Chapter 4: Theory of Production and Cost

Overview

Theory of Production & Cost

Core Concepts

Production is the process of transforming inputs (land, labor, capital, entrepreneurship) into outputs (goods/services). The goal is to create value/utility. This chapter analyzes the technical relationship between inputs and outputs (Production Function) and the monetary value of inputs (Cost Theory).

Fixed Inputs

Quantity cannot change immediately (e.g., Buildings, Machinery). Makes supply inelastic in the short run.

Variable Inputs

Quantity can change quickly to alter output (e.g., Unskilled labor, Raw materials).

The "Short Run" Definition

It is not a specific calendar time (e.g., "1 year"). It is a functional period where at least one input remains fixed. It varies by industry.

Product Curves

How output behaves as we add labor.

Total Product (TP)

The total output produced by all workers.

Starts at 0.
Increases fast (increasing returns).
Slows down (diminishing returns).
Reaches Max, then falls.

Average Product (AP)

The "productivity" per worker.

\( AP = \frac{TP}{Labor} \)

Geometrically: Slope of a line from origin to a point on the TP curve.

Marginal Product (MP)

Extra output from adding one more worker.

\( MP = \frac{\Delta TP}{\Delta Labor} \)

Geometrically: The slope of the TP curve itself.

Crucial Relationships

When AP is Rising

Marginal Product is greater than Average Product.
\( MP > AP \)

When AP is Max

Marginal Product equals Average Product.
\( MP = AP \)

When AP is Falling

Marginal Product is less than Average Product.
\( MP < AP \)

[Image of relationship between AP and MP curves]

Stages of Production

Determining the rational zone of operation.

Stage I: Increasing Returns (Irrational)

Range: From Origin to AP Max (where MP=AP)

Why here? Fixed inputs (like machinery) are abundant relative to labor. Adding more workers actually helps utilize the machines better, increasing efficiency significantly.
Why Irrational? Stopping here is foolish because adding another worker still raises the average productivity. You are wasting your fixed capital.

Stage II: Diminishing Returns (Rational Zone) Efficient

Range: From AP Max to MP = 0

Why here? You have reached the optimal balance. Total Product is still growing, but at a slower pace. MP is positive but declining.
Why Rational? The fixed factor is being fully utilized. You keep hiring as long as the extra worker adds more value than their cost.

Stage III: Negative Returns (Irrational)

Range: Where MP becomes Negative

Why here? Too many cooks in the kitchen! Workers are crowding each other. Total output actually falls if you hire more.
Why Irrational? You are paying wages to reduce your total output. MP is negative.

Cost Concepts

Economic vs. Accounting Costs.

Accounting Cost

Monetary value of all purchased inputs.

Includes

Explicit Costs (Wages, Materials, Rent).

Acct Profit = TR - Explicit Cost

Economic Cost

Monetary value of ALL inputs (Purchased + Self-owned).

Includes

Explicit Costs + Implicit Costs (Opportunity cost).

Econ Profit = TR - (Explicit + Implicit)

Short Run Cost Curves

Understanding the shapes and definitions.

1. Total Cost Family

TFC (Total Fixed Cost)

Costs that do not change with output (Rent, Admin salaries).

Graph: Horizontal Line.

TVC (Total Variable Cost)

Costs that rise with output (Materials, Wages).

Graph: Inverse S-shape (starts at 0).

TC (Total Cost)

Sum of Fixed and Variable costs.

Graph: Inverse S-shape (starts at TFC).

2. Per-Unit Cost Family

AFC (Average Fixed)

AFC = TFC / Q

Since TFC is constant, dividing by increasing Q makes this value fall continuously.

Shape: Rectangular Hyperbola (Approaches axes but never touches).

AVC (Average Variable)

AVC = TVC / Q

Falls initially due to increasing returns, then rises due to diminishing returns.

Shape: U-Shaped.

AC (Average Total)

AC = TC / Q

Sum of AFC + AVC. Vertical distance between AC and AVC gets smaller as Q increases (because AFC shrinks).

Shape: U-Shaped.

MC (Marginal Cost)

MC = ΔTC / ΔQ

Cost of producing one extra unit. Most important for decision making.

Shape: U-Shaped. Cuts AVC and AC at their minimum points.

Production & Cost Relationships

The "Mirror Image" Concept.

Cost and Production are two sides of the same coin. When a worker is highly productive (High MP), the cost of producing that extra unit is low (Low MC).

Marginal Cost vs. Marginal Product

\( MC = \frac{w}{MP_L} \)

(w = wage rate)

Inverse Relationship:

When MP rises → MC falls.
When MP is Maximum → MC is Minimum.
When MP falls → MC rises.

MC is the exact mirror image of MP.

Avg Variable Cost vs. Avg Product

\( AVC = \frac{w}{AP_L} \)

Inverse Relationship:

When AP rises → AVC falls.
When AP is Maximum → AVC is Minimum.
When AP falls → AVC rises.

AVC is the exact mirror image of AP.