Cost Theory and Long-Run Production Theory
Cost concepts, cost curves, the link between short-run cost and productivity, and returns to scale—BBA/MBA Business Economics
Abstract. A firm's profit is total revenue minus total cost, so managers must understand how costs behave as output changes. This paper reviews the main cost concepts (fixed, variable, total, average, and marginal cost) and the shapes of short-run cost curves. It then shows that these shapes follow from the productivity of variable inputs through the relationships MC = w / MP and AVC = w / AP. Finally, it moves to the long run, where all inputs are variable, and explains constant, increasing, and decreasing returns to scale and the associated economies and diseconomies of scale. A running example, the hypothetical Acharya Bag Industries, a school-bag manufacturer in Nepal, illustrates each idea. All figures are illustrative.
1. Introduction
Imagine a firm producing school bags. It buys fabric and zippers, hires workers, rents a factory, runs machines, pays for electricity, and delivers the finished product. Two questions follow naturally:
- How much does it cost to produce each bag?
- How can output be expanded while keeping the average cost of production low?
These questions are the core of cost theory and production theory. Because Profit = Total Revenue − Total Cost, understanding cost and production informs decisions on output level, labor and machinery needs, pricing, resource allocation, expansion, and long-term investment.
2. Cost Concepts
Cost is the expenditure a firm incurs to produce goods and services. For Acharya Bag Industries, monthly expenses might be as follows.
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Not all of these costs react to output in the same way, which leads to the distinction between fixed and variable costs.
2.1 Fixed cost (FC)
Fixed cost is a cost that stays unchanged in total, within a relevant period and capacity range, regardless of output (Greenlaw, Shapiro, and MacDonald, 2022, §7.3). Even with zero production, the firm must still pay rent, insurance, and certain salaries. Typical examples are factory rent, insurance, fixed administrative salaries, property taxes, and depreciation under a fixed method.
If monthly rent is Rs. 30,000, total fixed cost (TFC) is Rs. 30,000 at 0, 100, 200, or 500 bags. The TFC curve is therefore a horizontal line.
Average fixed cost is the fixed cost per unit:
AFC = TFC / Q
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AFC falls continuously as output rises, because the same fixed cost is spread over more units (the spreading effect). It approaches zero but never reaches it while the fixed cost is positive.
2.2 Variable cost (VC)
Variable cost changes with the level of output. For the bag factory it includes fabric, zippers, packaging, production-related electricity, and piece-rate wages. If each bag requires Rs. 200 of variable inputs, then TVC = 200Q.
Output Table
This constant per-unit cost is a simplification. In real production, variable cost per unit changes with productivity, input prices, and capacity limits, and Section 4 shows why. |
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2.3 Total cost (TC)
Total cost is the sum of fixed and variable costs:
TC = TFC + TVC
With TFC = Rs. 30,000 and TVC = 200Q, TC = 30,000 + 200Q. At 300 bags, TC = 30,000 + 60,000 = Rs. 90,000.
On a graph, TFC is horizontal, TVC starts at the origin, and TC starts at the level of fixed cost. The vertical gap between TC and TVC always equals TFC. |
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Figure 1. Total cost is fixed cost plus variable cost. Drawn with a barbershop example (Greenlaw et al., 2022, §7.3); the shapes match the bag-factory case.
2.4 Average total cost (ATC)
ATC = TC / Q = AFC + AVC
At 300 bags, ATC = 90,000 / 300 = Rs. 300 per bag.
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Managers monitor ATC because it informs pricing, competitiveness, and profitability.
2.5 Marginal cost (MC)
Marginal cost is the additional cost of producing one more unit:
MC = ΔTC / ΔQ (or dTC / dQ in continuous models)
Moving from 200 to 300 bags, TC rises from Rs. 70,000 to Rs. 90,000, so MC = 20,000 / 100 = Rs. 200 per bag.
Marginal and average cost are related by a simple rule of averages (Varian, 2014; Mankiw, 2021):
- When MC is below ATC, ATC falls.
- When MC is above ATC, ATC rises.
- MC crosses ATC at ATC's minimum, under the usual smooth-curve assumptions.
- The same holds between MC and AVC.
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Figure 2. MC falls, then rises, and cuts AVC and ATC at their minimum points (barbershop example; Greenlaw et al., 2022, §7.3).
