For the given supply and demand equations, find the consumer surplus.$\begin{array}{lr}\text { Demand }&\text { Supply }\
p=100-0.00006 x&p=80+0.00002 x
\end{array}$

A)$1,875,000
B)$2,812,500
C)$2,062,500
D)$2,250,000
E)$625,000

Question

For the given supply and demand equations, find the consumer surplus.$\begin{array}{lr}\text { Demand }&\text { Supply }\
p=100-0.00006 x&p=80+0.00002 x
\end{array}$

A)$1,875,000
B)$2,812,500
C)$2,062,500
D)$2,250,000
E)$625,000

Quizplus · Accepted Answer

Consumer surplus is the area below the demand curve and above the equilibrium price. The equilibrium price is found by setting the demand and supply equations equal to each other and solving for p.$$100-0.00006x=80+0.00002x$$$$0.00008x=20$$$$x=250,000$$$$p=100-0.00006(250,000)=80$$The consumer surplus is then:$$\int_0^{250,000}(100-0.00006x-80)dx=\int_0^{250,000}20dx=20x\bigg|_0^{250,000}=5,000,000$$$$CS=\frac{1}{2} 	imes 20 	imes 250,000 = 2,500,000$$

For the Given Supply and Demand Equations, Find the Consumer Demand Supply p=100−0.00006xp=80+0.00002x\begin{array}{lr}\text { Demand }&\text { Supply }\\p=100-0.00006 x&p=80+0.00002 x\end{array} Demand p=100−0.00006x​ Supply p=80+0.00002x​

For the Given Supply and Demand Equations, Find the Consumer $\begin{array}{lr}\text { Demand }&\text { Supply }\\p=100-0.00006 x&p=80+0.00002 x\end{array}$