1 Economic Concepts · 1.1 Microeconomics: demand, production, markets and factor pricing
1.1.4 Costs and revenue: short-run and long-run cost curves, average and marginal revenue
Short-run costs split into fixed and variable parts and give U-shaped AVC, ATC and MC curves; the long-run average cost curve is the envelope of short-run curves; revenue is TR = P × Q, AR = price and MR = the change in TR from one more unit.
- APPSC Paper I
- Advanced level
- 10 min read
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Core facts
- Short run: at least one factor is fixed (plant, machinery). Long run: all factors are variable, so all costs are variable.
- TC = TFC + TVC. TFC stays the same at every output, even at zero output. TVC is zero at zero output and rises with output.
- AFC = TFC ÷ Q, AVC = TVC ÷ Q, ATC (AC) = TC ÷ Q = AFC + AVC.
- MC = ΔTC ÷ ΔQ = ΔTVC ÷ ΔQ. Fixed cost does not affect MC.
- AFC falls continuously as output rises; its curve is a rectangular hyperbola (AFC × Q = TFC, a constant). It never touches either axis.
- AVC, ATC and MC are U-shaped in the short run because of the law of variable proportions (returns first increase, then diminish).
- MC cuts AVC and ATC at their minimum points, from below.
- Minimum AVC comes at a lower output than minimum ATC. The vertical gap ATC − AVC = AFC narrows as output rises.
- LAC is the envelope of the short-run AC curves (Jacob Viner, 1931); it is also called the planning curve. It is U-shaped because of economies and then diseconomies of scale (returns to scale), not the law of variable proportions.
- Opportunity cost: the value of the next best alternative given up. Economic cost = explicit cost + implicit cost (including normal profit).
- Revenue: TR = P × Q; AR = TR ÷ Q = P (so the AR curve is the demand curve); MR = ΔTR ÷ ΔQ.
- Perfect competition: price is fixed for the firm, so AR = MR = P, a horizontal line.
- Monopoly / imperfect competition: AR slopes down and MR lies below AR.
- MR = AR (1 − 1/e), where e is the price elasticity of demand (absolute value). At e = 1, MR = 0 and TR is maximum.
Explained
1. The cost schedule. A firm has TFC = ₹100. TVC is given; work out the rest.
| Q | TVC | TC | MC |
|---|---|---|---|
| 1 | 40 | 140 | 40 |
| 2 | 70 | 170 | 30 |
| 3 | 90 | 190 | 20 |
| 4 | 120 | 220 | 30 |
| 5 | 170 | 270 | 50 |
| 6 | 240 | 340 | 70 |
| Q | AFC | AVC | ATC |
|---|---|---|---|
| 1 | 100 | 40 | 140 |
| 2 | 50 | 35 | 85 |
| 3 | 33.33 | 30 | 63.33 |
| 4 | 25 | 30 | 55 |
| 5 | 20 | 34 | 54 |
| 6 | 16.67 | 40 | 56.67 |
How each column is found (Q = 5): TC = 100 + 170 = 270; AFC = 100/5 = 20; AVC = 170/5 = 34; ATC = 270/5 = 54 (= 20 + 34); MC = 270 − 220 = 50.
What the table shows:
- MC falls first (20 at the 3rd unit), then rises: increasing, then diminishing returns to the variable factor.
- Average–marginal rule: when MC < average, the average falls; when MC > average, the average rises; when MC = average, the average is at its minimum (unchanged). The 4th unit's MC (30) equals AVC (30), so AVC stays at 30, its lowest. The 5th unit's MC (50) is below ATC (55), so ATC falls to 54; the 6th unit's MC (70) is above 54, so ATC rises. Minimum ATC (Q = 5) comes after minimum AVC (Q = 3–4).
- AFC keeps falling: 100, 50, 33.33, 25, 20, 16.67, and AFC × Q is always 100.
2. Shapes of the total curves.
| Curve | Shape |
|---|---|
| TFC | Horizontal line |
| TVC | Starts at origin; rises slowly, then fast (inverse S) |
| TC | Same shape as TVC, shifted up by TFC |
| MC | Slope of TC (or TVC) |
3. Long-run costs. In the long run the firm chooses the plant size. Each plant has its own short-run AC (SAC). The LAC touches each SAC at one point and is the lowest cost of producing each output when plant size can change.
- Falling part of LAC: economies of scale (internal: technical, managerial, marketing, financial, risk-bearing; external: industry-wide benefits such as better transport or skilled labour).
- Rising part: diseconomies of scale (management becomes hard to coordinate).
- The optimum plant is the one whose SAC minimum touches LAC at the LAC minimum. Left of that point LAC touches the falling part of the SACs; right of it, the rising part.
- LMC cuts LAC at its minimum, as in the short run.
- Empirical studies often find an L-shaped LAC: costs fall, then stay flat over a wide range.
4. Revenue schedule (demand P = 20 − 2Q).
| Q | P = AR | TR | MR |
|---|---|---|---|
| 3 | 14 | 42 | 10 |
| 4 | 12 | 48 | 6 |
| 5 | 10 | 50 | 2 |
| 6 | 8 | 48 | −2 |
| 7 | 6 | 42 | −6 |
TR is highest (₹50) at Q = 5, where the demand is unit elastic; beyond it MR is negative and TR falls.
