a.Horizontal summation implies that the addition is taking place across quantities. Horizontal summation is appropriate when demands are competing. Competing demands imply the consumption by one individual detracts from the potential enjoyment of others.
Vertical assumption is appropriate when demands are non-competing so that consumption by one individual does not detract from the potential for others to enjoy the good. Non-competing demands imply zero marginal cost for additional users. Vertical summation implies that addition is across price.Vertical summation
P = P
A + P
B + P
C P = [(500 - 2Q
A) + (300 - Q
B) + (400 - 2Q
C)]
P = 1,200 - 5Q
To sum horizontally, we solve for Q (for Q < 200)
P
A = 500 - 2Q
A Q
A = 250 - 0.5P
A P
B = 300 - Q
B Q
B = 300 - P
B P
C = 400 - 2Q
C Q
C = 200 - 0.5P
C Q = Q
A + Q
B + Q
C Q = [(250 - 0.5P
A) + (300 - P
B) + (200 - 0.5P
C)]
Q = 750 - 2P
b.Since satellite transmission is a public good, the demands are non-competing. This suggests that a vertically summed demand curve is appropriate. Efficiency requires that P be set equal to MC, i.e., 0. This occurs where
i.e., where prize for consumer B is equal to 0.