Understanding Perfect Competition

Perfect Competition

• Describes a market with many small firms competing and selling identical products or services.

Characteristics of a Perfectly Competitive Market

• Large number of buyers and sellers exist, but none can influence the market individually.
• Products are homogeneous, meaning they are identical across sellers.
• Free entry and exit exist, with no significant barriers.
• Perfect information is available; all participants have complete and symmetric information.
• No transaction costs are incurred by buyers and sellers in making transactions.

Implications of Perfect Competition

• Firms are price takers and must accept the market price.
• Individual firms face a perfectly elastic demand curve at the market price.
• Zero economic profit exists in the long run due to entry and exit.

Examples of Perfect Competition

• Agricultural markets, where many farmers sell undifferentiated crops.
• Foreign exchange markets feature numerous buyers and sellers trading currencies.
• Online marketplaces allow many sellers to offer similar goods, and buyers to easily compare prices.
• Serves as a benchmark for evaluating market efficiency.

Demand Curve Faced by a Perfectly Competitive Firm

• Perfectly elastic (horizontal) at the market price.

Explanation

• Firms are price takers and cannot charge more than the market price.
• A firm raising its price above the market price will lose all customers.
• Buyers can purchase the same product from other firms at the market price.

Illustration

• Market Demand Curve: Downward sloping, reflecting overall market demand.
• Firm's Demand Curve: Horizontal line at the market price, indicating perfect elasticity.

Implications

• Firms can sell as much as they want at the market price.
• Marginal revenue equals the market price for each unit sold.
• Firms decide how much to produce at the given market price.

Mathematical Representation

• Demand curve:
  • ( D(p) = \begin{cases} \infty, & \text{if } p < P \ q, & \text{if } p = P \ 0, & \text{if } p > P \end{cases} )
  • $D(p)$ is the demand faced by the firm at price $p$
  • $q$ is the quantity the firm chooses to produce and sell at price $P$

Output Decisions

• Firms in perfect competition aim to maximize profit.

Profit Maximization

• Profit is the difference between total revenue and total cost:
  • ( \Pi(q) = TR(q) - TC(q) )

Marginal Revenue and Marginal Cost

• Firms maximize profit by producing where marginal revenue (MR) equals marginal cost (MC):
  • ( MR(q) = MC(q) )
• Marginal revenue equals the market price ((P)):
  • ( P = MC(q) )

Graphical Representation:

• Marginal Cost Curve: Upward sloping, showing increasing cost for each additional unit.
• Market Price Line: Horizontal.
• Optimal Quantity: Intersection of the marginal cost curve and the market price line.

Deriving the Supply Curve:

• Firm's supply curve is derived from its marginal cost curve above the minimum average variable cost (AVC).
• produce where if ( P > \text{minimum } AVC )
  • ( P = MC(q) )
• If ( P < \text{minimum } AVC ), the firm shuts down and produces zero output.

Shutdown Point

• Shutdown point is where the market price equals the minimum average variable cost:
  • ( P_{\text{shutdown}} = \text{minimum } AVC )

Short-Run Supply Curve

• Firm's short-run supply curve is the portion of its marginal cost curve lying above the minimum average variable cost curve.

The Firm's Supply Curve

• In perfect competition the firm's supply curve is equivalent to its marginal cost (MC) curve above the average variable cost (AVC) curve.

Conditions

• The firm produces where ( P = MC(q) ), given ( P \geq AVC )
• If ( P < AVC ), then the firm shuts down production in the short run.

Graphical Representation

• The supply curve is displayed by plotting the marginal cost (MC) curve above the average variable cost (AVC) curve. Supply is zero below this point.

