Source: Demski, Managerial Uses of Accounting Information, 2nd ed., Ch. 1–7
Difficulty: Intermediate | Prerequisites: Introductory financial accounting; comfort with basic algebra and linear cost functions
Product cost assessment is the first of three pillars in AMIS 3300 (the others being decision making and performance evaluation). This unit builds the economic and accounting foundations you will use for every topic that follows. You start with how economists think about cost, then see how accountants approximate those ideas in practice, and why the two views often disagree. By the end of Chapter 7 you should be comfortable moving between the economic ideal and the accounting shorthand. If you have not revised your introductory financial accounting material on overhead, direct vs. indirect costs, and basic cost–volume–profit relationships, do that before diving in.
Economists define cost as the value of the best forgone alternative (opportunity cost). Accountants approximate this with allocation systems that assign overhead to products. Different allocation methods (single‐rate, departmental, activity‐based) produce different product costs, and none perfectly matches economic cost. Understanding why and when they diverge is the core skill this unit teaches.
Opportunity cost
The value of the next‐best alternative you give up when choosing a course of action. In simple terms, it is what you sacrifice by picking option A over option B.
Sunk cost
A cost already incurred that cannot be recovered regardless of future decisions. Think of it as money already spent: it should not influence what you do next, though people routinely let it.
Product cost
The total cost assigned to a unit of output by the accounting system, typically comprising direct materials, direct labour, and allocated overhead.
Period cost
A cost expensed in the accounting period it is incurred rather than attached to a product. Selling and administrative expenses are the classic examples.
Cost driver
Any factor that causes a cost to change. In simple terms, it is the activity or volume measure that "drives" how much of a resource gets consumed (e.g. machine hours, number of setups).
Cost pool
A grouping of individual cost items that share a common cost driver and are allocated together. Think of it as a bucket: you toss in all costs driven by the same activity, then pour the bucket over products in proportion to their use of that driver.
Allocation base
The denominator used to spread a cost pool across cost objects. Direct labour hours and machine hours are traditional bases; activity‐based costing uses multiple, more targeted bases.
Synergy (in cost context)
The phenomenon where producing products together costs less than producing them separately. Multi‐product firms exist largely because of this.
Death spiral
A feedback loop in which overhead is allocated across fewer and fewer units (because some products appear unprofitable and are dropped), raising the per‐unit cost of the survivors, which then also appear unprofitable. The spiral continues until the firm has priced itself out of the market or shut down products it should have kept.
Impressionism school (of costing)
Demski's label for traditional, rough‐cut costing methods that use a small number of broad allocation bases (e.g. a single plant‐wide overhead rate). Quick, cheap, but imprecise.
Modernism school (of costing) / Activity‐based costing (ABC)
Demski's label for refined costing that traces overhead through multiple activity cost pools, each with its own driver. More accurate product costs, but more expensive to maintain.
Economic cost vs. accounting cost
Economic cost includes all opportunity costs (explicit and implicit). Accounting cost records only explicit, transaction‐based expenditures. The gap between the two is a recurring theme in this course.
Linear cost function
A cost expressed as TC = F + vq, where F is fixed cost, v is variable cost per unit, and q is quantity. Most of the textbook problems in Chapters 2–5 rely on this form.
The economist's starting point: cost as opportunity cost
Cost is always relative to a decision. The cost of doing X is the value of whatever you gave up to do X.
A firm's cost function C(q) describes the minimum expenditure needed to produce quantity q, given input prices and technology.
Total cost, marginal cost, and average cost
Total cost = fixed cost + variable cost. In the simplest case, TC = F + vq.
Marginal cost is the cost of one additional unit. For a linear cost function, marginal cost equals v (a constant).
Average cost = TC / q. It declines as fixed costs are spread over more units, then may rise if marginal cost increases.
Short run vs. long run
In the short run, at least one input is fixed (e.g. factory capacity), so the firm cannot fully adjust.
In the long run, all inputs are variable, and the firm can choose the cost‐minimising combination of inputs for any output level.
Why this matters for accounting
Accounting systems try to measure cost, but they rely on historical transactions rather than opportunity‐cost logic.
The gap between economic cost and accounting cost is where most of the interesting problems in this course live.
Why firms make more than one product
A firm produces multiple products when doing so is cheaper than separate firms each making one. This cost advantage is synergy.
Synergy arises from shared resources: a factory, a sales force, a distribution network, shared R&D.
Joint cost and cost allocation
When products share a production process (e.g. oil refining yields petrol, diesel, and kerosene), the common cost is a joint cost.
Allocating joint cost to individual products is necessary for financial reporting but inherently arbitrary. No allocation method captures the true economic cost of each product.
Multi-period considerations
Costs in one period can create benefits (or obligations) in later periods. Depreciation is the textbook example, but investments in training, R&D, and brand building are conceptually identical.
Accounting rules force us to split these multi‐period costs into periodic chunks, which rarely matches the underlying economics.
