x is the price in dollars per unit that consumers are willin

x) is the price, in dollars per unit, that consumers are willing to pay for x unit uilibrium point, (b) the consumer surplus at the equilibrium point, and (c) the D(x)=-15 x + 28, S(x)=+ 4 Find the equilibrium point. Type an ordered pair, using integers or decimals.) Find the consumer surplus at the equilibrium point. (Type an integer or a decimal) Find the producer surplus at the equilibrium point. (Type an integer or a decimal.) ryour answer in each of the answer boxes.

Solution

The demand function you are given is

D(x)= (-7/15)x + 28

The supply function you are given is

S(x) = x/3 + 4

Equate demand and supply to find the equilibrium quantity, x.

(-7/15)x + 28 = x/3 + 4

(12/15)x = 24

x = 30

The equilibrium price is obtained by substituting x=30 into either the demand or supply functions.

p = (-7/15)*30 + 28 = 14

Consumer surplus is the integral of [D(x)-p]dx from 0 to 30.

D(x) = (-7/15)x + 28

Integral of D(x) = (-7/30)x² + 28x

Producer surplus is the integral of [p-S(x)]dx from 0 to 30

Integral of S(x) = x²/6 + 4x

Hope this helps.