Production and Cost Analysis: Production Function, Returns to Scale, Cost Concepts and Cost Curves Questions

Q: Explain the law of variable proportions (brief) and mention its stages.

Law of variable proportions states that when increasing units of a variable factor are applied to a fixed factor, total output increases at first at an increasing rate, then at a decreasing rate, and finally may decline. Stages: (1) Increasing returns (MP rises), (2) Diminishing returns (MP falls but positive) — rational stage, (3) Negative returns (MP becomes negative). Firms operate in Stage II.

Q: Explain returns to scale and its types.

Returns to scale shows how output changes when all inputs are increased in the same proportion (long-run concept). Types: (1) Increasing returns to scale: output increases more than proportionate. (2) Constant returns: output increases proportionately. (3) Decreasing returns: output increases less than proportionate. Causes include economies of scale and management/coordination limits.

Question 1

Define production function.

Accepted Answer

A production function shows the relationship between physical inputs used and the physical output produced.

Question 2

What is marginal product (MP)?

Accepted Answer

Marginal product is the additional output produced by employing one more unit of a variable input (MP = ΔTP/ΔL).

Question 3

State the formula for total cost.

Accepted Answer

Total cost (TC) = Total fixed cost (TFC) + Total variable cost (TVC).

Question 4

What is average cost (AC)?

Accepted Answer

Average cost is total cost per unit of output (AC = TC/Q).

Question 5

What is the long run?

Accepted Answer

Long run is the period in which all factors of production are variable and the firm can change scale.

Question 6

What is a sunk cost?

Accepted Answer

A sunk cost is a past cost already incurred that cannot be recovered and is irrelevant for current decisions.

Question 7

Differentiate between short run and long run.

Accepted Answer

Short run is a time period where at least one factor (like plant size) is fixed, so output changes mainly by varying variable inputs such as labour.

Long run is a period where all factors are variable; the firm can change scale, plant size and technology.

Hence, law of variable proportions relates to short run, while returns to scale relates to long run.

Question 8

Explain TP, AP and MP and their relationship.

Accepted Answer

TP (Total Product) is total output produced. AP (Average Product) is output per unit of variable input (AP = TP/L). MP (Marginal Product) is additional output from one more unit of variable input (MP = ΔTP/ΔL).

Relationship: When MP > AP, AP rises; when MP < AP, AP falls; MP intersects AP at AP's maximum point.

These relationships explain the stages of the law of variable proportions.

Question 9

Explain the law of variable proportions (brief) and mention its stages.

Accepted Answer

Law of variable proportions states that when increasing units of a variable factor are applied to a fixed factor, total output increases at first at an increasing rate, then at a decreasing rate, and finally may decline.

Stages: (1) Increasing returns (MP rises), (2) Diminishing returns (MP falls but positive) — rational stage, (3) Negative returns (MP becomes negative).

Firms operate in Stage II.

Question 10

Explain returns to scale and its types.

Accepted Answer

Returns to scale shows how output changes when all inputs are increased in the same proportion (long-run concept).

Types: (1) Increasing returns to scale: output increases more than proportionate. (2) Constant returns: output increases proportionately. (3) Decreasing returns: output increases less than proportionate.

Causes include economies of scale and management/coordination limits.

Question 11

Define fixed and variable cost with examples.

Accepted Answer

Fixed cost is cost that does not change with output in the short run (rent, salaried staff). Variable cost changes with output (raw materials, power, piece-rate wages).

Total cost = fixed cost + variable cost.

Understanding fixed vs variable cost helps in break-even and pricing decisions.

Question 12

Explain relationship between AC and MC.

Accepted Answer

Relationship: When MC is less than AC, AC falls; when MC is greater than AC, AC rises. MC intersects AC at the minimum point of AC.

Similarly, MC intersects AVC at the minimum point of AVC.

This relationship is used to understand cost behaviour and optimal output decisions.

Question 13

Explain the law of variable proportions in detail with stages and managerial significance.

Accepted Answer

Law of variable proportions (short-run) explains output behaviour when one factor is fixed and the other is variable. When more units of a variable factor (labour) are applied to a fixed factor (plant), total output changes in three stages.

Stage I: Increasing returns
- TP increases at an increasing rate; MP rises and reaches maximum.
- Reasons: better utilisation of fixed factor, specialisation and improved efficiency.

Stage II: Diminishing returns (rational stage)
- TP increases but at decreasing rate; MP falls but remains positive.
- Reason: fixed factor becomes a constraint; overcrowding starts; additional units contribute less.

Stage III: Negative returns
- TP starts falling; MP becomes negative.
- Too much variable input causes inefficiency and coordination problems.

Managerial significance:
- The firm should operate in Stage II because resources are used efficiently and output still increases.
- This law explains why AVC and MC are U-shaped and helps managers decide optimal labour usage in the short run.

Thus, the law guides input decisions and cost control.

Question 14

Explain short-run cost curves. Define TFC, TVC, TC, AFC, AVC, AC and MC and explain why some curves are U-shaped.

Accepted Answer

In the short run, at least one factor is fixed, so costs are divided into fixed and variable parts.

1) Total Fixed Cost (TFC): remains constant with output (rent, plant maintenance).
2) Total Variable Cost (TVC): changes with output (raw material, power).
3) Total Cost (TC): TC = TFC + TVC.

Average costs:
- AFC = TFC/Q: continuously falls as output increases because fixed cost is spread over more units.
- AVC = TVC/Q: typically U-shaped due to the law of variable proportions (initial efficiency then diminishing returns).
- AC = TC/Q = AFC + AVC: also U-shaped because it depends mainly on AVC and AFC together.

Marginal Cost:
- MC = ΔTC/ΔQ (or ΔTVC/ΔQ): extra cost of producing one more unit. MC is also U-shaped due to increasing then diminishing marginal returns in production.

Why U-shape?
- At low output, better utilisation and specialisation reduce costs (MC/AVC fall).
- After a point, diminishing returns raise additional cost (MC rises), and AVC/AC also rise.

Thus short-run cost curves help managers understand cost behaviour and plan output.

Question 15

Explain long-run average cost (LAC) curve and economies/diseconomies of scale.

Accepted Answer

Long-run average cost (LAC) shows the minimum possible average cost of producing each output level when the firm can change all inputs and choose the best plant size. It is called an envelope curve because it envelopes various short-run average cost (SAC) curves.

Shape and explanation:
- Initially LAC falls due to economies of scale: large-scale production reduces average cost.
- In the middle range, LAC may become flat, showing constant returns to scale.
- At high output, LAC may rise due to diseconomies of scale.

Economies of scale (reasons):
1) Technical economies (better machines, efficient technology).
2) Managerial economies (specialisation and division of work).
3) Financial economies (cheaper credit, better bargaining power).
4) Marketing economies (bulk buying, advertising benefits).

Diseconomies of scale (reasons):
- coordination and communication problems, management complexity, delayed decisions.

Managerial significance:
- LAC helps decide optimal plant size and expansion policy to achieve minimum cost and remain competitive.

Production and Cost Analysis: Production Function, Returns to Scale, Cost Concepts and Cost Curves

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