Unit 2: Production function & theory of cost
Managerial Economics-I notes · PTU syllabus (BBAGE 101-18)
On this page
Unit summary
A firm must decide how to combine inputs to produce output at the lowest cost. This unit covers the production function, short-run and long-run production, isoquants, the least-cost combination of inputs, producer's equilibrium, returns to scale, and the concepts and theories of cost.
After this unit you can
- Explain the production function and the law of variable proportions
- Use isoquants and isocost lines to find the least-cost combination
- Explain returns to scale
- Explain cost concepts and short-run and long-run cost curves
PTU syllabus topics
- Production function
- productivity and technology
- short-run and long-run production function
- isoquants
- least-cost combination of inputs
- producer's equilibrium
- returns to scale
- cost concepts and determinants
- short-run and long-run cost theory
Increasing returns
Rises more than in proportion to inputs
Specialisation, economies of scale
Constant returns
Rises in the same proportion
Economies and diseconomies balance
Decreasing returns
Rises less than in proportion
Management difficulties, diseconomies
Topic 1
Production function
The production function shows the maximum output obtainable from given inputs with a given technology: Q = f(L, K), where L is labour and K is capital. Productivity is output per unit of input; better technology shifts the production function upward.
- Short run: at least one input (usually capital) is fixed.
- Long run: all inputs are variable.
Topic 2
Law of variable proportions (short run)
When more of a variable input is added to a fixed input, total product first rises at an increasing rate, then at a decreasing rate, and finally falls.
Stage I: increasing returns
Rises at an increasing rate
Rises, then falls but stays above AP
Stage II: diminishing returns
Rises at a decreasing rate
Falls but positive — rational stage
Stage III: negative returns
Falls
Negative
A rational producer operates in Stage II.
Topic 3
Isoquants and the least-cost combination
An isoquant shows all combinations of labour and capital giving the same output. It slopes downward and is convex; its slope is the marginal rate of technical substitution (MRTS). An isocost line shows combinations of inputs with the same total cost. Producer's equilibrium (least-cost combination): where the isocost line is tangent to the isoquant: MRTS = w / r, or equivalently MPL / w = MPK / r.
Topic 4
Returns to scale (long run)
Increasing returns
More than doubles
Specialisation, economies of scale
Constant returns
Exactly doubles
Economies and diseconomies balance
Decreasing returns
Less than doubles
Management difficulties, diseconomies
Topic 5
Cost concepts and theories
| Concept | Meaning |
|---|---|
| Fixed cost (FC) | Does not change with output (rent, salaries) |
| Variable cost (VC) | Changes with output (raw materials) |
| Total cost (TC) | FC + VC |
| Average cost (AC) | TC / Q |
| Marginal cost (MC) | Change in TC from one more unit |
| Opportunity, explicit and implicit costs | Forgone alternative; paid out; owner's own resources |
- Short run: AFC falls continuously; AVC, AC and MC are U-shaped because of the law of variable proportions; MC cuts AC and AVC at their minimum points.
- Long run: the LAC curve is an envelope of short-run AC curves; it is U-shaped (or flatter, L-shaped in modern theory) because of economies and then diseconomies of scale.
Determinants of cost: output level, input prices, technology, scale of plant and efficiency of management.
Key terms
- Production function
- Relationship between inputs and maximum output
- Isoquant
- Input combinations giving equal output
- MRTS
- Rate at which one input substitutes for another at constant output
- Returns to scale
- Output response when all inputs change proportionally
- Marginal cost
- Additional cost of producing one more unit
Quick revision
- Short run: some fixed inputs; long run: all variable.
- Rational production in Stage II.
- Least cost: MRTS = w/r, isocost tangent to isoquant.
- MC cuts AC at its minimum.
- LAC is the envelope of SAC curves.
Important exam questions
Practice questions written to the PTU exam pattern for this unit's syllabus: short answers (Section A style) and long answers (Sections B and C style).
Short-answer questions
- Q1.Define the production function.
- Q2.State the law of variable proportions.
- Q3.What is an isoquant?
- Q4.What is the least-cost combination of inputs?
- Q5.Differentiate between fixed and variable costs.
- Q6.Why is the short-run AC curve U-shaped?
Long-answer questions
- Q1.Explain the law of variable proportions with a diagram.
- Q2.Explain producer's equilibrium using isoquants and isocost lines.
- Q3.Explain returns to scale with examples.
- Q4.Explain short-run and long-run cost curves.
Stuck on this unit?
Message SBS on WhatsApp for help with Managerial Economics-I, or to ask about studying BBA at Synetic.