3. Short-Run Cost Curves
The short run is a period in which at least one factor of production is fixed (Greenlaw et al., 2022, §7.3). A bag factory, for example, may have a fixed building and a fixed number of sewing machines but can vary workers and materials. The standard short-run curves have these shapes:
- AFC falls continuously as fixed cost is spread over more output.
- AVC is U-shaped. It first falls as variable inputs become more productive, then rises under diminishing marginal productivity.
- ATC is also U-shaped. It falls at first because fixed cost is spread and productivity improves, then rises once increasing marginal cost outweighs the spreading effect. Since ATC = AFC + AVC, its minimum occurs at a higher output than the AVC minimum.
- MC is U-shaped (often drawn like a check mark). It falls while marginal productivity rises and rises once marginal productivity diminishes. It cuts AVC and ATC at their minimum points.
The next part explains why these shapes arise.
4. Short-Run Cost and Productivity
4.1 Production concepts
Productivity is the efficiency with which inputs are turned into output. If 5 workers produce 100 bags a day, labor productivity is 100 / 5 = 20 bags per worker. Three related measures describe production when one input (labor, L) is variable:
- Total product (TP): total output from all units of the variable input, given the fixed inputs.
- Average product (AP): AP = TP / L.
- Marginal product (MP): MP = ΔTP / ΔL.
4.2 The law of variable proportions
When units of a variable input are added to fixed inputs, output first rises quickly because workers specialize and divide tasks. Eventually additional workers must share limited machines and space, so each adds less than the one before. This is the law of diminishing marginal returns (Mankiw, 2021; Pindyck and Rubinfeld, 2018). Suppose the factory has a fixed set of sewing machines:
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Three stages are visible:
- Stage I, increasing marginal returns: MP rises (up to the third worker) as specialization improves use of the fixed resources.
- Stage II, diminishing marginal returns: MP falls but stays positive, so TP still rises, though more slowly.
- Stage III, negative marginal returns: MP is negative, so extra workers reduce total output through congestion and interference.
A profit-seeking firm normally operates in Stage II. Note also that MP intersects AP at AP's maximum, which is the same averaging rule seen in cost curves.
4.3 From productivity to cost
The central principle is this: with constant input prices, higher productivity lowers the cost of additional output, and lower productivity raises it. To see this (a standard result; see Varian, 2014), let labor be the only variable input and w the wage rate. Then TVC = wL, and since ΔTVC = wΔL,
MC = ΔTVC / ΔQ = wΔL / ΔQ = w / MP
Similarly, AVC = TVC / Q = wL / Q = w / AP
MC is inversely related to the marginal product of labor, and AVC is inversely related to its average product. If MP were zero, MC would become unbounded in this simplified model.
Numerical demonstration with a wage of Rs. 1,000 per worker per day:
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With the third worker, MP = 20 and MC = 1,000 / 20 = Rs. 50. With the sixth, MP = 5 and MC = 1,000 / 5 = Rs. 200. As marginal productivity falls, marginal cost rises.
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The U-shape of the short-run MC and AVC curves is therefore explained by the law of variable proportions, assuming constant input prices and conventional technology.
Figure 3. MP and AP (top) are mirrored by MC = w / MP and AVC = w / AP (bottom). Barbershop example with a wage of $80 per day; source data from Greenlaw et al. (2022), §7.3.
5. Long-Run Production Theory
The long run is a period in which all factors of production are variable (Greenlaw et al., 2022, §7.5): the firm can change factory size, machinery, labor, technology, and capacity. It is defined by the time needed to adjust all inputs, not by a fixed number of months or years.
Basis | Short run | Long run |
|---|---|---|
Factors of production | At least one fixed | All variable |
Capacity | Limited by fixed factors | Can be changed |
Main production concept | Law of variable proportions | Returns to scale |
Cost curves | Short-run curves | Long-run curves |
5.1 Returns to scale
Returns to scale describe how output responds when all inputs are increased in the same proportion. This differs from the law of variable proportions, in which at least one input is held fixed. If a firm doubles every input, output may more than double, exactly double, or less than double.
5.2 Increasing returns and economies of scale
With increasing returns to scale, a proportional increase in all inputs yields a more than proportional rise in output. Economies of scale exist when long-run average cost falls as the scale of production rises.
Example. The bag factory starts with 10 workers, 5 machines and Rs. 10 lakh of capital, producing 1,000 bags. Doubling all inputs to 20 workers, 10 machines and Rs. 20 lakh raises output to 2,500 bags: inputs up 100%, output up 150%.
