For the given supply and demand equations,find the consumer surplus. Demand
Supply $p = 100 - 0.00006 x$ $p = 80 + 0.00002 x$

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. Demand
Supply $p = 100 - 0.00006 x$ $p = 80 + 0.00002 x$ ​
​
A)$1,875,000
B)$2,812,500
C)$2,062,500
D)$2,250,000
E)$625,000

Quizplus · Accepted Answer

The consumer surplus is calculated as the area between the demand curve and the equilibrium price, up to the equilibrium quantity. First, find the equilibrium by setting demand equal to supply: $100 - 0.00006x = 80 + 0.00002x$. Solving gives $x = 250,000$. The equilibrium price is $p = 95$. The consumer surplus is the area of the triangle with base $250,000$ and height $5$ (difference between maximum price 100 and equilibrium price 95), which is $\frac{1}{2} \times 250,000 \times 5 = 625,000$.

For the Given Supply and Demand Equations,find the Consumer Surplus p=100−0.00006xp = 100 - 0.00006 xp=100−0.00006x

For the Given Supply and Demand Equations,find the Consumer Surplus $p = 100 - 0.00006 x$