3.3.2 - Revenue, costs and profits

Syllabus
2018
Topic
3.3.2
Level
A2

Learning objectives

3.3.21a - Formulae to calculate and understand the relationship between: • total revenue •Formulae to calculate and understand the relationship between:; total revenue; average revenue; marginal revenue.3.3.21b - Price elasticity of demand and its relationship to revenue concepts, includingPrice elasticity of demand and its relationship to revenue concepts, including calculations.3.3.22a - Derivation of short-run cost curves from the assumption of diminishing marginalDerivation of short-run cost curves from the assumption of diminishing marginal productivity.3.3.22b - law of diminishing returnsThe law of diminishing returns.3.3.22c - Formulae to calculate and understand the relationship between: • total cost • totalFormulae to calculate and understand the relationship between:; total cost; total fixed cost; total variable cost; average (total) cost; average fixed cost; average variable cost; marginal cost.3.3.22d - relationship between: • marginal product and marginal costs • average products andThe relationship between:; marginal product and marginal costs; average products and average cost; total product and total cost; short-run and long-run costs.3.3.23a - relationship between long-run cost curves and diseconomies of economies/diseconomies ofThe relationship between long-run cost curves and diseconomies of economies/diseconomies of scale. scale3.3.23b - Minimum efficient scaleMinimum efficient scale.3.3.23c - Distinction between internal/external economies of scaleDistinction between internal/external economies of scale.3.3.23d - Sources of internal economies of scale: • financial • technical • managerial •Sources of internal economies of scale:; financial; technical; managerial; marketing; purchasing; risk bearing.3.3.23e - Sources of external economies of scale: • availability of skilled labour • access toSources of external economies of scale:; availability of skilled labour; access to transport links; sharing knowledge.3.3.23f - Sources of diseconomies of scale: • communication problems • coordination problems •Sources of diseconomies of scale:; communication problems; coordination problems; X-inefficiency.3.3.24a - distinction between normal profit, supernormal profit and lossesThe distinction between normal profit, supernormal profit and losses.3.3.24b - Short-run and long-run shutdown pointsShort-run and long-run shutdown points.

Total, average and marginal revenue

$TR=P\times Q$; $AR=TR/Q$; $MR=\Delta TR/\Delta Q$

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,6 each,TR=600and600 andAR=6.Ifsellingunit101raisesTRto6. If selling unit 101 raises TR to604, that unit's MR=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=0MR=0.

Price elasticity and total revenue

$PED=\%\Delta Q_d/\%\Delta P$

Demand range Price falls Price rises
elastic, PED>1|PED|>1 TR rises TR falls
inelastic, PED<1|PED|<1 TR falls TR rises
unit elastic, PED=1|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.

From marginal productivity to short-run cost curves

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.

The law of diminishing returns

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.

Cost formulae and calculations

$TC=TFC+TVC$; $TFC=TC$ 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=TFC=500 and at 200 units TC=TC=2,500, then TVC=TVC=2,000, AFC=AFC=2.50, AVC=AVC=10 and AC=AC=12.50. If TC rises to 2,620at210units,2,620 at 210 units,MC=120/10=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.

Product and cost relationships

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.

Economies, diseconomies and LRAC

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

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.

Internal and external economies of scale

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.

Sources of internal economies of scale

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.

Sources of external economies of scale

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.

Why diseconomies of scale arise

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.

Normal profit, supernormal profit and loss

$economic\ profit=TR-TC=(AR-AC)\times Q$

State at chosen output Total comparison Per-unit comparison
supernormal profit TR>TCTR>TC AR>ACAR>AC
normal profit TR=TCTR=TC AR=ACAR=AC
loss TR<TCTR<TC AR<ACAR<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=MCMR=MC to minimise the loss, then applies the shutdown test.

Short-run shutdown and long-run exit

Horizon Continue condition Threshold Why
short run produce if ARAVCAR\ge AVC shutdown at minimum AVC where AR=AVCAR=AVC revenue covers variable cost and contributes to unavoidable fixed cost
long run remain if ARACAR\ge AC exit at minimum AC where AR=ACAR=AC all costs are avoidable in the long run

If AVC<AR<ACAVC<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.