Question

2. For each of the following situations solve for the amount of consumer, producer, and total surplus found in the market: a. Qd = -4p + 120; Qs = 2p b. Qd = -5p + 100; Qs = 4p - 44 c. Qd = -2p + 70; Qs = 3p + 20

Answer 1

a) -4P+120 = 2P

-4P-2P = -120

-6P = -120

P = 120/6 = 20

Q = 2P = 40

Maximum reservation price = 120/4 = 30

Minimum reservation price = 0

CS = 0.5*40*(30-20) = 200

PS = 0.5*40*(20-0) = 400

TS = CS+PS = 600

b) -5P+100 = 4P-44

-5P-4P = -44-100

P = 144/9 = 16

Q = 4P-44 = 20

CS = 0.5*20*(20-16) = 40

PS = 0.5*20*(16-10) = 60

TS = 40+60 = 100

c) -2P+70 = 3P+20

70-20 = 3P+2P

P = 50/5 = 10

Q= 3P+20 = 50

CS = 0.5*50*(35-10) = 625

PS = 0.5*50*(10-6.67) = 83.25

TS = 625+83.25 = 708.25