3.3.2 - Revenue, costs and profits
- Syllabus
- 2018
- Topic
- 3.3.2
- Level
- A2
$TR=P\times Q$; $AR=TR/Q$; $MR=\Delta TR/\Delta Q$
Total revenue is all sales income, average revenue is revenue per unit and marginal revenue is the addition to total revenue from one more unit. For a single-price firm, AR equals price and is its demand curve.
At 100 units sold for 6each,TR=600andAR=6.Ifsellingunit101raisesTRto604, that unit's MR=4.
MR is a change, not TR divided by output. TR is maximised where MR changes from positive to negative, so at the peak MR=0.
$PED=\%\Delta Q_d/\%\Delta P$
| Demand range | Price falls | Price rises |
|---|---|---|
| elastic, ∣PED∣>1 | TR rises | TR falls |
| inelastic, ∣PED∣<1 | TR falls | TR rises |
| unit elastic, ∣PED∣=1 | TR unchanged | TR unchanged |
TR changes according to whether the percentage quantity response outweighs the percentage price change. On a downward-sloping linear demand curve, MR is positive in the elastic range, zero at unit elasticity and negative in the inelastic range.
Use the absolute PED magnitude for elastic versus inelastic, while retaining the usual negative sign when reporting PED itself.
In the short run at least one factor is fixed. With a constant wage per variable worker, marginal cost is inversely related to marginal product: when an extra worker adds more output, the labour cost per extra unit falls.
$MC=\Delta VC/\Delta Q=wage/MP_L$ (when labour is the variable input and its wage is constant)
Initially specialisation may raise marginal product, so MC falls. Once diminishing marginal productivity begins, MP falls and MC rises. The same productivity forces help AVC become U-shaped; ATC is also U-shaped but includes AFC.
Diminishing marginal productivity is a short-run input relationship, not diseconomies of scale, which is a long-run relationship when all inputs can vary.
With at least one fixed factor, adding successive units of a variable factor eventually causes marginal product to fall, holding technology and the quality of inputs constant.
Early workers may specialise and use fixed capital more fully. Beyond some point, each additional worker has less fixed capital or space to work with, so the extra output from that worker declines.
When each extra input unit adds less output but still costs the same, the cost of producing an additional unit rises: diminishing returns cause the upward-sloping section of MC.
Total product can continue rising while marginal product falls. Diminishing returns means output rises at a decreasing rate, not necessarily that output falls.
$TC=TFC+TVC$; $TFC=TC$ when $Q=0$
$AC=TC/Q$; $AFC=TFC/Q$; $AVC=TVC/Q$; therefore $AC=AFC+AVC$
$MC=\Delta TC/\Delta Q=\Delta TVC/\Delta Q$
If TFC=500 and at 200 units TC=2,500, then TVC=2,000, AFC=2.50, AVC=10 and AC=12.50. If TC rises to 2,620at210units,MC=120/10=12 per extra unit.
Fixed cost does not change with current output, so it does not affect MC. Keep totals in currency and averages/marginals in currency per unit.
| Production measure | Cost counterpart | Relationship, with constant input price |
|---|---|---|
| marginal product | marginal cost | MP rising means MC falling; MP falling means MC rising |
| average product | average variable cost | AP rising means AVC falling; AP falling means AVC rising |
| total product | total variable/total cost | more variable input raises TP and TVC; slope changes mirror marginal values |
In the short run at least one input and some cost are fixed, creating TFC. In the long run all inputs are variable, so the firm chooses scale and there is no fixed input in the planning decision.
The inverse MP-MC and AP-AVC links require a constant price of the variable factor. A wage change can shift cost curves without a productivity change.
| Output range | LRAC movement | Interpretation |
|---|---|---|
| economies of scale | falls as output rises | output grows faster than long-run total cost |
| constant returns to scale | unchanged | output and long-run total cost grow proportionately |
| diseconomies of scale | rises as output rises | long-run total cost grows faster than output |
LRAC shows the lowest attainable average cost for each output when all inputs and plant size can be changed. It is commonly U-shaped because scale benefits are eventually outweighed by organisational costs.