Sources of economies of scale include:
- Technical: specialised machinery and advanced technology.
- Managerial: specialist managers in finance, marketing, production and HR.
- Purchasing: bulk buying and bargaining power.
- Financial: better access to credit and cheaper borrowing.
- Marketing: advertising and distribution costs spread over more output.
- Specialisation: workers and departments focus on narrow tasks.
Average cost then falls as output grows:
Output | Total cost | Average cost |
|---|---|---|
1,000 | Rs. 500,000 | Rs. 500 |
2,000 | Rs. 800,000 | Rs. 400 |
3,000 | Rs. 1,050,000 | Rs. 350 |
4,000 | Rs. 1,200,000 | Rs. 300 |
5.3 Decreasing returns and diseconomies of scale
With decreasing returns to scale, a proportional rise in all inputs yields a less than proportional rise in output. Diseconomies of scale occur when long-run average cost rises beyond the efficient scale.
Example. Doubling workers (20 to 40), machines (10 to 20) and capital (Rs. 20 lakh to Rs. 40 lakh) raises output only from 2,500 to 4,000, an increase of 60%.
Typical causes are:
- Management difficulties: coordinating many employees and departments becomes harder.
- Communication problems: information moves slowly through many layers.
- Bureaucracy: excessive procedures delay decisions.
- Coordination conflicts: departments compete over resources and priorities.
- Congestion: transport, storage and production bottlenecks.
- Employee issues: weaker connection to the organisation may reduce motivation.
Output | Total cost | Average cost |
|---|---|---|
4,000 | Rs. 1,200,000 | Rs. 300 |
5,000 | Rs. 1,600,000 | Rs. 320 |
6,000 | Rs. 2,100,000 | Rs. 350 |
7,000 | Rs. 2,800,000 | Rs. 400 |
5.4 Constant returns to scale
With constant returns to scale, output rises in exactly the same proportion as all inputs. Doubling workers (10 to 20), machines (5 to 10), and capital (Rs. 10 lakh to Rs. 20 lakh) doubles output from 1,000 to 2,000 bags. If input prices are constant and the process can simply be replicated, long-run average cost stays constant (for example, Rs. 500 at 1,000, 2,000, 3,000 and 4,000 bags).
5.5 Comparison
Basis | Increasing | Constant | Decreasing |
|---|---|---|---|
Input increase | 100% | 100% | 100% |
Output increase | More than 100% | Exactly 100% | Less than 100% |
Typical LRAC | Falling | Constant | Rising |
Main reason | Specialisation, scale advantages | Proportionate expansion | Coordination and management difficulty |
5.6 The Cobb-Douglas test
For the Cobb-Douglas production function (Cobb and Douglas, 1928) Q = A·K^α·L^β, multiply both inputs by a factor t:
Q′ = A(tK)^α (tL)^β = t^(α+β) · A·K^α·L^β = t^(α+β) · Q
So returns to scale depend on the sum of the exponents:
- α + β > 1: Q′ > tQ, increasing returns.
- α + β = 1: Q′ = tQ, constant returns.
- α + β < 1: Q′ < tQ, decreasing returns.
Production function | Sum of exponents | Returns to scale |
|---|---|---|
Q = K^0.7 · L^0.6 | 1.3 | Increasing |
Q = K^0.5 · L^0.5 | 1.0 | Constant |
Q = K^0.3 · L^0.4 | 0.7 | Decreasing |
5.7 The long-run average cost curve
The long-run average cost (LRAC) curve shows the minimum average cost of producing each output when all inputs can be varied (Viner, 1931; Varian, 2014). It is often called the firm's planning curve. In the traditional model it is U-shaped: falling under economies of scale, flat under constant returns, and rising under diseconomies of scale. The minimum efficient scale (MES) is the lowest output at which long-run average cost is minimised. Producing below it forgoes scale economies, and the firm must check whether market demand can support output at that scale.
Figure 4. The LRAC curve is the lower edge of the short-run average cost curves, one for each plant size. Illustrative shapes only, following the concept in Greenlaw et al. (2022), §7.5.
5.8 Returns to scale versus economies of scale
The two terms are related but not identical.
