Question

The supply and demand for squash are given by Q^D = 200,000 – 50,000P and Q^S = 90,000P – 80,000, where P is price per pound and Q measures pounds of squash.
a. What is the level of consumer surplus at the equilibrium price?
b. What is the level of producer surplus at the equilibrium price?

Answer 1

a. At equilibrium, QD = QS.
So, 200,000 - 50,000P = 90,000P - 80,000
So, 90,000P + 50,000P = 200,000 + 80,000
So, 140,000P = 280,000
So, P = 280,000/140,000
So, P = 2
Q = 200,000 – 50,000P = 200,000 – 50,000(2) = 200,000 – 100,000 = 100,000

Maximum P when QD = 0 is 0 = 200,000 – 50,000P
So, 50,000P = 200,000
So, Pmax = 200,000/50,000 = 4

CS = area of triangle = (1/2)*base*height = (1/2)*Q*(Pmax-P) = (1/2)*100,000*(4-2) = 100,000
So, CS = 100,000

b. Minimum P when QS = 0 is 90,000P – 80,000 = 0
So, 90,000P = 80,000
So, Pmin = 80,000/90,000 = 0.89

PS = area of triangle = (1/2)*base*height = (1/2)*Q*(P-Pmin) = (1/2)*100,000*(2-0.89) = 50,000*(1.11) = 55,500
So, PS = 55,500