The Theory of the Firm under Perfect Competition

Written and reviewed by Devendra Dubey, Mathematics & Commerce faculty at UniDrill (M.Sc. Mathematics, Osmania University · 10 years teaching). Based on NCERT Economics Class XII (Introductory Microeconomics), Chapter 4.

Why can't a wheat farmer name her own price?

Imagine you grow wheat in a village with hundreds of other farmers. The mandi rate today is ₹30 a kilogram. If you ask ₹31, every buyer walks to the next farmer, who sells identical wheat at ₹30. If you ask ₹29, you lose money for no reason, because you could have sold every kilogram at ₹30 anyway. So you do not choose a price. You take the market price as given, and your only real decision is how much to produce.

This chapter answers that one question. It builds the logic of a price taking firm step by step: its revenue, the output that gives it maximum profit, the price below which it stops, the supply curve that results, and finally how the supplies of many firms add up to market supply.

What makes a market perfectly competitive

A perfectly competitive market has four defining features. Each one has a job to do, and together they produce price taking.

Why price taking follows. Suppose every firm charges the market price and one firm raises its price. All buyers know the market price and all products are the same, so that firm loses every buyer. Those buyers move to other firms, and with so many firms there is no shortage or hassle in absorbing them. A firm that sets a price above the market price therefore sells nothing, while at the market price (or lower) it can sell as much as it likes. Since there is no reason to charge less, the price it sets is exactly the market price. The same holds for a buyer: asking for less than the market price gets her nothing, and paying the market price gets her as much as she wants.

Revenue: money coming in

Let the market price be $p$ and the firm sell $q$ units. Its total revenue is price times quantity.

$$\text{TR} = p \times q$$

Average revenue is revenue per unit, and marginal revenue is the extra revenue from selling one more unit.

$$\text{AR} = \dfrac{\text{TR}}{q} = p \qquad\qquad \text{MR} = \dfrac{\Delta \text{TR}}{\Delta q} = p$$

Why MR equals p. Each extra unit is sold at the same market price. So selling one more unit adds exactly $p$ to revenue. Algebraically, going from $q_1$ to $q_2$ units gives $\text{MR} = \dfrac{pq_2 - pq_1}{q_2 - q_1} = p$. This works only because $p$ does not change when the firm sells more, which is price taking. For a price taker, then, $\text{MR} = \text{AR} = p$.

The three revenue curves look like this when drawn.

Worked example: revenue schedule. The market price of a box of candles is ₹12. Complete TR, AR and MR for 0 to 5 boxes.

Thinking: TR is price times boxes. MR is the change in TR between successive rows ($24 - 12 = 12$), and AR is TR divided by boxes ($36 \div 3 = 12$). MR and AR both come out equal to the price, ₹12, in every row.

Common wrong step. Expecting MR to fall as sales rise, the way it does along a downward sloping demand curve. Under price taking, selling the fifth box brings in the same ₹12 as the first.

Pause and predict: a candle maker decides to charge ₹14 when the market price is ₹12. How many boxes does she sell?

Check your answer: None. Buyers are fully informed and every other maker sells the same candle at ₹12, so everyone switches. This is exactly what "the firm faces a perfectly elastic demand curve" means.

Profit maximisation: the marginal idea

Profit is total revenue minus total cost.

$$\pi = \text{TR} - \text{TC}$$

The firm wants the output $q_0$ that gives the highest $\pi$. Here is the intuition. Produce one more unit and revenue rises by MR while cost rises by MC. As long as MR is greater than MC, that unit adds more to revenue than to cost, so profit rises. When MR is less than MC, the unit costs more than it earns, so profit falls. Profit is therefore highest where MR equals MC. For a price taker MR is $p$, so the rule becomes $p = \text{MC}$.

If the firm produces a positive output at all, three conditions must hold at the profit-maximising output.

Why condition 2. Suppose $p = \text{MC}$ at output $q_1$ where the MC curve is sloping downward. Just to the left of $q_1$ the marginal cost is higher than the price, so those last units are losing money. Cutting output slightly raises profit. So $q_1$ is a profit trap, not a peak. The true peak is where $p = \text{MC}$ and MC is rising, because then producing less loses profit (MC below price) and producing more loses profit (MC above price).

Why condition 3 in the short run. In the short run fixed costs must be paid whether the firm produces or not. If it shuts down, its profit is $-\text{TFC}$. If it produces at a price below AVC, its revenue is less than its total variable cost, so its profit is (revenue − variable cost − TFC), which is worse than $-\text{TFC}$. It is better off producing nothing. Fixed costs are sunk, so only variable costs matter for the decision.

Why condition 3 in the long run. In the long run every cost is variable and a shut-down firm earns zero. If price is below average cost, TR is less than TC, the firm makes a loss, and zero is better. So it exits.

