Chapter 5.1, Problem 21E

In Exercises 17–22, a price ceiling or price floor is given along with demand and supply functions, where D(x) is the price, in dollars per unit, that consumers will pay for $x$ units, and S(x) is the price, in dollars per unit, at which producers will sell $x$ units. Find (a) the equilibrium point, (b) the point $(x_C,p_C\text{) }or\text{ (}{x}_F,p_F)$, (c) the new consumer surplus, (d) the new producer surplus, and (e) the deadweight loss.

21. $D\left(x\right)=30+{\left(x-\text{1}0\right)}^2,S\left(x\right)=x^2,P_C=\$30\left(Assumex\le \text{1}0\right)$