Preston owns a framing shop in his town. The market for picture frames can be described by two equations: Qd = 550 - 5P, Qs = 120 + 3P. He wants to increase the prices of his product to cover the shop’s rent expense. 

To help Preston determine the appropriate price for his picture frames, we can analyze the market equilibrium, which is the point where the quantity demanded (Qd) equals the quantity supplied (Qs). This will give us the equilibrium price (P) and quantity (Q) for picture frames in the market.

### Step 1: Set the demand and supply equations equal to each other.
\[ Q_d = Q_s \]

Substitute the given equations:
\[ 550 - 5P = 120 + 3P \]

### Step 2: Solve for the equilibrium price (P).
First, move all terms involving $ P $ to one side of the equation:
\[ 550 - 120 = 3P + 5P \]

Simplify:
\[ 430 = 8P \]

Now, solve for $ P $:
\[ P = \frac{430}{8} \]
\[ P = 53.75 \]

So, the equilibrium price is **$53.75**.

### Step 3: Find the equilibrium quantity (Q).
Now that we have the price, substitute $ P = 53.75 $ into either the demand or supply equation to find the equilibrium quantity. Let's use the demand equation:

\[ Q_d = 550 - 5(53.75) \]
\[ Q_d = 550 - 268.75 \]
\[ Q_d = 281.25 \]

So, the equilibrium quantity is **281.25 units**.

### Interpretation:
At an equilibrium price of **$53.75**, Preston can expect to sell approximately **281.25** picture frames. If Preston raises the price above this level, the quantity demanded will decrease, potentially affecting his sales volume. If the goal is to cover the shop’s rent, Preston should calculate the total revenue and compare it with his expenses.

If you would like more detailed analysis on how changes in price could impact his total revenue or have any other specific questions, feel free to ask!

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Would you like details or have any questions? Here are five related questions:

1. How would a change in rent costs affect Preston's pricing strategy?
2. What happens to the equilibrium quantity if Preston raises the price to $60?
3. How can Preston calculate the price elasticity of demand for his frames?
4. What would be the effect of a competitor entering the market on Preston’s pricing?
5. How can Preston use the concept of marginal cost to set optimal prices?

**Tip:** Always ensure that your pricing covers both fixed costs (like rent) and variable costs to maintain profitability.

Explore how to determine equilibrium price and quantity in supply and demand analysis. Solve the market equations Qd = 550 - 5P and Qs = 120 + 3P to find the equilibrium price of $53.75 and equilibrium quantity of 281.25 units. Understand the impact of pricing strategy on sales volume and profitability.

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