DSE Economics | Production and Costs Lesson-Prep Guide (Tutor Edition) | Cost Arithmetic, Marginal Cost and Economies of Scale

2026-11-02

Tutor lesson-prep guides · Secondary Economics

Students can chant “fixed cost does not change” yet still put rent inside variable cost. This lesson makes them build the cost table from one formula and read the curves off their own numbers.

Objectives — Students can: (1) separate total fixed cost from total variable cost and compute TC, ATC, AVC, AFC and MC from a cost formula; (2) explain why MC must cut ATC at its minimum and locate the profit-maximising output; (3) distinguish short-run diminishing returns from long-run economies of scale, and give one source and one limit of each.

01 Prerequisites (3-minute check)

If any of these fails, fix it before the lesson starts.

Skill	Quick check	Pass mark
Fixed and variable inputs	Which input cannot be changed next week	Capital such as machinery and rent
Averages	How is an average cost found	Total cost divided by output
Marginal reasoning	What does “the next unit” mean	The change caused by one more unit

02 Lesson flow (60 minutes)

Time	Stage	Tutor does	Student does
0-10 min	Sort the costs	Rent, insurance and salaries against materials and piece wages	Two columns, no mixing
10-24 min	Build the table	TC = TFC + TVC, then ATC, AVC, AFC	Fill three output rows
24-36 min	Marginal cost	MC = change in TC divided by change in output	Get 26 then 30
36-46 min	Reading the curves	MC below ATC pulls ATC down; above pushes it up	Mark the crossing
46-56 min	Scale effects	Double output, compare ATC, name the source	ATC 36 to 30
56-60 min	Exit check	Three questions marked on the spot	All three right

03 Teaching script (read it out)

Scene 1: Sort every cost before you compute anything

A workshop pays $3,000 a day in rent, insurance and salaried supervision whoever turns up: that is total fixed cost. Materials and piece-rate wages vary with output: TVC = 20Q + 0.02Q squared.
Build the table from that one formula. At Q = 100, TVC = $2,200.0 and TC = $5,200.0, so ATC = $52 and AFC = $30. At Q = 300, TC = $10,800.0 and ATC falls to $36.
Notice which average moves: AFC keeps falling because the same $3,000 is spread thinner, while AVC creeps up from $22 to $26. That split is the whole logic of the short run.

Ask students: if output is zero, which costs still exist (only fixed costs, so TC equals TFC).

Scene 2: Marginal cost decides output, not average cost

MC is the change in total cost divided by the change in output. From 100 to 200 units, TC rises by $2,600.0, so MC = $26; from 200 to 300 units MC rises to $30 because the variable input is becoming less productive.
MC below ATC drags the average down; MC above ATC pushes it up, so MC must cross ATC at the minimum of ATC. A student who says “produce where ATC is lowest” has confused cost efficiency with profit.
A firm maximises profit where marginal revenue equals marginal cost. If the market price is $40 and MC at 200 units is $26, expanding is still profitable; once MC passes $40, it is not.

Ask students: at 200 units with price $40, should the firm expand (yes, MC is below price).

Scene 3: Economies of scale belong to the long run

In the long run every input can change, so the question is not diminishing returns but scale. Doubling output from 300 to 600 units lowers total cost per unit from $36 to $30, a fall of 16.7%.
Sources are real: labour specialises, buying in bulk earns discounts, an indivisible machine is finally used near capacity. Limits are equally real: coordination gets harder, layers of management multiply, and transport costs spread out, which is why the long-run average cost curve is U-shaped rather than always falling.
Keep the two ideas apart in every answer: short-run rising MC comes from a fixed factor; long-run falling AC comes from scale.

Ask students: name one reason a second factory could raise average cost (management and coordination costs).

04 Question types and worked steps

Type	Example	Steps	Answer
Calculation	Total and average cost	TC = TFC + TVC, then divide by Q	$7,800.0 at Q = 200
Calculation	Marginal cost between two outputs	Change in TC divided by change in Q	$26 to $30
Explanation	Why MC cuts ATC at the minimum	Average is pulled by the marginal unit	Draw both curves
Essay	Should the firm expand?	Compare MC with price, then discuss scale and risk	Answer with figures

Sanity check (teach this): Fixed cost per unit always falls as output rises; total fixed cost never does.
Never divide total cost by output and call it marginal cost: MC uses the change in cost.
ATC is total cost over output, not TVC over output; AVC is the variable part only.
Check the direction of travel: if MC is below ATC, ATC must be falling. A table where that fails contains an arithmetic slip.

05 Independent practice (3 questions)

Question	Answer	What to watch
TFC $3,000 and TVC = 20Q + 0.02Q squared, find TC at Q = 200	$7,800.0	Compute TVC first, then add TFC
ATC at Q = 300	$36	TC 10,800.0 divided by 300
MC from 200 to 300 units	$30	Change in TC over 100 units

06 Common mistakes and what to say

Mistake	Student writes	Say this
Putting rent into variable cost	Writing “TVC = rent + materials”	Rent is paid whether the machines run or not, so it is fixed.
Using TC over Q as marginal cost	Answering MC = $39	MC is the change in cost, not the average; recompute from the two totals.
Producing where ATC is lowest	Answering “expand until average cost is minimum”	Profit is maximised where marginal revenue equals marginal cost.
Calling bulk buying a short-run effect	Answering “MC falls because of bulk discount”	Bulk discounts change the whole cost curve: that is a long-run scale effect.

07 Homework (paper, section and question numbers)

Secondary economics chapter index — All chapters and practice
All lesson-prep guides — Compare other subjects

08 Exit check (last 5 minutes)

Question	Answer	Decision
TC at Q = 200	$7,800.0	All three right: move to market structure
ATC at Q = 300	$36	One wrong: reteach the TFC/TVC split
MC between 200 and 300	$30	Two wrong: return to act two

09 Tutor FAQ

Must students memorise the cost formulas?

No. They must be able to rebuild TC from TFC and TVC and derive the averages, which is what exam data demands.

Is a falling ATC always good news?

Not by itself: the firm may be selling below cost, so pair the cost curve with revenue.

Why is the long-run average cost curve U-shaped?

Economies of scale dominate at low output, coordination and transport costs dominate at high output.

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A TutorZone lesson-prep guide. Written by the TutorZone team; questions and lesson flow are original and are not taken from any school or publisher material.