D(x) is the price, in dollars per unit, that consumers are willing to pay for x

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 produces 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) = 3500 -40 x, S(x) = 2150 + 5x What are the coordinates of the equilibrium point? What is the consumer surplus at the equilibrium point? What is the producer surplus at the equilibrium point?

Explanation / Answer

a) for equilibrium D(x)=S(x)

3600-40x=2150+5x

40x+5x=3500-2150

45x=1350

x=30

p=D(30)=3500-40*30=2300

coordinates are (x,p)=(30,2300)

b) consumer surplus =[0 to 30] D(x) -2300 dx

consumer surplus =[0 to 30] (3500-40x) -2300 dx

consumer surplus =[0 to 30] (1200-40x) dx

consumer surplus =[0 to 30] (1200x-20x2)

consumer surplus = (1200*30-20*302)-0

consumer surplus = 18000$

c)producersurplus =[0 to 30] 2300 -S(x) dx

producersurplus =[0 to 30] 2300 -(2150+5x) dx

producersurplus =[0 to 30] 150-5x dx

producersurplus =[0 to 30] 150x-(5/2)x2

producersurplus = 150*30-(5/2)302 -0

producersurplus = 2250$

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