social welfare is lost if Q continues to 18?
     In the diagram, the lost social welfare = C + D
     C. To find the area of C, we have to determine how high the supply
        curve is a at Q = 18:
          From equation (2):  Ps = 2 + (1/3)Q = 2 + (1/3)18 = ______
          So C = 1/2 x (______ - 6) x (18 - 12) = $______ million loss
     D. To find the area of D, we have to determine how high the demand
        curve is at Q = 18:
          From equation (1):  Pb = 12 - (1/2)Q = 12 - (1/2)18 = ______
          So D = 1/2 x (6 - ______) x (18 - 12) = $______ million loss
     So C + D = $______ million + $______ million = $______ million
     Society's gains from trade fall to $60 - $______ = $______ million
 
NOTE: These social welfare losses from underproduction and overproduction are also called deadweight losses or efficiency losses.