Returns to scale | Economies of scale |
|---|---|
Production concept, based on the production function | Cost concept, based on the cost function |
Output response to proportional input changes | Behaviour of long-run average cost |
Increasing, constant, decreasing returns | Economies, constant cost, diseconomies |
Under constant input prices and cost minimisation, increasing returns go with falling LRAC, constant returns with constant LRAC, and decreasing returns with rising LRAC. Changing input prices, technology and other scale-related factors can complicate this link.
6. Case Study: Expansion of Acharya Bag Industries
Acharya Bag Industries produces 1,000 bags a month. Fixed costs are rent of Rs. 30,000 plus depreciation of Rs. 10,000, so TFC = Rs. 40,000. Variable cost is Rs. 200 per bag, so TVC = Rs. 200,000 and TC = Rs. 240,000, giving ATC = Rs. 240. Management is considering expansion and has prepared these hypothetical projections:
Production | Total cost (Rs.) | Average cost (Rs.) |
|---|---|---|
1,000 | 240,000 | 240 |
2,000 | 400,000 | 200 |
3,000 | 540,000 | 180 |
4,000 | 680,000 | 170 |
5,000 | 900,000 | 180 |
6,000 | 1,200,000 | 200 |
Average cost falls from 1,000 to 4,000 bags, reaches its minimum at 4,000, and rises afterwards. Under these projections, 4,000 bags is the cost-minimising scale. Before expanding, management should still test whether that volume is commercially feasible, considering market demand, financing, input prices, product quality and operational capacity.
7. Practice Questions and Answers
- A firm has fixed costs of Rs. 50,000 and variable costs of Rs. 150 per unit. Find total cost at 500 units.
- Total fixed cost is Rs. 60,000. Find AFC at 200 and 400 units.
- TC rises from Rs. 100,000 to Rs. 125,000 as output rises from 500 to 600 units. Find MC.
- A worker paid Rs. 1,200 per day produces 12 additional units. Find MC, assuming labour is the only variable input.
- Capital and labour both rise by 50% and output rises by 80%. Identify the returns to scale.
- Given Q = A·K^0.4·L^0.8, identify the returns to scale.
Answers.
- TC = 50,000 + 150 × 500 = 50,000 + 75,000 = Rs. 125,000.
- AFC = 60,000 / 200 = Rs. 300; AFC = 60,000 / 400 = Rs. 150.
- MC = (125,000 − 100,000) / (600 − 500) = 25,000 / 100 = Rs. 250 per unit.
- MC = w / MP = 1,200 / 12 = Rs. 100 per unit.
- Output (80%) rises more than inputs (50%), so there are increasing returns to scale.
- α + β = 0.4 + 0.8 = 1.2 > 1, so there are increasing returns to scale.
Typical examination questions.
Define fixed and variable cost with examples.
Explain the relationship among TC, AC and MC.
Explain short-run cost curves with diagrams.
Explain the relationship between short-run cost and productivity.
State the law of variable proportions.
Distinguish the short run from the long run.
Explain economies and diseconomies of scale and their causes.
Explain constant returns to scale.
Distinguish returns to scale from the law of variable proportions.
Explain how the Cobb-Douglas function is used to determine returns to scale.
8. Conclusion
Short-run cost behaviour is explained largely by the productivity of variable inputs when some factors are fixed: rising marginal product lowers MC, and diminishing marginal product raises it, producing the familiar U-shaped curves. In the long run, when all inputs can change, the key issue is scale: increasing returns and economies of scale reduce average cost, constant returns keep it flat, and decreasing returns and diseconomies of scale raise it. A successful manager must understand both how efficiently resources are used and how the scale of operation affects the cost of doing business.
References
Cobb, C. W. and Douglas, P. H. (1928) 'A theory of production', American Economic Review, 18(1), Supplement, pp. 139–165.
Greenlaw, S. A., Shapiro, D. and MacDonald, D. (2022) Principles of Economics 3e. Houston, TX: OpenStax. Available at: openstax.org, section 7.3 Costs in the Short Run (accessed 14 November 2026).
Mankiw, N. G. (2021) Principles of Economics. 9th edn. Boston, MA: Cengage Learning.
Pindyck, R. S. and Rubinfeld, D. L. (2018) Microeconomics. 9th edn. Harlow: Pearson.
Varian, H. R. (2014) Intermediate Microeconomics: A Modern Approach. 9th edn. New York: W. W. Norton.
Viner, J. (1931) 'Cost curves and supply curves', Zeitschrift für Nationalökonomie, 3(1), pp. 23–46.