Economies of scale reduce average cost, not necessarily total cost. They are long-run scale effects, not the short-run spreading of fixed cost alone.
Minimum efficient scale (MES) is the lowest output at which a firm reaches the minimum point, or minimum flat range, of its long-run average cost curve and has exhausted available economies of scale.
A high MES relative to market demand favours a few large firms because entrants must achieve substantial output to match incumbents' unit costs. A low MES allows smaller firms to compete efficiently.
On an LRAC curve, move from low output along the falling section; the first output at which minimum LRAC is reached is MES. Output beyond MES does not create further scale cost savings.
MES is the minimum efficient output, not the maximum possible output and not automatically the profit-maximising output.
| Economy | Trigger | Who can benefit |
|---|---|---|
| internal | the individual firm expands | that firm, through its own scale and organisation |
| external | the whole industry or geographic cluster expands | firms in the industry or location, including firms that have not grown |
Internal economies cause movement down a firm's LRAC as its own output rises. External economies lower the attainable costs of firms at each output, shifting their cost conditions downward.
A benefit located outside the firm is not automatically an external economy. Classify by whether it arises from industry growth rather than the individual firm's expansion.
| Source | Why LRAC may fall as the firm expands |
|---|---|
| financial | lower borrowing rates or wider finance access |
| technical | indivisible, specialised machinery and larger production runs |
| managerial | specialist managers improve decisions and productivity |
| marketing | campaign/design cost spread over more sales |
| purchasing | bulk buying secures lower input prices |
| risk-bearing | diversified products/markets stabilise income and investment |
Name the source and complete the unit-cost chain. Bulk purchasing is internal; a skilled local labour pool created by an industry cluster is external.
| Industry-cluster development | Firm-level cost benefit |
|---|---|
| larger pool of skilled labour | lower recruitment/training cost and better matching |
| improved transport links | faster, cheaper movement of workers, inputs and output |
| shared knowledge and research networks | less duplicated R&D and faster diffusion of methods |
As an industry concentrates or grows, workers, suppliers, infrastructure and institutions specialise around it. These shared resources can reduce LRAC for many firms without each firm expanding.
Tax reductions may lower costs but are not one of the specified external economies unless linked to industry growth; do not confuse a general policy benefit with a scale economy.
| Source | Cost mechanism |
|---|---|
| communication problems | more layers and sites delay or distort information |
| coordination problems | complex divisions, inventories and decisions create duplication or mismatch |
| X-inefficiency | weak competitive/managerial pressure allows waste and low effort |
If these organisational costs grow faster than output, LRAC rises. Decentralisation, better information systems and stronger accountability may delay or reduce the problem.
Diseconomies are not inevitable at a specific size and are not the same as diminishing returns. They occur in the long run because managing scale becomes costly.
$economic\ profit=TR-TC=(AR-AC)\times Q$
| State at chosen output | Total comparison | Per-unit comparison |
|---|---|---|
| supernormal profit | TR>TC | AR>AC |
| normal profit | TR=TC | AR=AC |
| loss | TR<TC | AR<AC |
Normal profit is the minimum return needed to keep enterprise in its current use and is included in economic cost. It is therefore zero economic profit, not zero accounting income.
A profit-maximising firm can still make a loss when no output avoids it; it chooses MR=MC to minimise the loss, then applies the shutdown test.
| Horizon | Continue condition | Threshold | Why |
|---|---|---|---|
| short run | produce if AR≥AVC | shutdown at minimum AVC where AR=AVC | revenue covers variable cost and contributes to unavoidable fixed cost |
| long run | remain if AR≥AC | exit at minimum AC where AR=AC | all costs are avoidable in the long run |
If AVC<AR<AC, the firm makes a loss but continues in the short run because operating loses less than shutting immediately; it exits in the long run unless conditions improve.
Shutdown is a production decision and need not mean legal closure. Compare AR with AVC in the short run, not merely AR with AC.