a market is charactzed by the equations below: p=24+6q, p=400-2q. a price floor of $360 has been imposed on this market. what is the producer surplus after the price floor?

To find the producer surplus after a price floor of $360 is imposed, we need to follow these steps:

### Step 1: Find the equilibrium quantity and price
Set the supply equation equal to the demand equation to find the equilibrium quantity and price:

\[
24 + 6q = 400 - 2q
\]

Combining like terms gives:

\[
8q = 376 \implies q = 47
\]

Substitute $ q = 47 $ into either the supply or demand equation to find the equilibrium price:

\[
p = 24 + 6(47) = 24 + 282 = 306
\]

Thus, the equilibrium price and quantity are $ p = 306 $ and $ q = 47 $.

### Step 2: Calculate the new quantity supplied at the price floor
At the price floor of $360, use the supply equation to find the quantity supplied:

\[
360 = 24 + 6q \implies 6q = 336 \implies q = 56
\]

So, at the price floor, the quantity supplied is 56.

### Step 3: Calculate the producer surplus
The producer surplus is the area of the triangle below the price floor and above the supply curve. 

1. **Base of the triangle**: $ q = 56 $
2. **Height of the triangle**: $ 360 - 24 = 336 $

The area of the triangle representing the producer surplus is given by:

\[
\text{Producer Surplus} = \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 56 \times 336 = 9408
\]

Therefore, the producer surplus after the price floor is $9,408.

Would you like to know more details or have any questions? Here are five questions to expand your understanding:

1. What would happen to the producer surplus if the price floor was set at a different level?
2. How does the imposition of a price floor affect consumer surplus in this market?
3. Could there be any deadweight loss associated with the price floor, and if so, how would it be calculated?
4. What are the implications for government policy if the market supply or demand curves were different?
5. How would the outcome change if a price ceiling were imposed instead?

**Tip:** When calculating surpluses or deadweight loss, always pay attention to the area under the curves, as they represent economic values like consumer and producer surplus.

A market is characterized by the equations: p = 24 + 6q, p = 400 - 2q. A price floor of $360 has been imposed on this market. What is the producer surplus after the price floor?

Learn how to calculate the producer surplus after a price floor of $360 is imposed in a market defined by supply and demand equations. This step-by-step solution involves finding the equilibrium quantity and price, applying the price floor, and using geometric formulas to compute the producer surplus.

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