Firm and Industry Supply, ECN 312 Lecture 14 – Study Notes
Difficulty: Intermediate | Prerequisites: Cost functions, profit maximisation (Lectures 12–13), production functions.
This lecture builds on what you already know about cost functions and profit maximisation, and asks the next question: how does a firm decide how much to produce, and what does that look like when you zoom out to the whole market? The answer hinges on the market environment the firm operates in. Here, the focus is on pure (perfect) competition, where firms are price-takers. If you are comfortable with marginal cost and average cost curves, you have the tools you need. If those are still shaky, revisit the cost-function material first.
A competitive firm maximises profit by producing where price equals marginal cost, which gives us its supply curve. Producer surplus equals revenue minus variable costs (or equivalently, profit plus fixed costs). The industry supply curve is the horizontal sum of every firm's individual supply curve, and in the long run, free entry drives economic profit to zero.
Price-taker
A firm that accepts the market price as given and cannot influence it by changing its own output level. In simple terms, the firm is too small relative to the market for its decisions to move the price.
Technological constraint
The limitation imposed by the production function: a firm can only produce so much given its inputs and available technology. Think of it as the physical ceiling on what the factory floor can do.
Economic constraint
The limitation imposed by cost: firms must pay for inputs, so the cost function summarises what production costs at each output level.
Market constraint
The limitation imposed by demand: a firm can set any price it likes, but it can only sell as much as buyers are willing to purchase at that price.
Demand curve facing the firm
The relationship between the price a firm sets and the quantity it can sell. For a competitive firm this is a horizontal line at the market price. In simple terms, the firm can sell as much as it wants at the going price, but nothing at all above it.
Pure (perfect) competition
A market structure in which every firm is a price-taker. Requires many sellers, free entry and exit, identical products, and perfect information. Think of it as the theoretical benchmark where no single firm has any market power.
Producer surplus (PS)
Revenue minus variable costs: PS = py – c_v(y*). Equivalently, the area above the supply curve (MC curve) and below the market price. In simple terms, it measures the gain to the firm from selling at the market price, before fixed costs are subtracted.
Industry (market) supply curve
The horizontal summation of every individual firm's supply curve. At each price, add up the quantity every firm is willing to supply.
Pure profit / economic profit
Revenue minus all costs, including the opportunity cost of the owner's time and capital. In perfect competition, this is driven to zero in the long run by entry of new firms.
Shut-down point
The output level where price equals average variable cost. Below this price the firm loses money on every unit produced and is better off producing nothing (in the short run). In the long run, the shut-down point is where price equals average cost.
Inverse supply function
The supply relationship written with price as a function of quantity (p = MC(y)) rather than quantity as a function of price (y = s(p)).
Firms face three constraints, layered on top of one another:
Technological constraint (production function): determines the maximum output achievable from a given set of inputs.
Economic constraint (cost function): determines what the firm must pay to acquire those inputs.
Market constraint (demand): even if a firm can produce whatever it likes and set any price, it can only sell what buyers are willing to purchase. This is the new constraint introduced in this lecture.
The market constraint is what makes firms price-takers in competitive markets. The demand curve facing the firm captures this: it maps the price the firm charges to the quantity it can sell.
A market is purely competitive when each firm treats the market price as independent of its own output. Four conditions support this:
Large number of sellers: even the biggest firm produces a negligible share of total output.
Free entry and exit: no barriers prevent resources from moving into or out of the market.
Identical (homogeneous) products: consumers see no difference between one firm's output and another's.
Perfect information: every firm knows the most efficient production methods and input prices.
No real market satisfies all four conditions perfectly. The model is a useful approximation. Gas stations come close: the product is virtually identical, the technology is standard, and entry barriers are relatively low. Markets for everyday goods (candles, tissues, dishware, umbrellas) also behave roughly this way, because consumers treat similar products as interchangeable and buy whichever is cheapest.
Because a competitive firm is a price-taker, its demand curve is a horizontal line at the market price p*.
Above p*, the firm sells nothing (buyers switch to identical competitors).
At p*, the firm can sell as much as it wants.
Below p*, the firm would face the entire market demand, but has no reason to price below p* since it can already sell unlimited quantities at that price.
This is fundamentally different from the downward-sloping market demand curve. The market demand curve shows total quantity demanded at each price. The firm's demand curve shows how much that one firm can sell, and in competition, the answer is "as much as you like, at the going price."
