Question

In: Economics

The supply and demand for squash are given by QD = 200,000 – 50,000P and QS...

The supply and demand for squash are given by QD = 200,000 – 50,000P and QS = 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?

Solutions

Expert Solution

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


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