Theory of the firm

IB Economics SL· Unit 2: Microeconomics, Topic 7· 45 min read

1. Short Run vs Long Run Production★★☆☆☆⏱ 10 min

📘 Definition

Short Run

A period of production where at least one factor of production (typically capital) is fixed, meaning it cannot be adjusted to change output. Only variable factors (labour, raw materials) can be changed.

Example:

A coffee shop cannot expand its building in 4 weeks, so capital is fixed in the short run.

The distinction between short run and long run is the most basic starting point for analysing firm behaviour. In the long run, all factors of production are variable, so firms can change their entire production scale (e.g. build a new factory, close an existing location).

📐 Worked Example

A factory produces 100 chairs per day with 5 workers. Hiring a 6th worker increases total daily output to 114 chairs. What is the marginal product of the 6th worker?

1
Recall marginal product (MP) is the additional output from adding one extra unit of variable input (labour here). The formula is:
2
$MP = \frac{\Delta TP}{\Delta L}$
3
Calculate the change in total product (TP) and change in labour:
4
$\Delta TP = 114 - 100 = 14, \Delta L = 6 - 5 = 1$
5
So the marginal product of the 6th worker is 14 chairs per day.

Exam tip:

Always label axes correctly when drawing product curves; marginal product crosses average product at its maximum point.

2. Cost Classification and Cost Curves★★★☆☆⏱ 15 min

📘 Definition

Marginal Cost

MC

The additional cost incurred by producing one extra unit of output, calculated as the change in total cost divided by the change in quantity.

All production costs are split into fixed costs (FC: do not change with output, e.g. rent) and variable costs (VC: change with output, e.g. raw materials). The key identities for cost are:

$T C = F C + V C$ , $A F C = \frac{F C}{Q}$ , $A V C = \frac{V C}{Q}$ , $A C = \frac{T C}{Q} = A F C + A V C$ .

The core relationship between MC and average costs: MC crosses AVC and AC at their respective minimum points.

📐 Worked Example

A firm has fixed costs of $1000. When producing 100 units, total variable costs are $1500. Calculate AFC, AVC and ATC.

1
Calculate average fixed cost (AFC) by dividing fixed cost by quantity:
2
$AFC = \frac{1000}{100} = \$10 \text{ per unit}$
3
Calculate average variable cost (AVC) by dividing variable cost by quantity:
4
$AVC = \frac{1500}{100} = \$15 \text{ per unit}$
5
Calculate average total cost (ATC) as the sum of AFC and AVC:
6
$ATC = 10 + 15 = \$25 \text{ per unit}$

Exam tip:

The vertical distance between ATC and AVC is always AFC, which shrinks as output increases because fixed costs are spread over more units.

3. Revenue and Firm Objectives★★★☆☆⏱ 12 min

📘 Definition

Profit Maximisation

The default objective assumed for firms in IB Economics, where firms aim to maximise the difference between total revenue and total cost.

While alternative objectives (sales maximisation, satisficing, corporate social responsibility) exist, IB exams almost always expect you to assume profit maximisation unless stated otherwise. Key revenue identities are:

$T R = P \times Q$ , $A R = \frac{T R}{Q} = P$ , $M R = \frac{Δ T R}{Δ Q}$ .

📐 Worked Example

A price-setting firm sells 20 units at $10 each, and 21 units at $9.5 each. Calculate the marginal revenue of the 21st unit.

1
Calculate total revenue for 20 units and 21 units:
2
$TR_{20} = 20 \times 10 = \$200$
3
$TR_{21} = 21 \times 9.5 = \$199.5$
4
Marginal revenue is the change in total revenue, so:
5
$MR = 199.5 - 200 = -\$0.5$

Exam tip:

For a downward-sloping demand curve, marginal revenue always lies below average revenue (price).

4. The Profit Maximisation Rule★★★★☆⏱ 15 min

The profit maximisation rule applies to all firms, regardless of market structure. To maximise profit, a firm produces at the output level where marginal revenue equals marginal cost ( $M R = M C$ ).