The competitive firm's problem is straightforward. It chooses output y to maximise profit:
max π = py – c(y)
The first-order condition gives p = MC(y). This is the key result: a competitive firm produces where price equals marginal cost. The MC curve (above the shut-down point) is the firm's supply curve.
Why MC and not AC? Because the firm is deciding whether to produce one more unit. If the price exceeds the marginal cost of that unit, producing it adds to profit. If price falls below marginal cost, that unit costs more to make than it brings in.
Producer surplus measures how much better off the firm is from producing and selling at the market price, compared to producing nothing. There are three equivalent ways to calculate it:
Revenue minus variable costs: PS = py – c_v(y*). This is the most direct calculation. Take total revenue, subtract only the variable costs (not fixed costs).
Area above the MC curve: PS = py – ∫₀^{y*} MC(y) dy. Because integrating MC recovers variable cost (the integral of the derivative of total cost gives back total cost minus the constant of integration, which is the fixed cost), this gives the same answer.
Area to the left of the supply curve: geometrically, producer surplus is the area between the price line and the supply curve (MC curve), from zero output up to the firm's chosen quantity.
All three methods yield the same number.
Since total cost c(y) = c_v(y) + F:
Profit: π = py – c_v(y) – F
Producer surplus: PS = py – c_v(y)
So π = PS – F, or equivalently PS = π + F.
This means producer surplus equals profit plus fixed costs. Fixed costs do not change when price or output changes, so the change in producer surplus equals the change in profit: ΔPS = Δπ. This is a useful shortcut in problems that ask about welfare changes.
Worked example: c(y) = ½y² + 100. Here MC(y) = y, and fixed cost F = 100.
At price p*, the firm produces y* = p* (from p = MC = y).
PS = py – c_v(y*) = py – ½(y*)².
Profit = PS – 100.
The industry (market) supply curve is the sum of all individual firms' supply curves:
S(p) = Σ sᵢ(p), summed over i = 1 to n.
At each price, add up the quantity every firm wants to supply.
Worked example: c(y) = ½(y + 10)². Then MC(y) = y + 10, so the inverse supply is p = y + 10 and the individual supply function is y = p – 10.
With 10 identical firms: S(p) = 10(p – 10) = 10p – 100.
With 100 identical firms: S(p) = 100(p – 10) = 100p – 1000.
As more firms enter, the market supply curve becomes flatter (more elastic). For firms with increasing marginal costs (decreasing returns to scale), each additional firm adds a relatively modest amount of output at any given price, but the cumulative effect is a much more responsive market.
In the long run, there are no fixed costs (all inputs are variable), which simplifies the analysis:
Any firm earning negative profit will exit the market.
Therefore the minimum long-run profit is zero.
Zero profit means AC(y) = AVC(y) = MC(y). All three cost curves meet at the same point.
Positive economic profit attracts entry. New firms enter, total supply increases, the market price falls, and profit per firm shrinks. Entry continues until profit reaches zero.
Zero economic profit does not mean the firm earns nothing. It means every factor of production, including the owner's time and capital, is being paid exactly its opportunity cost. There is no surplus reward ("pure profit") left over. With no fixed costs in the long run, zero economic profit also means zero accounting profit.
The cellphone industry illustrates the dynamic. When Apple demonstrated a production technology that was inexpensive relative to consumer willingness to pay, profits were high. Competitors copied the technology and entered the market, driving prices and margins down over time.
\max_y \pi = py - c(y)First-order condition (the supply rule):
p = MC(y)Total cost decomposition:
c(y) = c_v(y) + FProducer surplus (revenue minus variable cost):
PS = p^* y^* - c_v(y^*)Producer surplus (integral form):
PS = p^* y^* - \int_0^{y^*} MC(y) \, dyProfit and producer surplus relationship:
\pi = PS - F \quad \Leftrightarrow \quad PS = \pi + FChange in producer surplus:
\Delta PS = \Delta \pi + \Delta F = \Delta \pi(Because fixed costs do not change in the short run.)
Industry supply curve:
S(p) = \sum_{i=1}^{n} s_i(p)Long-run zero-profit condition:
AC(y) = AVC(y) = MC(y)The p = MC rule is how commodity producers (wheat farmers, oil refiners, steel mills) decide how much to produce each period. They cannot influence the market price, so they ramp up production as long as the next unit costs less than the going price.
