1. Production Function — Basic Idea

• Production function expresses technical relationship between inputs (factors) and output: how much output can be produced from given inputs.
• General form: Q = f(L, K, T, …) where Q = output, L = labour, K = capital, T = technology, etc.
• It is a technological relation — not a behavioural one. It shows maximum feasible output for given inputs and technology.
• Short-run vs Long-run: distinction depends on which inputs are fixed vs variable.

2. Short Run and Long Run

• Short run: at least one input (usually capital K) is fixed; firms can vary variable inputs (labour, raw materials) to change output.
• Long run: all inputs are variable; firm can change scale of production, adopt new technology, enter/exit industry.
• Short-run decisions: how much labour to hire given fixed plant. Long-run decisions: what size of plant to build.

3. Total Product (TP), Average Product (AP) & Marginal Product (MP)

3.1 Total Product (TP)

• TP = total output produced by a firm using a given amount of variable input (with other inputs fixed in short run).
• Example tabulation: labour (L) vs TP showing increasing TP at first, then diminishing increments.

3.2 Average Product (AP)

• Average product of labour = output per unit of labour: AP = TP / L
• AP shows productivity per worker; peaks where MP = AP.

3.3 Marginal Product (MP)

• Marginal product of labour = additional output from one extra unit of labour: MP = ΔTP / ΔL
• MP initially may rise (due to specialization), later falls (crowding/fixed capital).

4. Law of Diminishing Marginal Product & Law of Variable Proportions

• Law of diminishing marginal product (short run): holding other inputs fixed, as more units of a variable input are added, beyond some point the extra output from each additional unit eventually declines.
• Reason: fixed inputs become overloaded; congestion; decreasing marginal returns to the variable factor.
• Law of variable proportions: describes three stages when varying one input while others fixed:
1. Stage I: Increasing MP and AP — specialization; not efficient to produce at very low levels because MP>AP.
2. Stage II: MP positive but falling; AP rising then falling; economically relevant region — rational producers operate here (between MP>0 and MP crosses zero).
3. Stage III: MP negative — adding more variable input reduces total output; irrational to operate here.

5. Shapes of TP, MP and AP Curves

• Total Product (TP): S-shaped: initially concave upward (increasing slope), then concave downward (diminishing slope), eventually flattening.
• Marginal Product (MP): MP curve initially rises, peaks, then declines and may cross zero when TP reaches maximum.
• Average Product (AP): AP curve lies between MP and TP behaviour; AP reaches maximum where MP = AP; MP intersects AP at AP’s maximum.
• Important relationships:
1. When MP > AP → AP rising.
2. When MP < AP → AP falling.
3. MP crosses AP at AP’s maximum point.

6. Returns to Scale (Long Run Concept)

• Returns to scale examines how output responds when all inputs are scaled up proportionally in the long run.
• Types:
• Increasing returns to scale (IRS): output increases by a greater proportion than inputs (e.g., double inputs → more than double output). Reasons: specialization, indivisibilities, spreading of fixed costs.
• Constant returns to scale (CRS): output increases in same proportion as inputs (double inputs → double output).
• Decreasing returns to scale (DRS): output increases by a smaller proportion (double inputs → less than double output). Reasons: management inefficiencies, coordination problems at large scale.
• Empirically, a firm may experience IRS at low scale, CRS at an intermediate range, and DRS at very large scales.

7. Costs — Overview

• Cost concepts differ between short run and long run because of fixed vs variable inputs.
• Firm’s objective: typically minimize cost for a given output, or maximize profit (revenue − cost).

8. Short-Run Costs

• In short run, some costs are fixed (do not vary with output) and some are variable (depend on output).
• Key short-run cost measures:

Cost	Definition / Formula
Total Fixed Cost (TFC)	Costs that do not vary with output (rent, interest on capital). TFC > 0 even if Q=0.
Total Variable Cost (TVC)	Costs that vary with output (wages, raw materials).
Total Cost (TC)	TC = TFC + TVC
Average Fixed Cost (AFC)	AFC = TFC / Q (falls as Q rises).
Average Variable Cost (AVC)	AVC = TVC / Q
Average Total Cost (ATC)	ATC = TC / Q = AFC + AVC
Marginal Cost (MC)	MC = ΔTC / ΔQ = ΔTVC / ΔQ

• Typical shapes:
• AFC declines continuously as Q increases (spreading effect).
• AVC is U-shaped due to diminishing marginal returns (falls initially, then rises).
• ATC is U-shaped, lying above AVC by amount AFC; minimum of ATC occurs at higher Q than minimum of AVC.
• MC intersects AVC and ATC at their respective minimum points.

9. Long-Run Costs

• In the long run all inputs and costs are variable — there is no fixed cost.
• Long-run average cost (LRAC) curve is the envelope of short-run average cost (SRAC) curves for different plant sizes.
• LRAC typically U-shaped due to economies and diseconomies of scale:
• Economies of scale: LRAC falls as output increases (due to specialization, bulk buying, indivisibilities, managerial efficiency).
• Constant returns to scale: LRAC flat over a range.
• Diseconomies of scale: LRAC rises at large output levels (coordination problems, managerial inefficiencies).
• Long-run marginal cost (LRMC) links to LRAC: LRMC intersects LRAC at LRAC’s minimum.

10. Relationship between Production & Cost

• In short run, diminishing marginal product implies rising marginal cost: as MP of labour falls, additional units of output require increasingly more labour → MC rises.
• Mathematically, if wage w is constant: MC = w / MP_L
• Therefore MP and MC move inversely: MP ↑ → MC ↓ ; MP ↓ → MC ↑.

11. Cost Minimization & Scale Choice

• In long run a firm chooses plant/scale that minimizes LRAC for expected output.
• If demand expected to be high, firm may choose larger plant to exploit economies of scale.
• In the short run firm selects output where MC = MR (profit maximization) but must consider SRAC (if price < AVC → shut down decision).

12. Shutdown & Break-even Points (Short Run)

• Shutdown rule: In short run, if P < minimum AVC, firm should shut down (produce Q=0) because it cannot cover variable costs.
• Break-even point: Price equals minimum ATC → firm earns zero economic profit (normal profit). Above this price, positive profit; below this price (but above AVC) firm produces with loss but covers variable costs.

13. Examples & Numerical Illustrations

• Example 1 — TP, AP, MP table:

L	TP	MP	AP
0	0	–	–
1	10	10	10
2	24	14	12
3	36	12	12
4	44	8	11

• Example 2 — Cost calculation: Suppose TFC = 100, wage per worker = 20, and labour units L=1..4 with MP given above. Then TVC = w × L; TC = TFC + TVC; AFC, AVC, ATC, MC can be computed accordingly — plot to see U-shapes and MC intersections.

14. Short Notes — Key Points to Remember

• Production function shows technical possibility: Q = f(L, K, …).
• Short run: at least one fixed input; long run: all inputs variable.
• TP, AP, MP relationships and the law of diminishing MP guide short-run behavior.
• Costs: TFC, TVC, TC, AFC, AVC, ATC, MC — shapes and intersections are fundamental.
• Returns to scale explain long-run cost behavior (economies/diseconomies of scale).
• MC relates inversely to MP: useful for linking production to cost curves.
• Shutdown rule: compare price to minimum AVC; break-even: price = min ATC.