Question
determining the long-run equilibrium price in a perfectly competitive industry where firms have identical cost structures
Answers
GPT-4o mini
In a perfectly competitive market, the long-run equilibrium price is determined by the interaction of supply and demand, ensuring that firms earn zero economic profit. Here’s how to determine the long-run equilibrium price in an industry where firms have identical cost structures:
### Steps to Determine Long-Run Equilibrium Price:
1. **Understand Cost Structures**:
- Firms in a perfectly competitive market have identical cost structures, meaning they have the same marginal cost (MC), average total cost (ATC), and average variable cost (AVC) curves.
- Identify the fixed costs (FC) and variable costs (VC) to derive the ATC:
\[
\text{ATC} = \frac{FC + VC}{Q}
\]
- Marginal cost (MC) represents the cost of producing one additional unit of output and is derived from the variable cost function.
2. **Establish Market Demand and Supply**:
- Determine the market demand curve, which is typically downward sloping, indicating that as price decreases, quantity demanded increases.
- The market supply curve in long-run equilibrium is typically horizontal at the price where firms are making zero economic profits. This is often at the minimum point of the ATC curve.
3. **Identify the Price (P = ATC)**:
- In long-run equilibrium, firms will enter or exit the market until they are earning zero economic profits. This occurs when the market price (P) equals the minimum average total cost (ATC).
- Therefore, you need to find the minimum point on the ATC curve. Graphically, this is where the ATC curve intersects the MC curve.
4. **Find Equilibrium Quantity**:
- Once the equilibrium price is identified (let's denote it as \( P^* \)), find the corresponding equilibrium quantity by substituting \( P^* \) back into the demand curve to find the quantity demanded at that price.
- The total quantity supplied at \( P^* \) will also match the quantity demanded, indicating equilibrium.
5. **Long-Run Equilibrium Condition**:
- At long-run equilibrium, the following conditions are met:
- \( P^* = MC \) (Firms are producing at the point where price equals marginal cost)
- \( P^* = ATC \) (Firms are making zero economic profit)
- Zero economic profit implies that firms are covering their opportunity costs.
### Example:
1. Suppose the ATC curve is given by \( ATC = 10 + \frac{100}{Q} \).
2. The marginal cost (MC) is constant at \( MC = 15 \).
3. To find the long-run equilibrium, set \( P^* = MC = 15 \).
4. To find equilibrium quantity, substitute \( P = 15 \) into the ATC equation:
- \( 15 = 10 + \frac{100}{Q} \)
- Solving for \( Q \):
\[
5 = \frac{100}{Q} \implies Q = 20
\]
5. Long-run equilibrium price is \( P^* = 15 \) at a quantity of \( Q = 20 \).
### Conclusion:
In a perfectly competitive industry with identical cost structures, the long-run equilibrium price is established where the market demand meets the long-run supply at the point where \( P = MC = ATC \). This ensures that firms can cover all their costs but earn zero economic profit in the long run.
### Steps to Determine Long-Run Equilibrium Price:
1. **Understand Cost Structures**:
- Firms in a perfectly competitive market have identical cost structures, meaning they have the same marginal cost (MC), average total cost (ATC), and average variable cost (AVC) curves.
- Identify the fixed costs (FC) and variable costs (VC) to derive the ATC:
\[
\text{ATC} = \frac{FC + VC}{Q}
\]
- Marginal cost (MC) represents the cost of producing one additional unit of output and is derived from the variable cost function.
2. **Establish Market Demand and Supply**:
- Determine the market demand curve, which is typically downward sloping, indicating that as price decreases, quantity demanded increases.
- The market supply curve in long-run equilibrium is typically horizontal at the price where firms are making zero economic profits. This is often at the minimum point of the ATC curve.
3. **Identify the Price (P = ATC)**:
- In long-run equilibrium, firms will enter or exit the market until they are earning zero economic profits. This occurs when the market price (P) equals the minimum average total cost (ATC).
- Therefore, you need to find the minimum point on the ATC curve. Graphically, this is where the ATC curve intersects the MC curve.
4. **Find Equilibrium Quantity**:
- Once the equilibrium price is identified (let's denote it as \( P^* \)), find the corresponding equilibrium quantity by substituting \( P^* \) back into the demand curve to find the quantity demanded at that price.
- The total quantity supplied at \( P^* \) will also match the quantity demanded, indicating equilibrium.
5. **Long-Run Equilibrium Condition**:
- At long-run equilibrium, the following conditions are met:
- \( P^* = MC \) (Firms are producing at the point where price equals marginal cost)
- \( P^* = ATC \) (Firms are making zero economic profit)
- Zero economic profit implies that firms are covering their opportunity costs.
### Example:
1. Suppose the ATC curve is given by \( ATC = 10 + \frac{100}{Q} \).
2. The marginal cost (MC) is constant at \( MC = 15 \).
3. To find the long-run equilibrium, set \( P^* = MC = 15 \).
4. To find equilibrium quantity, substitute \( P = 15 \) into the ATC equation:
- \( 15 = 10 + \frac{100}{Q} \)
- Solving for \( Q \):
\[
5 = \frac{100}{Q} \implies Q = 20
\]
5. Long-run equilibrium price is \( P^* = 15 \) at a quantity of \( Q = 20 \).
### Conclusion:
In a perfectly competitive industry with identical cost structures, the long-run equilibrium price is established where the market demand meets the long-run supply at the point where \( P = MC = ATC \). This ensures that firms can cover all their costs but earn zero economic profit in the long run.