Solution:
In free trade equilibrium, quantity demanded equals quantity supplied:
100 - 10p = 10p
20p = 100
p = 5
q = 10 x 5 = 50
When p = 6, this is the market price for a price support program, since it is above equilibrium price and therefore, is binding.
Quantity demanded = 100 - (10 x 6) = 100 - 60 = 40
Quantity supplied = 10 x 6 = 60
Surplus = 60 - 40 = 20
Deficiency payment = 6 x 20 = 120
Since producers will sell only the quantity that consumers will buy, relevant quantity = 40.
From demand function, when q = 0, p = 100/10 = 10 (reservation price)
Consumer surplus (CS) = Area between demand curve and market price
CS before price floor = (1/2) x (10 - 5) x 50 = 25 x 5 = 125
CS after price floor = (1/2) x (10 - 6) x 40 = 20 x 4 = 80
Decrease in CS due to price floor = 125 - 80 = 45
When quantity supplied = 60, from demand function: 60 = 100 - 10p, or 10p = 40, or p = 4
Producer surplus (PS) = Area between supply curve and market price
PS before price floor = (1/2) x (5 - 0) x 50 = 25 x 5 = 125
PS after price floor = (1/2) x [(6 - 0) + (6 - 4)] x 40 = 20 x (6 + 2) = 20 x 8 = 160
Increase in PS after price floor = 160 - 125 = 35
Deadweight loss = (1/2) x (6 - 4) x (50 - 40) = (1/2) x 2 x 10 = 10