If $M R > M C$ , producing an extra unit adds more to revenue than cost, so profit increases. If $M R < M C$ , producing the last unit adds more to cost than revenue, so profit decreases. Only at $M R = M C$ is profit maximised.

📐 Worked Example

A firm currently produces 100 units, where $M R = $15$ and $M C = $12$ . Should the firm increase or decrease output to maximise profit?

1
Compare the marginal revenue and marginal cost of the 100th unit:
2
$MR (\$15) > MC (\$12)$
3
This means the 100th unit added $3 to total profit, so producing additional units will continue to add to profit as long as MR > MC.
4
Conclusion: The firm should increase output until MR equals MC.

Exam tip:

Always explicitly state the MR = MC rule in written answers to earn full marks, do not just reference your diagram.

5. Common Pitfalls

Wrong move:

Claiming all factors of production are fixed in the short run

Why:

The definition of the short run only requires at least one factor to be fixed; variable factors can always be adjusted to change output.

Correct move:

Define the short run as a period where at least one factor of production is fixed, and the long run as a period where all factors are variable.

Wrong move:

Confusing marginal cost with average variable cost, calculating MC as VC/Q

Why:

Average variable cost is the average cost of all units produced, marginal cost is the cost of just the last extra unit.

Correct move:

Always calculate marginal cost as the change in total cost divided by the change in output.

Wrong move:

Calculating economic profit using only explicit costs

Why:

IB questions regularly test the distinction between accounting and economic profit, so omitting implicit (opportunity) costs loses marks.

Correct move:

Subtract both explicit out-of-pocket costs and the opportunity cost of owner-supplied resources from total revenue to get economic profit.

Wrong move:

Claiming profit is maximised where AR = AC

Why:

AR = AC is the break-even point where economic profit is zero, not the output level that maximises total profit.

Correct move:

Always use the MR = MC rule to find the profit-maximising output level, for any market structure.

Wrong move:

Drawing MC crossing AC at AC's maximum point

Why:

When MC is below AC it pulls average cost down, and when it is above AC it pulls average cost up, so intersection only occurs at the minimum.

Correct move:

Draw MC intersecting AVC and AC at their respective minimum points.

6. Quick Reference Cheatsheet

Concept	Formula	Key Rule
Marginal Product (MP)	$\frac{Δ T P}{Δ L}$	Crosses AP at AP's maximum
Total Cost (TC)	$F C + V C$	Fixed costs do not change with output
Average Total Cost (ATC)	$\frac{T C}{Q} = A F C + A V C$	Vertical gap to AVC = AFC, falls with output
Marginal Cost (MC)	$\frac{Δ T C}{Δ Q}$	Crosses AVC/ATC at their minima
Total Revenue (TR)	$P \times Q$	AR always equals price
Economic Profit ( $π$ )	$T R - (E x pl i c i t + I m pl i c i tC os t s)$
Profit Maximisation	$π = T R - T C$	Profit max at $M R = M C$

7. Frequently Asked

What is the difference between accounting and economic profit?

Accounting profit only subtracts explicit (out-of-pocket) costs from total revenue. Economic profit subtracts both explicit costs and implicit (opportunity) costs of owner-supplied resources, which IB exams regularly test.

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2022 · 1
Short run cost curves question
2023 · 1
Profit maximisation rule explanation
2024 · 2
Cost calculation for a firm

Going deeper

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What's Next

Theory of the firm is the foundational framework for all analysis of market structures, which account for a large share of marks on both Paper 1 and Paper 2 of IB Economics SL. Every concept you learned here — cost curves, revenue curves, the MR = MC profit maximisation rule — applies directly to the analysis of perfect competition, monopoly, monopolistic competition and oligopoly. You will also use these core concepts when evaluating efficiency, market failure and government intervention in product markets. Mastery of this topic makes understanding all subsequent microeconomics topics much easier, as it builds the consistent analytical approach examiners reward.