Cost, Revenue and Production – Short-Run & Long-Run Concepts

Learning Intentions

  • Be able to:

    • Explain & calculate short-run production concepts: fixed/variable factors, total product (TP), average product (AP), marginal product (MP), \text{Law of Diminishing Marginal Returns}.

    • Explain & measure short-run costs: fixed cost (FC), variable cost (VC), total cost (TC), average costs (AFC, AVC, ATC), marginal cost (MC). Understand the shapes of ATC & MC curves.

    • Explain long-run production: all factors variable; derive isoquants & identify returns to scale.

    • Explain long-run costs: derive long-run average cost (LRAC), minimum efficient scale (MES); relate to economies/diseconomies of scale.

    • Distinguish & compute total, average, marginal revenue.

    • Distinguish normal, sub-normal & super-normal profit; calculate each.

Economics in Context – Container Shipping & Economies of Scale

  • Container-ship capacity has tripled since the 1950s; OOCL Hong Kong (launched 2019) carries 21 000 TEU, length 400 m, weight 190 000 t.

  • Motivation for mega-ships: lowering long-run average cost (economies of scale → lower cost per container → only \$0.25 to ship a garment from Asia ➔ Europe).

  • Supply-chain effects: allows production in low-labour-cost countries while remaining competitive even after transport cost.

  • Negative externalities: one container ship ≈ emissions of 50 million cars; CO₂ + toxic oxides + sea pollution → raises debate on environmental costs vs. scale benefits.

  • Economists can: quantify cost savings; measure external costs; model optimal ship size; advise on carbon pricing/regulation.

Introduction to Production

  • Firms demand factors (land, labour, capital, enterprise) derived from need to produce.

  • Clothing industry example:

    • Global production centres: SE Asia, N Africa, Central Europe.

    • Key decision: labour-capital mix. In low-wage economies → labour-intensive; in high-wage economies → capital-intensive (automation).

  • Goal: find least-cost / most efficient combination for given output.

Isoquants & Alternative Techniques

  • Fig 34.3: three techniques to make 100 units of clothing.

    • Line A: equal labour & capital.

    • Line B: 2× capital vs labour.

    • Line C: 2× labour vs capital.

  • Isoquant: curve joining all (L,K) pairs yielding same output; helps map substitution possibilities.

Short-Run Production Function

  • Short run: at least one factor (usually capital) fixed; labour variable.

  • Example table (workers 0→6): shows TP, MP, AP.

    • MP=\Delta TP/\Delta L; declines as more labour hired.

  • Law of Diminishing Returns (a.k.a. variable proportions): beyond some point, adding extra variable input to fixed inputs causes MP to fall; can become negative.

  • Average product AP=TP/L – measure of labour productivity.

Graphical Insights

  • Production function: TP vs labour (Fig 34.4).

  • MP & AP curves: MP intersects AP at AP’s maximum.

Short-Run Cost Function

Cost Types & Formulas

  • Fixed Cost (FC): independent of output (rent, insurance, interest). Horizontal line at all Q.

  • Variable Cost (VC): varies directly with Q (labour, raw materials).

  • Total Cost TC=TFC+TVC.

  • Average Costs

    • AFC=TFC/Q (falls continuously).

    • AVC=TVC/Q.

    • ATC=TC/Q = AFC+AVC.

  • Marginal Cost MC = \Delta TC/\Delta Q.

Shapes

  • ATC: U-shaped because AFC ↓ but AVC ↑ (diminishing returns); minimum where MC = ATC.

  • MC crosses both AVC & ATC at their minimum points (Fig 34.6/34.7).

  • Optimum (productively efficient) output: Q where ATC minimal.

Decision Rule (short run)

  • Expand output while expected marginal revenue (>) marginal cost.

Long-Run Production Function

  • Long run: all factors variable; firms can alter scale and factor mix.

  • Optimal factor choice condition:
    \frac{MPA}{PA}=\frac{MPB}{PB}=\frac{MPC}{PC}=\dots ensuring least-cost combination.

Isoquant Map & Returns to Scale

  • Fig 34.9a: isoquants for 100, 200, 300, 400, 500 units.

    • Distance between isoquants indicates scale returns:

    • Narrower spacing → increasing returns to scale (output ↑ faster than inputs).

    • Wider spacing → decreasing returns to scale.

  • Isocost lines (Fig 34.9b): combinations of L & K with same cost; slope = relative factor prices.

  • Expansion path: locus of tangencies between isoquants & isocosts → firm’s long-run production function in cost terms.

  • Practical caveats: firms rarely know exact isoquants; factor substitution may be limited; social obligations may deter labour shedding.

Long-Run Cost Function

LRAC (Envelope Curve)

  • LRAC traced by lowest ATC achievable for each output when plant size chosen optimally. Flatter U-shape than SRATCs.

  • Constructed as envelope of successive SRAC curves as firm scales up (Fig 34.10).

Minimum Efficient Scale (MES)

  • Lowest Q where LRAC reaches its minimum.

    • Low MES → many small firms viable.