Mathematical Representation

• The firm's supply curve is expressed as:
  • ( q_s(P) = \begin{cases} \text{arg} { q \mid MC(q) = P }, & \text{if } P \geq \text{min } AVC \ 0, & \text{if } P < \text{min } AVC \end{cases} )
  • ( q_s(P) ) is the quantity supplied at price ( P )
  • ( MC(q) ) marginal cost function
  • ( \text{min } AVC ) is the minimum average variable cost

Example

• Marginal cost is ( MC(q) = 2q ) and minimum ( AVC = 5 )
• The firm's supply curve is: - ( q_s(P) = \begin{cases} \frac{P}{2}, & \text{if } P \geq 5 \ 0, & \text{if } P < 5 \end{cases} )

Market Supply Curve

• The market supply curve is the horizontal summation of the individual firms’ supply curves.
  • If ( n ) is the number of firms, and ( q_{si}(P) ) each has a supply curve, the market supply curve is ( Q_s(P) )
• Expressed as: - ( Q_s(P) = \sum_{i=1}^{n} q_{si}(P) )
• Represents what all firms are willing to supply at each price level.

Market Equilibrium

• Occurs when the quantity supplied equals the quantity demanded in the market.
• Determined by the intersection of the market supply and market demand curves.

Equilibrium Conditions

• Market Supply ((Q_s(P))) = Market Demand ((Q_D(P))).
• Equilibrium Price ((P^)) and Equilibrium Quantity ((Q^)):
  • ( Q_S(P^) = Q_D(P^) = Q^* )

Graphical Representation

• Market Demand Curve: Downward sloping.
• Market Supply Curve: Upward sloping.
• Equilibrium Point: Intersection of demand and supply curves, indicating (P^) and (Q^).

Firm Behavior at Equilibrium

• Each firm produces where ( P^* = MC(q_i) ), with ( q_i ) being the quantity produced by firm ( i ).
• Firms earn economic profits if ( P^* > ATC(q_i) ), where ( ATC ) is average total cost.

Example

• Market demand: ( Q_D(P) = 100 - 2P )
• Market supply: ( Q_S(P) = 3P )
• Equilibrium:
  • ( 100 - 2P = 3P )
  • ( 5P = 100 )
  • ( P^* = 20 )
• Equilibrium quantity:
  • ( Q^* = 3 \times 20 = 60 )

Implications

• Market equilibrium determines the market price and quantity in the short run.
• Firms adjust their output to maximize profit at this price.

Long-Run Equilibrium

• Firms can enter or exit the market based on economic profits.

Dynamics of Entry and Exit

• Entry: If firms are making positive economic profits, new firms enter, increasing market supply and driving down the market price.
• Exit: Firms making losses exit the market, decreasing market supply and driving up the market price.

Long-Run Equilibrium Conditions

• Economic profit is zero ((P = ATC)): Firms earn normal profits, and there is no incentive for entry or exit.
• Price equals minimum average total cost ((P = \min ATC)): Firms operate at the most efficient scale.
• Market supply equals market demand ((Q_S(P) = Q_D(P))): The market is cleared.

Graphical Representation

• Market Diagram: Supply and demand curves intersect at the equilibrium price and quantity.
• Firm Diagram: The firm’s marginal cost (MC) curve intersects its average total cost (ATC) curve at the minimum point. The market price equals this minimum ATC.

Implications

• Efficiency: Resources are allocated efficiently because firms produce at the minimum average total cost.
• Stability: Stable market conditions as there is no incentive for firms to enter or exit.
• Constant-Cost Industry: The entry of new firms doesn't affect the cost structure of existing firms; the long-run supply curve is horizontal at the minimum average total cost.

Adjustments to Equilibrium

• Increase in Demand: A rise in demand initially lifts prices and profits, encouraging new firms to enter the market which pushes the supply curve to the right and lowering the price until economic profits erode.
• Decrease in Demand: A drop in demand initially depresses the price and causes economic losses, this encourages firms to exit, which shifts the supply curve to the left, raising the price until economic losses are eliminated.

Conclusion

• Long-run equilibrium leads to efficient resource allocation and stable market conditions. driven by entry, exit, and the pursuit of zero economic profit.