Find the consumer surplus and producer surplus.
Demand $p = 100 - 0.03 x$
Supply $p = 35 + 0.1 x$
A)Consumer surplus: $3,750Producer surplus: $12,800
B)Consumer surplus: $3,750Producer surplus: $12,500
C)Consumer surplus: $3,750Producer surplus: $12,600
D)Consumer surplus: $3,750Producer surplus: $12,900
E)Consumer surplus: $3,750Producer surplus: $12,700

Question

Find the consumer surplus and producer surplus. 
Demand $p = 100 - 0.03 x$  
Supply $p = 35 + 0.1 x$  
A)Consumer surplus: $3,750Producer surplus: $12,800
B)Consumer surplus: $3,750Producer surplus: $12,500
C)Consumer surplus: $3,750Producer surplus: $12,600
D)Consumer surplus: $3,750Producer surplus: $12,900
E)Consumer surplus: $3,750Producer surplus: $12,700

Quizplus · Accepted Answer

To find the equilibrium price and quantity, set the demand and supply equations equal to each other: $100 - 0.03x = 35 + 0.1x$. Solving for $x$ gives $0.13x = 65$, so $x = 500$. Substituting $x = 500$ into either the demand or supply equation to find the equilibrium price, $p = 35 + 0.1(500) = 85$. Consumer surplus is the area of the triangle above the supply curve and below the demand curve up to the equilibrium quantity. The formula for the area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$, where the base is the equilibrium quantity (500) and the height is the difference between the maximum price consumers are willing to pay (100) and the equilibrium price (85). Thus, consumer surplus = $\frac{1}{2} \times 500 \times (100 - 85) = \frac{1}{2} \times 500 \times 15 = 3750$.Producer surplus is the area below the equilibrium price and above the supply curve up to the equilibrium quantity. The base is again the equilibrium quantity (500) and the height is the difference between the equilibrium price (85) and the minimum price producers are willing to accept (35). Thus, producer surplus = $\frac{1}{2} \times 500 \times (85 - 35) = \frac{1}{2} \times 500 \times 50 = 12500$.Therefore, the correct answer is Consumer surplus: $3,750, Producer surplus: $12,500.

Find the Consumer Surplus and Producer Surplus p=100−0.03xp = 100 - 0.03 xp=100−0.03x

Find the Consumer Surplus and Producer Surplus $p = 100 - 0.03 x$