Cost and Revenue Analysis: Cost Concepts, Cost Curves, Revenue Curves and Profit

Meaning of cost

Cost is the monetary value of resources used in producing a commodity. It includes payments to factors of production and other expenses incurred to produce and sell output.

Cost concepts (important)

1. Money cost: cost expressed in money terms (actual expenditure).
2. Real cost: sacrifice of resources (effort, pain, time).
3. Opportunity cost: cost of next best alternative foregone.
4. Explicit cost: actual cash payments (wages, rent, raw materials).
5. Implicit cost: imputed value of owned resources (owner’s salary, own building rent).
6. Fixed cost: cost that does not change with output in short run (rent, insurance).
7. Variable cost: cost that changes with output (raw materials, wages of casual labour).
8. Total cost: sum of fixed and variable costs.
9. Accounting cost vs economic cost: economic cost includes explicit + implicit + opportunity costs.

Short run cost: total and per unit costs

Total costs

• TFC (Total Fixed Cost): remains constant in short run.
• TVC (Total Variable Cost): changes with output.
• TC (Total Cost): $TC = TFC + TVC$

Per unit costs

• AFC (Average Fixed Cost): $AFC = \\frac{TFC}{Q}$
• AVC (Average Variable Cost): $AVC = \\frac{TVC}{Q}$
• AC (Average Cost): $AC = \\frac{TC}{Q} = AFC + AVC$
• MC (Marginal Cost): $MC = \\frac{\\Delta TC}{\\Delta Q} = \\frac{\\Delta TVC}{\\Delta Q}$ (Because TFC does not change with output.)

Short run cost curves: shapes and relationships

1. AFC curve: continuously falls as output increases (rectangular hyperbola).
2. AVC curve: U-shaped due to law of variable proportions.
3. AC curve: U-shaped; lies above AVC because AC = AFC + AVC.
4. MC curve: U-shaped; intersects AVC and AC at their minimum points.

Key relationships:

• When MC < AC, AC falls; when MC > AC, AC rises; MC = AC at AC minimum.
• When MC < AVC, AVC falls; when MC > AVC, AVC rises; MC = AVC at AVC minimum.

Long run cost curves (LAC, LMC)

In the long run, all factors are variable and the firm can change scale of production.

• LAC (Long Run Average Cost) is also called the envelope curve because it envelopes short-run average cost curves (SACs). It is typically U-shaped due to economies and diseconomies of scale.
• LMC (Long Run Marginal Cost) is the marginal cost in the long run and intersects LAC at its minimum point.

Economies and diseconomies of scale (brief)

• Economies of scale: cost advantages of large scale (specialisation, bulk purchase, technical economies).
• Diseconomies of scale: cost disadvantages of very large scale (management and coordination problems).

Revenue: TR, AR and MR

Revenue is income received from sale of output.

• Total Revenue (TR): $TR = P \\times Q$
• Average Revenue (AR): $AR = \\frac{TR}{Q}$ AR is generally equal to price (P).
• Marginal Revenue (MR): $MR = \\frac{\\Delta TR}{\\Delta Q}$

Revenue curves under different market forms (basic)

Perfect competition

• Firm is price taker: AR = MR = Price (horizontal demand curve).
• TR increases proportionately with output.

Monopoly / imperfect competition

• Firm faces downward sloping demand curve: AR slopes downward.
• MR lies below AR because to sell more, firm must reduce price.

Profit: meaning and types

Profit is excess of total revenue over total cost: $\\pi = TR - TC$ Types (basic):

• Normal profit: minimum profit necessary to keep firm in business (part of cost in economic sense).
• Supernormal profit: profit above normal profit.
• Loss: when TR < TC.

Profit maximisation condition (basic)

Profit is maximised when:

1. MR = MC (necessary condition), and
2. MC cuts MR from below (MC rising) (sufficient condition).

Alternatively, profit maximisation occurs where the gap between TR and TC is maximum.

Break-even analysis (basic)

Break-even point is the level of output/sales where total revenue equals total cost (no profit, no loss). $TR = TC$ Uses: planning output, deciding minimum sales, analysing profit at different output levels.

Quick recap (1-minute revision)

• TC = TFC + TVC; AC = AFC + AVC; MC = ΔTC/ΔQ.
• AFC falls continuously; AVC, AC and MC are U-shaped; MC cuts AC and AVC at minimum.
• Long run: LAC is envelope of SAC; economies → falling LAC; diseconomies → rising LAC.
• TR = P×Q; AR = TR/Q; MR = ΔTR/ΔQ.
• Profit maximisation: MR = MC and MC rising.
• Break-even: TR = TC (no profit, no loss).