Synergy and the cost function
If C(q1, q2) < C(q1, 0) + C(0, q2), the firm is synergistic. Problems 3‐14 and 3‐15 ask you to verify this numerically.
Synergy can come from economies of scope (shared fixed cost) or from complementarities in production technology.
The core tension
Economic cost requires information (opportunity costs, future states of the world) that accountants rarely have. Accounting cost is a pragmatic substitute built on verifiable, historical transactions.
Neither view is wrong. They serve different purposes: economics gives the theoretically correct benchmark; accounting gives a workable, auditable measurement system.
How accounting systems approximate economic cost
Direct costs (materials, labour) are traced to products. These are usually close to their economic equivalents.
Indirect costs (overhead) are allocated using one or more allocation bases. The choice of base determines how cost is spread, and different bases yield different product costs.
Full absorption costing
GAAP requires that all manufacturing costs, including fixed overhead, be attached to products (absorbed into inventory). This distorts marginal‐cost information because fixed costs are treated as though they vary with output.
Variable (direct) costing
An alternative that assigns only variable manufacturing costs to products and treats fixed overhead as a period expense. More useful for internal decision making, but not permitted for external financial reporting under GAAP.
The allocation problem in practice
A single plant‐wide rate (total overhead / total direct labour hours) is simple but lumps together costs driven by very different activities.
Departmental rates refine this by grouping costs within departments, each with its own base.
Activity‐based costing refines further, as covered in Chapter 7.
What Demski means by "impressionism"
Traditional costing methods that paint a rough picture of product cost using broad averages. Like an impressionist painting, they capture the general shape but blur the details.
Single overhead rate
All overhead is pooled together and spread using one base (typically direct labour hours or machine hours).
Works tolerably when products consume overhead in roughly the same proportions. Fails when they do not.
Where impressionism breaks down
If Product A uses mostly machine time and Product B uses mostly manual assembly, a single labour‐hour rate overcharges B and undercharges A.
The distortion is called cross‐subsidisation: simple, high‐volume products subsidise complex, low‐volume ones (or the reverse).
Why firms used it anyway
Before cheap computing, detailed tracking was prohibitively expensive. A rough number was better than no number.
Impressionist costing also satisfies GAAP's requirement to attach overhead to products, even if the attachment is imprecise.
The ABC idea
Instead of one or two overhead pools, identify the distinct activities that consume resources (machine setups, quality inspections, purchase orders, engineering changes) and create a cost pool for each.
Each pool gets its own cost driver. Products are charged based on how much of each activity they consume.
Steps in an ABC system
Identify activities and group related costs into activity cost pools.
Select a cost driver for each pool (number of setups, inspection hours, number of purchase orders, etc.).
Compute a rate per unit of driver for each pool.
Assign costs to products by multiplying the rate by the product's consumption of that driver.
What ABC reveals
Low‐volume, complex products often consume disproportionate amounts of setup, inspection, and engineering resources. Under a single overhead rate, their true cost is hidden.
ABC typically shows that these products are more expensive than the traditional system reported, and that high‐volume, simple products are cheaper.
The death spiral (Ralph's Death Spiral problem)
When overhead is allocated per unit and a product is dropped because it appears unprofitable, the remaining products must absorb more overhead per unit. If the new per‐unit cost makes another product look unprofitable, it too gets dropped, and the spiral continues.
This is a direct consequence of treating fixed costs as though they are variable at the product level.
The antidote is recognising that dropping a product removes its revenue but not the fixed cost that was allocated to it.
Limitations of ABC
Expensive to implement and maintain.
Requires subjective judgement about which activities to track and how to measure their drivers.
Still an approximation: it does not eliminate the allocation problem, it just uses finer‐grained allocations.
Linear cost function
TC = F + vq, where F = fixed cost, v = variable cost per unit, q = quantity.
Average cost
AC = TC / q = (F / q) + v. Note that F / q declines as q rises (spreading fixed cost), so AC is a decreasing function of q when v is constant.
Marginal cost (linear case)
MC = dTC / dq = v (a constant for a linear function).
Overhead rate
Overhead rate = Total overhead cost / Total allocation base (e.g. direct labour hours).
ABC rate per activity
Rate = Cost pool total / Total units of cost driver.
Synergy test
Synergy exists when C(q1, q2) < C(q1, 0) + C(0, q2). Compute both sides and compare.
Applied overhead
Applied overhead = Overhead rate x Actual allocation base consumed by the product.
Activity‐based costing was pioneered in manufacturing (the original Harvard Business School cases came from companies like John Deere and Schrader Bellows), but the logic applies anywhere overhead is significant: hospitals costing procedures, banks costing loan products, universities costing degree programmes. The death‐spiral concept explains real pricing failures, particularly in industries with high fixed costs and declining volumes (print newspapers, legacy airlines). Any time you hear that a company "lost money on every unit but tried to make it up on volume," the underlying accounting was probably spreading fixed cost per unit and watching the number climb.
