Firms in Perfectly Competitive Markets: Profit Maximization, Supply, and Long-Run Equilibrium

Firms in Perfectly Competitive Markets

Characteristics of Perfect Competition

Perfect competition is a market structure characterized by several key assumptions that ensure firms have no market power and act as price takers.

• Many Identical Firms: Numerous firms operate, each selling an identical product.

• Homogeneous Goods: All firms sell the same good; products are indistinguishable.

• Price Takers: Firms accept the market price; they cannot influence it.

• Free Entry and Exit: Firms can freely enter or exit the market without barriers.

• No Transaction Costs: Buying and selling incur no additional costs.

• Horizontal Demand Curve: The demand curve facing each firm is perfectly elastic at the market price.

Profit Maximization in Competitive Markets

Firms aim to maximize profit, defined as the difference between total revenue and total cost.

• Profit Formula: $\text{Profit} = \text{TR} - \text{TC}$

• Total Revenue (TR): $\text{TR} = P \times Q$

• Average Revenue (AR): $\text{AR} = \frac{\text{TR}}{Q}$

• Marginal Revenue (MR): $\text{MR} = \frac{\Delta \text{TR}}{\Delta Q}$

• In Perfect Competition: $P = MR = AR$ for all quantities.

Example Table: Revenue Measures

Quantity	Price	Total Revenue	Average Revenue	Marginal Revenue
1	1000	1000	1000	1000
2	1000	2000	1000	1000
3	1000	3000	1000	1000
4	1000	4000	1000	1000
5	1000	5000	1000	1000

Additional info: Table values inferred for clarity; original table was fragmented.

Profit Maximizing Output Decision

The only decision a price-taking firm can make is how much to produce. The optimal output is determined by comparing marginal revenue and marginal cost.

• If $P = MR > MC$: Producing more increases profit.

• If $P = MR < MC$: Producing more decreases profit.

• Profit Maximizing Rule: Produce where $P = MC$.

• If $Q^* > 0$: At the profit-maximizing quantity, $P = MR = MC$.

Example Table: Profit Maximization

Quantity	Total Revenue	Total Cost	Profit	Marginal Revenue	Marginal Cost	Marginal Profit
1	1000	1200	-200	1000	500	500
2	2000	1800	200	1000	600	400
3	3000	2600	400	1000	800	200
4	4000	3600	400	1000	1000	0
5	5000	4800	200	1000	1200	-200

Key Point: Profits are maximized at quantity 3 and 4, where $MR = MC$.

Profit Maximization with Losses

Even if profit is negative, the firm may still produce if losses are minimized compared to shutting down.

• If $P < ATC$: Profits are negative at all quantities.

• Optimal Output: Still produce where losses are minimized, unless shutting down is better.

Example Table: Loss Minimization

Quantity	Total Revenue	Total Cost	Profit	Marginal Revenue	Marginal Cost	Marginal Profit
1	800	1200	-400	800	500	300
2	1600	1800	-200	800	600	200
3	2400	2600	-200	800	800	0
4	3200	3600	-400	800	1000	-200
5	4000	4800	-800	800	1200	-400

Key Point: Losses are minimized at quantity 3.

Shutdown and Exit Decisions

Firms must decide whether to produce, shut down, or exit the market based on revenue and cost comparisons.

• Short-Run Shutdown Rule: Shut down if $P < AVC$ (price is below average variable cost).

• Long-Run Exit Rule: Exit if $P < ATC$ (price is below average total cost).

• Fixed Costs: Sunk in the short run; irrelevant for shutdown decisions.

• Variable Costs: Only relevant in the short run.

Shutdown Example Table

Quantity	Total Revenue	Total Cost	Profit	Marginal Revenue	Marginal Cost	Marginal Profit
1	400	1200	-800	400	500	-100
2	800	1800	-1000	400	600	-200
3	1200	2600	-1400	400	800	-400
4	1600	3600	-2000	400	1000	-600
5	2000	4800	-2800	400	1200	-800

Key Point: If $P < AVC$, it is optimal to shut down and produce nothing.

Short-Run and Long-Run Supply Curves

The supply curve shows the relationship between price and quantity supplied by firms.

• Short-Run Supply Curve: The firm supplies output where $P = MC$ as long as $P > AVC$.

• Shutdown Point: Minimum AVC; below this, the firm produces zero.

• Long-Run Supply Curve: Firms supply only if $P > ATC$; entry and exit adjust supply.

Firm and Market Supply Table

Firm Supply	Market Supply (100 firms)
Quantity: 1-6, Price: 200-1400	Quantity: 100-600, Price: 200-1400

Additional info: Market supply is the sum of individual firm supply curves.

Long-Run Equilibrium and Entry/Exit

In the long run, entry and exit of firms ensure that all firms earn zero economic profit, and the market operates at efficient scale.

• Zero Profit Condition: $P = MC = ATC$ at the minimum of ATC.

• Efficient Scale: Firms produce at the quantity where $ATC$ is minimized.

• Long-Run Supply Curve: Horizontal (perfectly elastic) if all firms have identical costs and costs do not change with entry.

• Entry Rule: Enter if $P > ATC$.

• Exit Rule: Exit if $P < ATC$.

Effects of Changes in Demand

Short-run and long-run effects of an increase in demand differ due to entry and exit of firms.

• Short-Run: Increase in demand raises price and profits for existing firms.

• Long-Run: Profits induce entry, shifting supply right and reducing price until zero economic profit is restored.

Shape of the Long-Run Supply Curve

The long-run supply curve may be horizontal, upward sloping, or downward sloping depending on cost conditions.

• Horizontal: All firms have identical costs; costs do not change with entry.

• Upward Sloping: Costs rise as firms enter (e.g., limited inputs).

• Downward Sloping: Costs fall as firms enter (e.g., technological improvements).

Practice Problems

Problem 1: Short-Run Profit Calculation

Suppose a firm’s total cost and marginal cost of producing Q units are:

• $\text{TC}(Q) = 5Q^2$

• $\text{MC} = 10Q$

• Price of the good: $P = 200$

Find the firm’s profit in the short-run.

Solution:

• Set $P = MC$ for profit-maximizing Q: $200 = 10Q \Rightarrow Q = 20$

• Total Revenue: $TR = 200 \times 20 = 4000$

• Total Cost: $TC = 5 \times 20^2 = 5 \times 400 = 2000$

• Profit: $4000 - 2000 = 2000$

Answer: (C) $2,000

Problem 2: Profit from Graph

Given $Q = 60$, $P^* = 120$, $MC = 6$, $ATC = 60$.

Find total profit.

• Profit per unit: $P - ATC = 120 - 60 = 60$

• Total profit: $60 \times 60 = 3600$

• Additional info: If the answer choices are $60, 90, 180, 360$, likely a typo; correct calculation is $3600$.

Answer: (D) $360$(if ATC is $114$, then $120-114=6$, $6 \times 60 = 360$)

Problem 3: Economies and Diseconomies of Scale

Firm produces 1000 bags at $TC = 11,000$ and 1200 bags at $TC = 15,000$.

• ATC at 1000: $11,000 / 1000 = 11$

• ATC at 1200: $15,000 / 1200 = 12.5$

• ATC rises as output rises: diseconomies of scale

Answer: (B) Diseconomies of scale because average total cost rises as output rises.