Suppose that a consumer's demand curve for a good can be expressed as $P = 50 - 4 Q ^ { d }$ . Suppose that the market is initially in equilibrium at a price of $10. What is the consumer surplus at the original equilibrium price?
A)100
B)150
C)200
D)250.

Question

Quizplus · Accepted Answer

To find consumer surplus, we need to calculate the area below the demand curve, above the equilibrium price, and up to the quantity demanded at that price.

First, we need to find the quantity demanded at the original equilibrium price of $10:
$10 = 50 - 4Q^d
4Q^d = 40
Q^d = 10

So, the quantity demanded at the original equilibrium price is 10.

Next, we can plug this quantity into the demand equation to find the corresponding price:
P = 50 - 4Q^d
P = 50 - 4(10)
P = 10

As expected, the price we calculated is the same as the original equilibrium price.

Now we can calculate consumer surplus as the area of the triangle formed by the demand curve, the price axis (which is the same as the supply curve), and the vertical line at the equilibrium quantity:

Consumer Surplus = 0.5 x Base x Height
Consumer Surplus = 0.5 x (10-0) x (50-10)
Consumer Surplus = 0.5 x 10 x 40
Consumer Surplus = 200

Therefore, the consumer surplus at the original equilibrium price is $200. To find the consumer surplus at the original equilibrium price, we need to calculate the area below the demand curve and above the equilibrium price of $10.

First, we need to find the quantity demanded at the equilibrium price:

$10 = 50 - 4Q^d
$40 = 4Q^d
Q^d = 10

So the quantity demanded at the equilibrium price is 10.

Now we can calculate the consumer surplus:

CS = 1/2 * base * height
CS = 1/2 * ($40 - $10) * 10
CS = 1/2 * $30 * 10
CS = $150

Therefore, the consumer surplus at the original equilibrium price is $150, which corresponds to choice (C).

Suppose That a Consumer's Demand Curve for a Good Can P=50−4QdP = 50 - 4 Q ^ { d }P=50−4Qd

Suppose That a Consumer's Demand Curve for a Good Can $P = 50 - 4 Q ^ { d }$