A competitive firm's central problem is choosing how much output to produce. The answer comes from a clean rule: produce where marginal revenue equals marginal cost ( $MR = MC$ ).

In a perfectly competitive market, each firm is a price taker, meaning it can sell as many units as it wants at the going market price without affecting that price. This makes the firm's demand curve a horizontal line at the market price. Because every additional unit sells for the same price, marginal revenue equals price for all units. The profit-maximizing condition therefore becomes:

$P = MR = MC$

The intuition is straightforward:

If $MR > MC$ , the firm earns more on the next unit than it costs to produce. It should increase output.
If $MR < MC$ , the next unit costs more than it brings in. The firm should decrease output.
At $MR = MC$ , there's no way to squeeze out more profit by adjusting quantity in either direction.

One subtlety that's easy to overlook: the MC curve can cross the MR line at more than one point (especially if MC has a downward-sloping segment at low output levels). The second-order condition tells you to pick the intersection where MC is rising. Only on the upward-sloping portion of MC is the firm actually at a maximum rather than a minimum.

Steps for Finding the Profit-Maximizing Output

Identify the market price. In perfect competition, this is given by market supply and demand. The firm takes it as fixed.
Set $P = MC$ and solve for quantity. Use the firm's marginal cost function to find the output level where this holds.
Confirm you're on the upward-sloping portion of MC. If MC is falling at that quantity, you've found a profit minimum, not a maximum. Check that $\frac{dMC}{dQ} > 0$ .
Check the shutdown condition (covered below) to make sure the firm should produce at all.
Calculate profit: $\pi = TR - TC = P \cdot Q - TC(Q)$ . Compare price to average total cost (ATC) at that quantity. If $P > ATC$ , the firm earns positive economic profit. If $P = ATC$ , it breaks even. If $P < ATC$ , it operates at a loss (but may still produce in the short run).

Supply Curve Derivation for Competitive Firms

Short-Run Supply Curve

The firm's short-run supply curve isn't a separate curve you need to memorize. It's just a specific segment of the MC curve.

Because the firm always chooses the quantity where $P = MC$ (on the upward-sloping part), you can trace out how quantity responds to different prices by moving along the MC curve. As price rises, the firm produces more; as price falls, it produces less. That relationship is the supply curve.

But there's a floor. If the price drops so low that the firm can't even cover its average variable cost (AVC), it should shut down and produce zero. Why? In the short run, fixed costs (rent, equipment leases) are sunk whether the firm operates or not. The only question is whether revenue covers variable costs (labor, materials). If $P < AVC$ , every unit produced loses money on variable costs alone, so the firm is better off producing nothing and just absorbing its fixed costs.

The shutdown point is the minimum of the AVC curve, which is exactly where MC intersects AVC from below. You can verify this: at the minimum of any average curve, the marginal curve crosses through it.

Putting it together:

At prices below the shutdown point: quantity supplied = 0
At prices at or above the shutdown point: the supply curve follows the upward-sloping MC curve

The steepness of the MC curve determines supply elasticity. A steeply rising MC means the firm can't increase output much when price rises (less elastic supply). A flatter MC means output responds more to price changes (more elastic supply).

Profit Maximization Rule, Profit Maximization in a Perfectly Competitive Market | Microeconomics

Long-Run Supply Curve

The long run changes things because firms can enter and exit the market, and existing firms can adjust plant size, adopt new technology, and reallocate all inputs. There are no fixed costs in the long run; every input is variable.

For an individual firm, the long-run supply curve is the portion of the long-run marginal cost (LRMC) curve above the long-run average cost (LRAC) curve. The relevant threshold shifts from a shutdown point to an exit point: if price falls below the minimum of LRAC, the firm exits the industry entirely because it can't cover the full opportunity cost of all its resources.

For the industry as a whole, long-run supply depends on what happens to input costs as the industry expands:

Constant-cost industry: Input prices don't change as the industry grows. New firms enter with the same cost structure, so the long-run industry supply curve is perfectly elastic (horizontal) at the minimum LRAC.
Increasing-cost industry: Expansion bids up input prices (e.g., scarce specialized labor becomes more expensive), raising costs for all firms. The long-run industry supply curve slopes upward.
Decreasing-cost industry: Industry growth creates cost savings (e.g., better supplier networks, shared infrastructure). The long-run industry supply curve slopes downward. This is the least common case.

