Next-nano inc. is about to release a software upgrade that includes some new functionalities. The market study reveals that the demand to be
q = D(p) = 1000sqrt(200-2p) . The willingness to order such an upgrade is given by the supply curve q = S(p) = 1000sqrt(10p-400).
b) Determine the consumers’ surplus at the equilibrium price (p = 50, q = 10000)
c) Determine the producers’ surplus at the equilibrium price (p = 50, q = 10000)
To find the equilibrium price and quantity, we need to set the demand equal to the supply:
1000sqrt(200-2p) = 1000sqrt(10p-400)
200-2p = 10p-400
12p = 600
p = 50
Substituting p = 50 into either the demand or the supply curve gives us the equilibrium quantity:
q = D(50) = S(50) = 1000sqrt(100) = 10000
b) To find the consumers’ surplus, we need to calculate the area between the demand curve and the equilibrium price line (a horizontal line at q = 10000 and p = 50):
Consumers' surplus = ½ (200-50) * (10000 - 1000sqrt(150)) = $87,287.68
c) To find the producers’ surplus, we need to calculate the area between the supply curve and the equilibrium price line:
Producers' surplus = ½ (50-0) * (1000sqrt(150) - 0) = $5,590.17
Note: We assume that the cost of producing the software upgrade is the same for all producers, so the producers' surplus is the same as the profit they make.