Perfect Competition: Short-Run and Long-Run Analysis

Perfect Competition

Short-Run Decisions and Loss Minimization

In a perfectly competitive market, firms may face situations where they incur losses in the short run. The decision to continue operating or to shut down depends on the relationship between revenue and variable costs.

• Short-Run Costs: In the short run, some costs are fixed (sunk costs) and cannot be avoided even if the firm shuts down.

• Loss Minimization: A firm minimizes its losses by producing the quantity where the difference between total revenue (TR) and total variable cost (VC) is maximized, even if this results in a negative profit overall.

• Shutdown Decision: The firm compares average total revenue (ATR) to average variable cost (AVC):

  • If $\frac{TR}{q} > \frac{VC}{q}$ (i.e., ATR > AVC), the firm should continue operating in the short run.

  • If $\frac{TR}{q} < \frac{VC}{q}$ (i.e., ATR < AVC), the firm should shut down immediately.

• Example: If a firm produces 4 units (q=4), with TR = $40, TC = $46, and VC = $26, then$TR - VC = $14$, which helps cover part of the fixed costs.

Key Formulas:

• Average Total Revenue: $ATR = \frac{TR}{q}$

• Average Variable Cost: $AVC = \frac{VC}{q}$

Shut Down Point: The minimum point of the AVC curve is called the shut down point. If the market price falls below this point, the firm should cease production in the short run.

Graphical Representation of Short-Run Supply

The firm's short-run supply curve is the portion of its marginal cost (MC) curve that lies above the AVC curve. If the price is below the minimum AVC, the firm shuts down.

• Economic Profit: At price $p^* = 10$ and $q^* = 4$, economic profit is $q^* \times (p^* - AVC(q^*)) = 4 \times (10 - 6.5) = $14$ (using $AVC(q^*) = 26/4 = 6.5$).

• Negative Profit: If the price drops below the minimum AVC, the firm incurs a loss greater than its fixed costs and should shut down.

• Indifference Point: If the price equals the minimum AVC, the firm is indifferent between operating and shutting down, as economic profit is zero.

Short-Run Supply Curve Table

The following table summarizes the firm's cost and profit at different output levels:

q	Total Cost (TC)	Marginal Cost (MC)	Marginal Revenue (MR)	Profit
0	20	-	-	-20
1	25	5	10	-15
2	30	5	10	-10
3	37	7	10	-7
4	46	9	10	-6
5	57	11	10	-7
6	70	13	10	-10

Additional info: The table illustrates that the loss is minimized at q = 4 units, where profit is -6.

Perfect Competition and Long-Run Equilibrium

Entry and Exit in the Long Run

In the long run, firms can enter or exit the market in response to economic profits or losses, driving the market toward equilibrium.

• Positive Profits: If firms earn positive profits ($TR > TC$), new firms enter the market, increasing supply and reducing the market price. This process continues until profits are eliminated.

• Negative Profits: If firms incur losses, some firms exit the market, decreasing supply and increasing the market price. This continues until remaining firms earn zero economic profit.

• Long-Run Equilibrium Condition: In the long run, firms earn zero economic profit, and the following condition holds:

  • $MR = MC = p^* = ATC = \min(ATC)$

Efficiency in Perfect Competition

Perfect competition leads to allocative and productive efficiency in the long run.

• Allocative Efficiency: The market price ($p^*$) equals the marginal benefit to society, ensuring resources are allocated optimally.

• Productive Efficiency: Firms produce at the minimum point of their average total cost (ATC) curve.

Summary Table: Short-Run vs. Long-Run in Perfect Competition

Aspect	Short Run	Long Run
Entry/Exit	No entry/exit	Firms can enter/exit
Profit	Can be positive, zero, or negative	Zero economic profit
Equilibrium Condition	$MR = MC = p$	$MR = MC = p = ATC = \min(ATC)$
Efficiency	Not necessarily efficient	Allocative and productive efficiency

Additional info: In the long run, the process of entry and exit ensures that only the most efficient firms survive, and the market price reflects the minimum possible cost of production.