Microsoft's early strategy with MS-DOS is a vivid example of marginal-cost thinking applied at the contract level. By charging IBM per computer built (not per computer sold with MS-DOS installed), Microsoft made the marginal cost of including its OS zero to manufacturers, while rival operating systems still cost $50–$100 per installation. Manufacturers responded to marginal cost, not total cost, and MS-DOS became the default. The result was a near-monopoly built on a pricing structure that exploited exactly the logic covered in this lecture.
"Price-taker means the firm has no control over anything." The firm still chooses how much to produce. What it cannot choose is the price. The output decision is where all the action is.
"Producer surplus and profit are the same thing." They differ by exactly the fixed cost F. Producer surplus = profit + fixed costs. Only when F = 0 (the long run) are they equal.
"Zero economic profit means the firm should exit." Zero economic profit means every input, including the owner's effort, is earning its opportunity cost. The firm is doing exactly as well as its next best option. There is no reason to leave.
"The supply curve is the entire MC curve." The supply curve is only the portion of the MC curve at or above average variable cost (the shut-down point). Below that price the firm produces zero.
⚠️ Be ready to derive the supply curve from a cost function. The steps are: differentiate c(y) to get MC(y), set p = MC(y), then solve for y in terms of p. This is the individual supply function s(p).
⚠️ Know all three methods for computing producer surplus and be able to show they give the same answer. Exam problems often give you a cost function and ask for PS at a specific price.
⚠️ The relationship PS = π + F is a common shortcut question. If you know profit and fixed cost, you have producer surplus immediately.
⚠️ Industry supply questions typically ask you to sum n identical firms' supply functions. Watch the algebra: S(p) = n × s(p), which means multiplying the quantity expression, not the inverse supply.
⚠️ Long-run equilibrium: expect questions that ask what happens when firms earn positive profit. The answer is entry, increased supply, lower price, until profit = 0.
True or false: A competitive firm's supply curve is its entire marginal cost curve.
False. Only the portion at or above the average variable cost curve.
Fill in the blank: Producer surplus equals profit plus ______.
Fixed costs (F).
True or false: In long-run competitive equilibrium, firms earn zero accounting profit.
True (with no fixed costs in the long run, zero economic profit implies zero accounting profit as well).
Fill in the blank: The industry supply curve is the ______ sum of individual supply curves.
Horizontal (we add quantities at each price).
True or false: If price is above marginal cost, the firm should produce more.
True. Each additional unit where p > MC adds to profit.
Q: A firm has cost function c(y) = ½y² + 100. If the market price is p = 20, what is the firm's optimal output, profit, and producer surplus?
A: MC(y) = y. Set p = MC: 20 = y, so y* = 20. Revenue = 20 × 20 = 400. Total cost = ½(400) + 100 = 300. Profit = 400 – 300 = 100. Variable cost = ½(400) = 200. Producer surplus = 400 – 200 = 200. Check: PS = π + F = 100 + 100 = 200.
Q: Suppose there are 50 identical firms, each with supply function s(p) = p – 10 for p ≥ 10. What is the market supply curve?
A: S(p) = 50 × (p – 10) = 50p – 500, for p ≥ 10.
Q: Explain why a firm earning zero economic profit does not exit the market.
A: Zero economic profit means every factor of production is earning exactly its opportunity cost. The owner is being compensated for their time and capital at the rate they could earn elsewhere. There is no better alternative, so there is no reason to exit.
Q: A competitive industry is in long-run equilibrium. A positive demand shock increases the market price. Describe the sequence of events that returns the market to long-run equilibrium.
A: The higher price causes existing firms to move up their MC curves, increasing output and earning positive economic profit. Positive profit attracts new entrants. As more firms enter, market supply shifts right, driving the price back down. Entry continues until price returns to the minimum of average cost and economic profit is again zero.
Q: Why does the change in producer surplus equal the change in profit?
A: Because PS = π + F, a change gives ΔPS = Δπ + ΔF. Fixed costs do not change in the short run (ΔF = 0), so ΔPS = Δπ.
This material connects directly to cost theory (Lectures 12–13): the supply curve is just the MC curve viewed from the output-choice side. It also sets up welfare analysis, because producer surplus is half of total surplus (the other half is consumer surplus), which you will need when analysing taxes, subsidies, and deadweight loss. The long-run zero-profit result connects to the theory of the firm and market structure: once you relax the assumptions of perfect competition (fewer firms, product differentiation, barriers to entry), you move into monopoly and oligopoly, where firms are no longer price-takers and the analysis changes considerably.
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