Students often assume that the "correct" product cost exists and the accountant's job is to find it. In a multi‐product, shared‐overhead environment there is no single correct product cost. Every allocation method is a choice, and the choice affects what the numbers say.
Students confuse sunk costs with fixed costs. All sunk costs are past costs; fixed costs may be future commitments that have not yet been incurred. A factory lease signed yesterday is a sunk cost for the decision made yesterday, but the remaining payments are fixed future costs relevant to whether to continue operating.
Students treat the death spiral as a rare edge case. It is common in practice whenever managers use fully allocated unit costs to make product‐line keep/drop decisions without separating fixed from variable components.
Students assume ABC is always better than traditional costing. ABC is more refined, but it still allocates costs and can still produce misleading numbers if the activity drivers are poorly chosen or if cost behaviour is non‐linear.
⚠️ The exam format is problems and short essay (cumulative). Expect to compute product costs under different allocation methods and explain why the numbers differ.
⚠️ Be able to demonstrate synergy numerically: given a cost function for two products, show whether C(q1, q2) < C(q1, 0) + C(0, q2).
⚠️ Understand the death spiral well enough to trace it step by step. If you are given a scenario where a product is dropped, you should be able to recalculate the overhead rate for remaining products and explain the feedback loop.
⚠️ Know the difference between absorption costing and variable costing and when each is appropriate.
⚠️ Ralph's Warm Up and Ralph's Shadow are introductory problems. Make sure you can reproduce their logic before moving on; later Ralph problems build on the same framework.
True or false: Opportunity cost and accounting cost are the same thing when all costs are explicit cash payments. (True, but only in that narrow case.)
Fill in the blank: When a single plant‐wide overhead rate is used, low‐volume complex products are typically _______ (overcosted / undercosted). (Undercosted.)
True or false: Dropping a product always reduces total cost by the full amount of cost allocated to that product. (False. The fixed overhead allocated to it does not disappear.)
Fill in the blank: A cost function exhibits synergy when C(q1, q2) is _______ than C(q1, 0) + C(0, q2). (Less.)
True or false: ABC eliminates the need for cost allocation. (False. It uses more allocation pools and drivers, but it still allocates.)
Q: A firm produces two products using a single factory. Total overhead is $600,000. Product A uses 10,000 direct labour hours; Product B uses 2,000. Under a single plant-wide rate, what overhead is assigned to each product?
A: Rate = $600,000 / 12,000 DLH = $50 per DLH. Product A: $500,000. Product B: $100,000.
Q: Suppose an ABC analysis reveals that Product B causes 60% of machine setups and 70% of quality inspections, even though it uses only 17% of direct labour hours. What does this tell you about the single-rate allocation above?
A: The single rate undercosted Product B by spreading overhead on labour hours alone. Product B's true resource consumption is far higher than its labour‐hour share suggests. ABC would shift cost from A to B.
Q: Explain, in three sentences, why the death spiral happens.
A: When fully allocated fixed overhead is used to compute per‐unit cost, dropping a product removes its revenue but not the fixed cost. The remaining products must absorb that fixed cost, raising their per‐unit cost. If the higher cost makes another product appear unprofitable and it too is dropped, the cycle repeats.
Q: A firm's joint cost function is C(q1, q2) = 100 + 4q1 + 3q2. The cost of producing each product alone is C(q1, 0) = 80 + 4q1 and C(0, q2) = 70 + 3q2. Is there synergy?
A: Produce separately: (80 + 4q1) + (70 + 3q2) = 150 + 4q1 + 3q2. Produce together: 100 + 4q1 + 3q2. Since 100 < 150, there is synergy: the shared fixed cost is lower than the sum of standalone fixed costs.
Q: What is the key difference between absorption costing and variable costing, and when does the distinction matter most?
A: Absorption costing includes fixed manufacturing overhead in product cost; variable costing excludes it, treating it as a period expense. The distinction matters most when inventory levels change between periods: absorption costing can show higher profit by building inventory (deferring fixed cost recognition), while variable costing ties profit more closely to sales volume.
The cost functions and allocation methods here feed directly into Chapters 8–12 on decision making. You cannot evaluate a keep/drop decision (Ch. 11) without understanding which costs are relevant and which are allocated artefacts. The death spiral reappears in strategic framing (Ch. 10), where pricing decisions depend on whether managers use full cost or marginal cost. Performance evaluation (Ch. 13+) circles back to ask whether the cost numbers used to judge a manager's performance are fair, which depends on how overhead was allocated in the first place.
Cost accounting, product costing, overhead allocation, cost allocation, absorption costing, full costing, variable costing, direct costing, activity-based costing, ABC, cost driver, cost pool, allocation base, joint cost, opportunity cost, sunk cost, marginal cost, average cost, fixed cost, variable cost, cost-volume-profit, CVP, economies of scope, synergy, cross-subsidisation, death spiral, impressionism costing, modernism costing, Demski, AMIS 3300, Ohio State, managerial accounting, cost behaviour, overhead rate, predetermined overhead rate, applied overhead, cost function