In all three cases, long-run equilibrium requires $P = \min(LRAC)$ for the marginal firm, meaning zero economic profit in the long run. The slope of the industry supply curve just tells you whether that minimum LRAC itself shifts as the number of firms changes.

Price, Marginal Revenue, and Marginal Cost

Relationships in Competitive Markets

The graphical picture of a competitive firm ties everything together. On a standard cost-and-revenue diagram:

Price/MR appears as a horizontal line. This reflects the perfectly elastic demand facing the individual firm.
MC is the familiar U-shaped curve, driven by diminishing marginal returns. MC initially falls as the firm benefits from specialization, then rises as adding more variable inputs to fixed inputs yields smaller and smaller output gains.
The optimal output is where the horizontal price line crosses the upward-sloping portion of MC.

Producer surplus is the area between the price line and the MC curve, from zero up to the quantity produced. It represents the gain the firm captures above and beyond the variable cost of producing each unit. In the short run, producer surplus equals profit plus fixed costs ( $PS = \pi + FC$ ). So a firm can have positive producer surplus while still earning negative profit, as long as it covers variable costs.

When the market price changes, the firm doesn't shift its MC curve. Instead, the horizontal price line moves up or down, and the firm slides along its MC curve to a new optimal quantity. Tracing out these quantity responses at every possible price is exactly how you derive the supply curve from the MC curve.

Graphical Analysis

To build the full picture step by step:

Draw the MC curve (U-shaped) along with the AVC and ATC curves.
Draw a horizontal line at the market price. This is the firm's demand curve and its MR curve.
Find the intersection of the price line with the upward-sloping MC. That's the profit-maximizing quantity, $Q^*$ .
Assess profitability. Look at where $Q^*$ falls relative to ATC:
- If the price line is above ATC at $Q^*$ , the firm earns positive economic profit (the rectangle between P and ATC, with width $Q^*$ ).
- If the price line equals ATC at $Q^*$ , the firm breaks even (zero economic profit).
- If the price line is below ATC but above AVC, the firm operates at a loss but continues producing because it covers variable costs and part of fixed costs.
- If the price line falls below AVC, the firm shuts down.
Shade producer surplus as the area between the price line and the MC curve up to $Q^*$ .
Derive the supply curve by imagining different price levels and marking the corresponding $Q^*$ at each one. The resulting locus of points traces the MC curve above the minimum of AVC.

Short-Run Profit Maximization: Scenarios and Decisions

The Four Price Scenarios

The market price determines which situation the firm faces. These are worth knowing cold for exams:

Price Level	Condition	Profit/Loss	Decision
High price	$P > ATC$ at $Q^*$	Positive economic profit	Produce at $Q^*$
Break-even price	$P = ATC$ at $Q^*$	Zero economic profit (normal profit)	Produce at $Q^*$
Loss-minimizing price	$AVC < P < ATC$ at $Q^*$	Loss, but smaller than total fixed costs	Produce at $Q^*$
Shutdown price	$P < AVC$	Loss equals total fixed costs	Shut down, produce zero

The loss-minimizing case trips people up the most. Here's the logic: if the firm shuts down, it still pays fixed costs and earns zero revenue, so its loss equals total fixed costs ( $TFC$ ). If it operates and revenue covers all variable costs plus some fixed costs, the loss is smaller than $TFC$ . Operating at a loss can be the rational short-run choice whenever $P \geq AVC$ .

Profit Calculation

At the optimal output $Q^*$ :

$\pi = TR - TC = (P \times Q^*) - (ATC \times Q^*) = (P - ATC) \times Q^*$

Profit per unit is $P - ATC$ , and total profit is that margin times quantity. On a graph, profit (or loss) appears as a rectangle with height $|P - ATC|$ and width $Q^*$ .

How Cost Changes Affect the Firm

Changes in input prices or technology shift the cost curves, which changes the profit-maximizing output even if the market price stays the same.

A rise in raw material prices shifts MC upward. The new intersection with the price line occurs at a lower quantity, and profit falls. The supply curve shifts left (less supplied at every price).
A technological improvement shifts MC downward. The firm produces more at the same price, and profit rises. The supply curve shifts right.

These shifts also change the supply curve itself, since the supply curve is the MC curve above AVC. A downward shift in MC means the firm is willing to supply more at every price, and the shutdown point may change too if AVC shifts.