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

Question

D(x) is the price, in dollar per unit, that the 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)=(x-7)^2, S(x)=x^2+2x+33

Find:

A) The equilibrium point

B) The consumer surplus at the equilibrium point

C) The producer surplus at the equilibrium point

*PLEASE ROUND TO THE NEAREST CENT AS NEEDED

Explanation / Answer

D(x)=(x-7)^2, S(x)=x^2+2x+33

a)(x-7)^2=x^2+2x+33

x^2 -14x +49 =x^2+2x+33

16x =16

x =1

p=(1-7)2 =36

equilibrium at x =1, p=36

b)consumer surplus =[0 to 1] (x-7)^2 -36 dx

consumer surplus =[0 to 1] (1/3)(x-7)^3 -36x

consumer surplus =(1/3)(1-7)^3 -36 -(1/3)(0-7)^3 +0

consumer surplus =6.33

c)producer surplus =[0 to 1] 36-(x^2+2x+33) dx

producer surplus =[0 to 1] 3-x^2-2x dx

producer surplus =[0 to 1] 3x-(1/3)x^3-x^2

producer surplus =[3*1-(1/3)1^3-1^2]-[0-0-0]

producer surplus =1.67

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