D(x) is the price, in dollars per unit, that consumers are willing to pay for x
ID: 2893778 • 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 (a) the equilibrium point, (b) the consumer surplus at the equilibrium point, and (c) the producer surplus at the equilibrium point. D(x) = 3000 - 30x, S(x) = 300 + 15x (a) What are the coordinates of the equilibrium point? __ (Type an ordered pair.) (b) What is the consumer surplus at the equilibrium point? $__ (Round to the nearest cent as needed.) (c) What is the producer surplus at the equilibrium point? $___ (Round to the nearest cent as needed.)Explanation / Answer
given D(x)=3000-30x,S(x)=300+15x
(a)
for equilibrium ,D(x)=S(x)
3000-30x=300+15x
=>45x=2700
=>x=60
p=S(60)=300+(15*60) = 1200
equilibrium point is (p,x)=(1200,60)
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(b)
consumer surplus =[0 to 60](D(x)-p) dx
consumer surplus =[0 to 60](3000-30x -1200) dx
consumer surplus =[0 to 60](1800-30x) dx
consumer surplus =[0 to 60](1800x-15x2)
consumer surplus =(1800*60-15*602) -(1800*0 -15*02)
consumer surplus =(108000-54000) -0
consumer surplus =54000 $
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(c)
producer surplus =[0 to 60](p-S(x)) dx
producer surplus =[0 to 60](1200- 300-15x) dx
producer surplus =[0 to 60](900-15x) dx
producer surplus =[0 to 60](900x-(15/2)x2)
producer surplus =(900*60-(15/2)*602) -(900*0-(15/2)*02)
producer surplus =(54000-27000) -0
producer surplus =27000 $
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