    • High MES → industry tends to oligopoly/monopoly.

  • Point Q on Fig 34.10.

Economies & Diseconomies of Scale

  • LRAC downward segment → economies; upward → diseconomies.

Internal Economies of Scale (firm-specific)

  • Technical: indivisibilities, special machinery, mass-production lines (vehicle assembly).

  • Purchasing: bulk-buy discounts; Walmart negotiating power; narrower SKU range further lowers prices.

  • Marketing: cheaper ad rates per viewer; logistics savings; IT platforms (Amazon).

  • Managerial: specialist functional managers improve efficiency.

  • Financial: lower interest rates & easier capital market access due to perceived lower risk.

External Economies of Scale (industry-wide)

  • Arise from industry growth, benefit all nearby firms; shift LRAC downward for everyone (Fig 34.12).

    • Skilled labour pool.

    • Local specialised suppliers.

    • Shared R&D, knowledge spillovers.

    • Improved infrastructure.

  • Geographic clusters: Silicon Valley (IT), Guzhen (lighting), Cambridge UK (biotech/electronics).

Diseconomies of Scale

  • Internal: coordination & communication problems; layers of bureaucracy; worker alienation, low morale, repetitive tasks → rising costs.

  • External: congestion, land scarcity (↑ FC), skill shortages (↑ wages).

  • May prompt firm break-ups into smaller units.

Revenue Concepts

  • Total Revenue TR=P\times Q.

  • Average Revenue AR=TR/Q = price in both perfect & imperfect competition.

  • Marginal Revenue MR = \Delta TR/\Delta Q.

Market Structure Effect

  • Price taker (perfect competition): horizontal demand; AR=MR=P (Fig 34.14b).

  • Price maker (monopoly/oligopoly): downward-sloping demand; MR below AR (Fig 34.15).

  • Elasticity zones on AR: where PED>1, MR positive; PED=1, MR zero; PED<1, MR negative.

Profit Concepts

  • Profit = TR - TC (TC includes opportunity cost of owner’s resources).

  • Normal profit: minimum earnings to keep resources in current use; treated as cost inside TC.

  • Supernormal profit = (TR - TC) - \text{Normal profit}; signal for entry.

  • Sub-normal profit: earnings < normal; if persistent → exit in long run.

Applied Case Studies & Examples

Cost Structure of a Firm (Fig 34.8)

  • Composition: Wages 35 %, Materials 25 %, Bank interest 16 %, Insurance 10 %, Marketing 5 %, Profit 9 %.

    • Identify fixed vs variable: interest, insurance = fixed; wages, materials = variable; marketing partly variable.

  • Could represent a manufacturing firm with substantial labour & material share.

Airbus A380 & Economies of Scale (Activity 34.4)

  • A380 (max 853 pax) sought to exploit technical & passenger-density economies on hub-spoke routes.

  • Market shift to smaller fuel-efficient twin-engine long-haul (B787, A350) reduced orders → Airbus ceased A380 production (2019).

  • Illustrates risk: economies of scale can be overtaken by tech change & demand patterns.

Coffee Shop Profit Breakdown (Think like an Economist)

  • Large cappuccino price £2.60.

    • Coffee £0.09, Milk £0.09, Cup+lid £0.19, Staff £0.63, Overheads £0.76, Profit £0.32, VAT £0.52.

  • Coffee+milk < cost of disposable cup! Highlights:

    • Value added concentrated in labour & overheads (rent, utilities, franchise fees).

    • Illustrates importance of correct cost attribution & mark-ups in service sector.

Common Mistakes & Tips

  • Confuse product (total output) with productivity (output per worker).

  • Use total instead of marginal when applying profit-max condition MC=MR.

  • Mix up diminishing returns (short run, one variable factor) with diseconomies of scale (long run, all factors variable).

  • Forget that normal profit is part of cost.

Formula & Definition Summary

  • TP, AP=TP/L, MP=\Delta TP/\Delta L.

  • TC=TFC+TVC; AFC=TFC/Q; AVC=TVC/Q; ATC=TC/Q; MC=\Delta TC/\Delta Q.

  • TR=P\times Q; AR=TR/Q; MR=\Delta TR/\Delta Q.

  • MES: lowest Q where LRAC=\min.

  • Economies of Scale: LRAC ↓ as Q ↑; Diseconomies: LRAC ↑ beyond MES.

  • Profit categories as detailed above.

Ethical, Environmental & Practical Implications

  • Mega-ships cut costs but raise severe pollution externalities → policy debate on carbon tax, IMO fuel rules.

  • Tech change (automation, robots) boosts scale efficiency yet displaces labour → social considerations in factor substitution.

  • Excessive industry clustering may harm local quality of life (congestion, high rents) despite cost savings.

  • Coffee supply chain: tiny producer share of retail price raises equity questions.

Connections to Earlier Principles

  • Division of labour (Ch 3) → technical economies.

  • Externalities (Ch 33) → shipping pollution & congestion from clustering.

  • Market structures (perfect vs imperfect competition) influence AR/MR relationships explored here.