Calculate the consumers' surplus at the indicated unit price

p
for the demand equation. HINT [See Example 1.] (Round your answer to the nearest cent.)

p = 150 − q; p = 30

Calculate the consumers' surplus at the indicated unit price

p
for the demand equation. HINT [See Example 1.] (Round your answer to the nearest cent.)
p = 10 − 2q; p = 1

Calculate the consumers' surplus at the indicated unit price

p
for the demand equation. HINT [See Example 1.] (Round your answer to the nearest cent.)
p = 12 − 2q; p = 2

Sure, let's start by finding the quantity demanded when p = 30. We can rearrange the demand equation to solve for q:

p = 150 - q

Substituting p = 30:

30 = 150 - q

Now let's solve for q:

q = 150 - 30
q = 120

So, when the unit price is 30, the quantity demanded is 120 units.

To calculate the consumer surplus, we need to find the area under the demand curve up to the unit price of 30. The formula for consumer surplus is:

Consumer Surplus = (1/2) * Base * Height

The base is the quantity demanded (120) and the height is the difference between the equilibrium price (150) and the unit price (30). Let's calculate it:

Consumer Surplus = (1/2) * 120 * (150 - 30)
Consumer Surplus = (1/2) * 120 * 120
Consumer Surplus = 60 * 120
Consumer Surplus = 7200

Therefore, the consumer surplus at the unit price of 30 is $7200.

To calculate the consumers' surplus at the indicated unit price, we'll first solve the demand equation for the quantity (q) at the given unit price (p).

Given:
Demand equation: p = 150 - q
Unit price: p = 30

We can substitute p = 30 into the demand equation and solve for q:

30 = 150 - q

Rearranging the equation, we have:
q = 150 - 30
q = 120

Now that we know the quantity (q) corresponding to the unit price (p = 30), we can calculate the consumers' surplus.

Consumers' Surplus = (1/2) * (Quantity at Original Price - Quantity at Given Price) * (Original Price)

Using the values we found:
Consumers' Surplus = (1/2) * (120 - 0) * (150)

Calculating further:
Consumers' Surplus = (1/2) * 120 * 150
Consumers' Surplus = 60 * 150
Consumers' Surplus = 9000

Therefore, the consumers' surplus at the indicated unit price is $9000.

Hint: substitute 30 for p and solve for q.