5. Using MR = AR (1 − 1/e).
Example 1. Price (AR) is ₹10 and elasticity of demand is 2. Find MR. Solution. MR = 10 × (1 − 1/2) = 10 × 0.5. Answer: ₹5
Example 2. AR = ₹30, MR = ₹20. Find the elasticity of demand. Solution. e = AR ÷ (AR − MR) = 30 ÷ 10. Answer: 3
Example 3. AFC at 10 units is ₹60. Find AFC at 30 units. Solution. TFC = 60 × 10 = 600; 600 ÷ 30. Answer: ₹20
Deeper
1. Cost functions with calculus. For a cubic TVC, AVC and MC are quadratic (U-shaped).
Example 4. TC = Q³ − 6Q² + 15Q + 10. Find the minimum AVC and show that MC equals it there. Solution.
- TFC = 10; TVC = Q³ − 6Q² + 15Q.
- AVC = Q² − 6Q + 15. dAVC/dQ = 2Q − 6 = 0 → Q = 3. AVC = 9 − 18 + 15 = 6.
- MC = dTC/dQ = 3Q² − 12Q + 15. At Q = 3: 27 − 36 + 15 = 6.
- Answer: minimum AVC = 6 at Q = 3, where MC = 6. This is the firm's shutdown price under perfect competition.
- ATC = Q² − 6Q + 15 + 10/Q has its minimum at Q ≈ 3.43, where ATC = MC ≈ 9.10 (the break-even price). Minimum ATC comes at a larger output than minimum AVC, as the rule says.
2. Linear demand and MR. If P = a − bQ, then TR = aQ − bQ² and MR = a − 2bQ. The MR line has the same intercept and twice the slope, so it cuts the quantity axis at half the output of the AR line (it bisects any horizontal line from the price axis to AR).
- Point elasticity on the line: e = P ÷ (bQ). For P = 20 − 2Q at Q = 5: e = 10 ÷ 10 = 1, and MR = 20 − 20 = 0. ✓
3. Relationships to remember.
| Elasticity e | MR | TR as output rises |
|---|---|---|
| e > 1 | Positive | Rises |
| e = 1 | Zero | Maximum |
| e < 1 | Negative | Falls |
| e = ∞ | MR = AR | Rises at a constant rate |
4. Kinds of cost (definitions asked in degree exams).
- Explicit cost: money actually paid (wages, rent, raw materials). Implicit cost: value of the owner's own resources (own land, own capital, own time).
- Accounting profit = TR − explicit cost; economic profit = TR − explicit − implicit cost. Normal profit is part of cost.
- Private cost vs social cost: social cost adds the cost borne by others (pollution, an external cost).
- Sunk cost: already spent and not recoverable; it should not affect current decisions.
- Prime cost = variable cost; supplementary (overhead) cost = fixed cost (Marshall's terms).
5. Why AVC and LAC are U-shaped for different reasons. Short-run AVC turns up because adding more variable factor to a fixed plant brings diminishing marginal returns. LAC turns up only if the whole scale of operation brings diseconomies of scale; with constant returns to scale it is horizontal.
6. Modern (saucer / L-shaped) costs. Koutsoyiannis notes that firms keep reserve capacity, so short-run AVC is saucer-shaped with a flat stretch, and long-run costs are L-shaped once technical economies are used up.
Common traps
- ✗ "Fixed cost is zero at zero output." ✓ TFC is the same at every output, including zero; TVC is zero at zero output.
- ✗ "MC depends on fixed cost." ✓ MC = ΔTVC/ΔQ; fixed cost does not affect MC.
- ✗ "AFC is U-shaped." ✓ AFC falls continuously (rectangular hyperbola).
- ✗ "MC cuts ATC at the minimum of MC." ✓ MC cuts AVC and ATC at their minimum points, from below.
- ✗ "Minimum ATC comes before minimum AVC." ✓ Minimum AVC comes first (at a smaller output).
- ✗ "LAC is U-shaped because of the law of variable proportions." ✓ That explains the short-run curves; LAC depends on returns to scale.
- ✗ "TR is maximum where MR is maximum." ✓ TR is maximum where MR = 0 (e = 1).
- ✗ "Under perfect competition MR is below AR." ✓ Under perfect competition AR = MR = P.
Quick revision
- TC = TFC + TVC; ATC = AFC + AVC.
- MC = ΔTC/ΔQ = ΔTVC/ΔQ.
- AFC: rectangular hyperbola, always falling.
- MC cuts AVC and ATC at their minimum, from below.
- Minimum AVC before minimum ATC.
- LAC = envelope (planning) curve, Viner; U-shape from economies/diseconomies of scale.
- AR = P = demand curve; MR = ΔTR/ΔQ.
- MR = AR(1 − 1/e); e = 1 → MR = 0, TR maximum.
- Linear demand: MR has twice the slope of AR.
- Perfect competition: AR = MR = P (horizontal).
Go deeper: Mains writing (beyond what APPSC Paper I usually asks)
Mains writing Mains writing
- Frame: cost curves link the production function (returns) to the firm's supply decision.
- Analysis:
- MC above minimum AVC is the competitive firm's short-run supply curve.
- Economies of scale explain why some industries (power, railways, telecom) tend towards a few large firms.
- Elasticity decides whether a price cut raises revenue: useful for pricing public services such as bus fares.
- Example: a bus already running on a route has low MC per extra passenger, so filling empty seats at a lower fare can raise revenue without much extra cost.
Practise this topic. Questions on Production, costs & market structures, with answers explained.
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