Profit as a picture. At the chosen output $q_0$, total revenue is the area of the rectangle price × $q_0$ and total cost is the area of the rectangle (average cost) × $q_0$. The profit is therefore the rectangle of height (price − average cost) and width $q_0$. This is positive when the price curve lies above the average cost curve at $q_0$.

Worked example: choosing output from a schedule. A competitive firm faces a market price of ₹10. Its total cost (TC) schedule is given. Find the profit maximising output.

Thinking: TR is $10q$. Profit is TR − TC. MC for a unit is the rise in TC when that unit is added ($38 - 31 = 7$ for the fifth unit). The firm keeps adding units while MC is no more than MR = ₹10. The fifth unit costs ₹7, less than ₹10, so it is worth producing. The sixth costs ₹11, more than ₹10, so profit falls from ₹12 to ₹11. The profit maximising output is 5 units with a profit of ₹12. Check condition 3: TFC is ₹5, so TVC at 5 units is ₹33 and AVC is ₹6.60, below the price of ₹10.

Common wrong step. Stopping at 1 unit because MC equals ₹10 there. MC is falling at that point (₹10, then ₹7, ₹5, ₹4), so condition 2 fails. Profit at 1 unit is −₹5, while at 5 units it is ₹12. Setting $p = \text{MC}$ alone is not enough.

Pause and predict: in the same table, what happens to the profit-maximising output if the price rises to ₹14?

Check your answer: The firm now compares MC with ₹14. The seventh unit costs ₹14, which equals the price and adds nothing, and the eighth costs ₹18 and would lose ₹4. So it supplies 7 units, more than before. A higher price pushes the firm up its rising MC curve.

The supply curve of a firm

A firm's supply is the quantity it chooses to sell at each price, given its technology and input prices. The table of such quantities is a supply schedule and its graph is the supply curve. The idea of the whole chapter is that this curve is a part of the marginal cost curve, because the firm at each price picks the output where $p = \text{MC}$ on the rising part.

Case 1: the price is at or above the minimum AVC. Equate the price with SMC on its rising part. All three conditions hold, so the firm produces that output.

Case 2: the price is below the minimum AVC. For every positive output AVC is above the price, so condition 3 fails. The firm produces zero.

The shut down point. Moving down the supply curve, the last price at which the firm still produces is the minimum of AVC, where SMC cuts AVC. This is the short-run shut down point. In the long run it is the minimum of LRAC.

Normal profit and break even. Normal profit is the minimum profit needed to keep a firm in its business. It is counted as part of total cost because it is the opportunity cost of the entrepreneur's effort and money. Profit above this is super-normal profit. The break even point is the point on the supply curve where the firm earns only normal profit, which is the minimum of the average cost curve (LRAC in the long run, SAC in the short run). Here TR equals TC, with normal profit already inside TC.

What the short run looks like as price falls.

Beyond the textbook. For the exam: normal profit is part of cost, so a break even firm has "zero profit" in the sense TR = TC. In reality: an accountant's profit and an economist's profit differ for this very reason. A shopkeeper who owns her shop and works in it may show a ₹40,000 monthly surplus in her books, but if she could earn ₹30,000 as someone else's employee and ₹15,000 in rent from letting the shop, the economist counts ₹45,000 of opportunity cost, so she is earning less than normal profit.

Worked example: should the firm shut down? A short-run firm has total fixed cost of ₹12. Its total variable cost for 1 to 6 units is given.

The lowest AVC is ₹5, at 3 units, so the shut down price is ₹5. Test three market prices.

Thinking: at ₹4 no output has AVC at or below the price (the lowest AVC is ₹5), so revenue never covers variable cost. At ₹6 the firm still makes a loss, but producing earns ₹3 more than it spends on variable inputs, and that ₹3 goes toward the fixed cost it has to pay anyway.

Common wrong step. "The firm is making a loss, so it should close." In the short run a loss is acceptable as long as price is at least minimum AVC, because shutting down does not remove the fixed cost. Also wrong is comparing the price with average total cost for this decision.

Pause and predict: in the long run, the price is still ₹6 and the firm's lowest LRAC is ₹8. What will the firm do?

Check your answer: It exits. In the long run there is no fixed cost to hide behind, and a price below the minimum LRAC means a loss at every output, while leaving gives zero.

Worked example: reading a supply curve off the MC schedule. A firm's marginal cost for the first six units is given, and its minimum AVC is ₹7, reached at 2 units. Find its supply at different prices.

Rule: below the minimum AVC supply is zero; at and above it, produce every unit whose MC is not more than the price, on the rising part of MC.

Common wrong step. At a price of ₹8 reading off "1 unit" because the first unit's MC is ₹8. That point is on the falling part of MC, so it fails condition 2. The supply at ₹8 is 2 units, not 1.

What shifts a firm's supply curve

Since supply is a piece of the MC curve, anything that moves MC moves supply.

A unit tax is a tax charged per unit of output sold. For instance a tax of ₹2 on a firm selling 10 units is ₹20.

