D(x) is the price, in dollars per unit, that consumers are willing to pay for x
ID: 2880597 • Letter: D
Question
D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. Find the equilibrium point, the consumer surplus at the equilibrium point, and the producer surplus at the equilibrium point. D(x) = -5/6x + 18, S(x) = 1/2x + 2 D(x) is the price, in dollars per unit, that consumers are willing to pay for x units of an item, and S(x) is the price, in dollars per unit, that producers are willing to accept for x units. Find the equilibrium point, the consumer surplus at the equilibrium point, and the producer surplus at the equilibrium point. D(x) = -7/10x + 15, S(x) = 1/2x + 3Explanation / Answer
1)D(x)=(-5/6)x +18 ,S(x)=(1/2)x +2
for equilibriu D(x)=S(x)
(-5/6)x +18=(1/2)x +2
(1/2)x +(5/6)x=18-2
(8/6)x=16
x=16*6/8
x=12
equilibrium point x =12
at x =12
p=S(12)=(1/2)*12 +2
p=6+2
p=8
b) consumer surplus =[0 to 12](D(x) -p) dx
consumer surplus =[0 to 12]((-5/6)x +18 -8) dx
consumer surplus =[0 to 12]((-5/6)x +10) dx
consumer surplus =[0 to 12]((-5/6)(1/2)x2 +10x)
consumer surplus =[0 to 12]((-5/12)x2 +10x)
consumer surplus =((-5/12)122 +10*12)-((-5/12)02 +10*0)
consumer surplus =(-60 +120)-0
consumer surplus =60$
c) producer surplus =[0 to 12](p-S(x)) dx
producer surplus =[0 to 12](8-(1/2)x -2) dx
producer surplus =[0 to 12](6-(1/2)x) dx
producer surplus =[0 to 12](6x-(1/2)(1/2)x2)
producer surplus =[0 to 12](6x-(1/4)x2)
producer surplus =(6*12-(1/4)122) -(6*0-(1/4)02)
producer surplus =(72-36) -0
producer surplus =36$
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