Unit 3: Production, Cost & Revenue

---

Meaning of Production

In economics, production is the process of combining various inputs (factors of production: land, labor, capital, entrepreneurship) to create an output (goods and services) that has utility and is capable of satisfying human wants.

A production function is a mathematical equation that shows the technical relationship between physical inputs and the maximum physical output that can be produced from them, given the current state of technology.

Q = f(L, K)

Where: Q = Output, L = Labor, K = Capital

---

Short Run and Long Run

In economics, the "run" is not a specific length of time, but a conceptual period based on the flexibility of inputs.

Short Run

• Definition: The short run is a period of time in which at least one factor of production is fixed.
• Typically, Capital (K) (like the factory, machines) is considered fixed.
• Production can only be increased by adding more variable factors, like Labor (L).
• The law that applies here is the Law of Variable Proportions.

Long Run

• Definition: The long run is a period of time in which all factors of production are variable.
• The firm can change its factory size, build new plants, and adopt new technology. There are no fixed inputs.
• The law that applies here is the Returns to Scale.

---

Law of Variable Proportions (Short Run)

This law is also known as the "Law of Diminishing Marginal Returns."

The Law of Variable Proportions states that in the short run, as we increase the quantity of a variable input (Labor) while keeping other fixed inputs (Capital) constant, the Marginal Product (MP) of the variable input will eventually decline.

Key Concepts:

• Total Product (TP): Total quantity of output produced.
• Average Product (AP): Total Product per unit of variable input. AP = TP / L
• Marginal Product (MP): The additional output produced by using one more unit of the variable input. MP = ΔTP / ΔL

The Three Stages of Production

This law is illustrated by three stages of production, as shown in the diagram below.

[]

Stage	Description	Total Product (TP)	Marginal Product (MP)
Stage 1: Increasing Returns	From origin to where AP is maximum.	Increases at an increasing rate, then at a decreasing rate.	Increases, reaches max, then starts to fall. (MP > AP).
Stage 2: Diminishing Returns	From where AP is max to where MP is zero.	Increases at a diminishing rate, reaches its maximum.	Continues to fall, becomes zero. (MP < AP).
Stage 3: Negative Returns	After MP becomes zero.	Starts to fall.	Becomes negative.

---

Returns to Scale (Long Run)

This law explains the behavior of output when all inputs are changed by the same proportion (i.e., the "scale" of the firm changes) in the long run.

• 1. Increasing Returns to Scale (IRS):
  • Definition: When a proportional increase in all inputs leads to a more than proportional increase in output.
  • Example: 10% increase in L and K → 15% increase in Q.
  • Reason: Specialization, division of labor, use of large-scale machinery (economies of scale).
• 2. Constant Returns to Scale (CRS):
  • Definition: When a proportional increase in all inputs leads to an exactly proportional increase in output.
  • Example: 10% increase in L and K → 10% increase in Q.
• 3. Decreasing Returns to Scale (DRS):
  • Definition: When a proportional increase in all inputs leads to a less than proportional increase in output.
  • Example: 10% increase in L and K → 5% increase in Q.
  • Reason: Managerial difficulties, coordination problems (diseconomies of scale).

---

Iso-quant and Iso-cost Lines

Iso-quant (IQ)

• Definition: An Iso-quant (from "iso" meaning equal and "quant" meaning quantity) is a curve that shows all the possible combinations of two inputs (e.g., Labor and Capital) that produce the same level of output.
• It is also called an "equal-product curve" or "production indifference curve."
• Properties: They are downward sloping, convex to the origin (due to diminishing MRTS), and two iso-quants never intersect.

[]

Iso-cost Line

• Definition: An Iso-cost line shows all the combinations of two inputs (Labor and Capital) that a firm can purchase with a given budget (Total Cost) and given input prices (Wage and Rent).
• It is the producer's "budget line."
• Equation: (Price_Labor × L) + (Price_Capital × K) = Total Cost

[]

---

Producers Equilibrium

Producer's Equilibrium (or the "least-cost combination") is the point where a firm produces the maximum possible output for a given cost OR produces a given level of output at the minimum possible cost.

This equilibrium occurs at the point of tangency between an iso-quant and an iso-cost line.

[]

At the point of tangency (E), the condition is:

Slope of Iso-quant = Slope of Iso-cost line
MRTS_lk = Price_l / Price_k

(Where MRTS is the Marginal Rate of Technical Substitution)

---

Cost of Production - Types

Cost refers to the expenditure incurred by a firm on the factors of production.

• Explicit Costs (Accounting Costs): Direct, out-of-pocket payments made to outsiders for resources.
  Examples: Wages, rent, cost of raw materials.
• Implicit Costs (Opportunity Costs): The value of self-owned or self-employed resources that are not paid for directly.
  Examples: The salary an entrepreneur could have earned working elsewhere.
• Economic Cost = Explicit Costs + Implicit Costs.
• Fixed Costs (FC) (Short Run): Costs that do not change with the level of output (e.g., rent, insurance).
• Variable Costs (VC) (Short Run): Costs that do change directly with the level of output (e.g., raw materials, wages).

---

Short Run and Long Run Cost Curves

Short Run Cost Curves

• Total Cost (TC): TC = TFC + TVC
• Average Fixed Cost (AFC): AFC = TFC / Q. It continuously falls.
• Average Variable Cost (AVC): AVC = TVC / Q. It is U-shaped due to the Law of Variable Proportions.
• Average Total Cost (ATC): ATC = TC / Q or ATC = AFC + AVC. It is also U-shaped.
• Marginal Cost (MC): The additional cost of producing one more unit of output. MC = (Change in TC) / (Change in Q). It is also U-shaped.

[]

Key Relationships (Exam Focus):

• The MC curve cuts both the AVC and ATC curves at their minimum points.
• When MC < AC, AC is falling.
• When MC > AC, AC is rising.
• When MC = AC, AC is at its minimum.

Long Run Cost Curves

In the long run, all costs are variable. The Long Run Average Cost (LRAC) curve is also U-shaped, but for different reasons.

• Derivation: The LRAC is an "envelope curve" that is tangent to all the possible Short Run Average Cost (SRAC) curves.
• Falling Portion (Economies of Scale): The LRAC falls initially due to Economies of Scale (cost advantages of becoming larger, like specialization, bulk buying).
• Rising Portion (Diseconomies of Scale): The LRAC eventually rises due to Diseconomies of Scale (cost disadvantages of becoming too large, like management and coordination problems).

[]

---

Revenue: TR, AR & MR, Revenue and Elasticity of Demand

Revenue Concepts

• Total Revenue (TR): The total amount of money a firm receives from selling its output. TR = Price (P) × Quantity (Q)
• Average Revenue (AR): Revenue per unit of output sold. It is always equal to the price. AR = TR / Q = (P × Q) / Q = P
  The AR curve is the same as the firm's Demand Curve.
• Marginal Revenue (MR): The additional revenue earned from selling *one more* unit of output. MR = (Change in TR) / (Change in Q)

Revenue and Elasticity of Demand (Relationship)

The relationship between TR, MR, and the price elasticity of demand (PED) is crucial, especially for a firm (like a monopoly) that faces a downward-sloping demand curve.

Elasticity	Value (Absolute)	What it means	Marginal Revenue (MR)	Effect on Total Revenue (TR)
Elastic	PED > 1	% Change in Q > % Change in P	MR is positive	If P falls, TR increases.
Unitary Elastic	PED = 1	% Change in Q = % Change in P	MR is zero	If P falls, TR is at its maximum.
Inelastic	PED < 1	% Change in Q < % Change in P	MR is negative	If P falls, TR decreases.

[]