Worked example: a unit tax on supply. A long-run firm has a minimum LRAC of ₹20 at 10 units, and its LRMC rises as shown. The government imposes a unit tax of ₹3. Find the supply before and after.

The minimum LRAC moves from ₹20 to ₹23 as well, so the firm now starts supplying only at ₹23.

Thinking: after tax each unit costs ₹3 more, so the firm needs ₹3 more to supply the same output. Price ₹30 after tax behaves like ₹27 before tax, which supports 12 units.

Common wrong step. Shifting the curve right, or saying the firm supplies the same quantity at a price lower by the tax. The tax raises the cost, so the supply curve moves left (equivalently, upward).

Beyond the textbook. For the exam: a firm below minimum AVC produces nothing in the short run. In reality: this is why a hotel in a hill town stays open in the off-season while charging low room rates. Rent and the building loan are fixed costs the owner pays either way. As long as each night's room rate covers the extra cost of that night (cleaning, electricity, staff for the day), staying open loses less money than closing. If even the room rate cannot cover those variable costs, the hotel shuts for the season.

Market supply: adding up the firms

The market supply at a price is the sum of what all firms supply at that price. Graphically, it is the horizontal summation of the individual supply curves: at each height (price) you add the quantities. With two firms where firm 1 starts supplying at a lower price, the market supply curve is zero below that price, follows firm 1 alone between the two starting prices, and above the higher one is the sum of both, so it becomes flatter. If the number of firms rises (falls), the market supply curve shifts right (left).

Worked example: adding two supply curves. Firm 1 supplies nothing below ₹4 and $2p - 8$ units at ₹4 or more. Firm 2 supplies nothing below ₹8 and $p - 8$ units at ₹8 or more. Find the market supply.

For $p \ge 8$ the equation is $S_m = (2p - 8) + (p - 8) = 3p - 16$. Check at ₹10: $3 \times 10 - 16 = 14$.

Common wrong step. Using $3p - 16$ at every price. At ₹6, that gives 2, but firm 2 is not yet producing, so the market supply is firm 1's 4 units. Add the equations only in the range where every firm is in the market. The other common error is adding prices; always add quantities at a given price.

Price elasticity of supply

How strongly does quantity supplied respond to price? Price elasticity of supply is the percentage change in quantity supplied divided by the percentage change in price.

$$e_S = \dfrac{\%\,\Delta Q}{\%\,\Delta P} = \dfrac{\Delta Q}{Q} \times \dfrac{P}{\Delta P}$$

A vertical supply curve has $e_S = 0$ (no response). A positively sloped curve has a positive $e_S$. Like demand elasticity, it is a ratio of percentages, so it does not depend on units.

Worked example: elasticity by the percentage method. When the price of a cricket ball rises from ₹20 to ₹25, the market supply rises from 80 to 120 balls. Find $e_S$.

Elasticity of 2 means supply rises 2% for every 1% rise in price.

Common wrong step. Using the new values as the base (40/120 and 5/25), which gives about 1.67, or quoting the slope $\Delta Q / \Delta P = 8$ as the elasticity. Elasticity uses percentages, with the starting values as the base.

Worked example: given the elasticity, find the quantity. At ₹10 a firm supplies 4 units. The price rises to ₹30 and $e_S = 1.25$. How much does it supply?

The geometric method. For a straight line supply curve, elasticity at a point $S$ on the curve is the ratio $\dfrac{Mq_0}{Oq_0}$, where $q_0$ is the foot of the perpendicular from $S$ to the quantity axis, $O$ is the origin and $M$ is where the extended line meets the quantity axis. The reason is that $e_S = \dfrac{\Delta Q}{\Delta P} \times \dfrac{P}{Q}$; for a straight line the inverse slope $\dfrac{\Delta Q}{\Delta P}$ is $\dfrac{Mq_0}{Sq_0}$, and $\dfrac{P}{Q}$ is $\dfrac{Sq_0}{Oq_0}$. The $Sq_0$ cancels and leaves $\dfrac{Mq_0}{Oq_0}$.

Worked example: checking the rule with three lines. Take the point where output is 10 on each line.

Common wrong step. Judging elasticity from steepness alone. A line through the origin has elasticity 1 whether it is steep or flat. What matters is the axis the line meets.

Beyond the textbook. For the exam: supply elasticity can be measured at any point with the formula above. In reality: elasticity depends on how easily output can be changed. A vegetable farmer can raise the supply of tomatoes only after a growing season, while a factory with spare capacity can raise output within days. The same price rise therefore brings a very different response, which is why supply is more elastic in the long run than in the short run.

Short run and long run at a glance

Exam traps

Formula sheet

60-second revision

Where this chapter connects

• Previous: Production and Costs supplies the MC, AVC and average cost curves that this chapter turns into a supply curve.
• Same side of the market: Theory of Consumer Behaviour builds the demand side that meets this supply side.
• Next: Market Equilibrium puts market demand and market supply together to find price and quantity.