Output and Cost – Microeconomics Study Notes (Chapter 10)

Output and Cost

Introduction

This chapter explores how firms make production and cost decisions in both the short run and long run. It covers the concepts of economic cost, profit, production functions, and the behavior of cost curves, providing foundational knowledge for understanding firm behavior in microeconomics.

Economic Cost and Profit

Definition of a Firm

• Firm: An institution that hires factors of production and organizes them to produce and sell goods and services.

• Goal of the Firm: To maximize profit.

Economic Accounting

• Economists measure a firm's profit to predict decisions aimed at maximizing economic profit.

• Economic profit is defined as total revenue minus total cost, where total cost is measured as the opportunity cost of production.

• Formula: $\text{Economic Profit} = \text{Total Revenue} - \text{Total Opportunity Cost}$

Opportunity Cost of Production

• The value of the best alternative use of resources used in production.

• Opportunity cost includes:

  • Resources bought in the market

  • Resources owned by the firm

  • Resources supplied by the firm's owner

Types of Resources and Their Costs

• Bought in the Market: The amount spent is an opportunity cost because the firm could have used these resources elsewhere.

• Owned by the Firm: Opportunity cost arises because the firm could have sold the capital and rented it instead. This is called the implicit rental rate of capital.

• Implicit Rental Rate of Capital:

  • Economic depreciation: Change in market value of capital over a period. Example: If a machine's value drops from $400,000 to $375,000 in a year, the $25,000 loss is economic depreciation.

  • Interest forgone: The return the firm could have earned by investing funds elsewhere.

• Supplied by the Firm's Owner: Includes entrepreneurship and labor. The return to entrepreneurship is normal profit, which is an opportunity cost. The opportunity cost of the owner's labor is the wage income forgone from the best alternative job.

Economic Accounting: Example Table

The following table summarizes economic accounting for Cindy's sweater company:

Item	Amount
Total Revenue	$400,000
Cost of Resources Bought in Market
Wood	$60,000
Utilities	$20,000
Wages	$120,000
Computer lease	$5,000
Bank interest	$5,000
Cost of Resources Owned by Firm
Economic depreciation	$25,000
Interest forgone	$15,000
Cost of Resources Supplied by Owner
Cindy's normal profit	$45,000
Cindy's forgone wages	$55,000
Opportunity Cost of Production	$370,000
Economic Profit	$30,000

Decision Time Frames

• Firms make decisions in two time frames:

  • Short run: At least one input is fixed (usually capital/plant).

  • Long run: All inputs, including plant size, can be varied.

• Sunk cost: A cost that cannot be changed and is irrelevant to current decisions.

Production Function

Inputs and Technology

• A firm uses a technology or production process to transform inputs (factors of production) into outputs.

• Labor (L): Human services, including managers, skilled and less-skilled workers.

• Capital (K): Long-lived inputs such as land, buildings, and equipment.

Production Function Definition

• The production function describes the relationship between quantities of inputs used and the maximum output that can be produced, given current technology and organization.

• Mathematical Form: $q = f(L, K)$ where $q$ is output, $L$ is labor, and $K$ is capital.

Short-Run Technology Constraint

Key Concepts

• To increase output in the short run, a firm must increase the amount of labor employed (capital is fixed).

• Three important measures:

  1. Total product (TP): Total output produced in a given period.

  2. Marginal product of labor (MPL): Change in total product from a one-unit increase in labor, holding other inputs constant. $MP_L = \frac{\Delta q}{\Delta L}$

  3. Average product of labor (APL): Total product divided by quantity of labor employed. $AP_L = \frac{q}{L}$

Product Schedules and Curves

• As labor increases:

  • Total product increases.

  • Marginal product increases initially, then decreases.

  • Average product decreases.

• Product curves show how TP, MP, and AP change as labor varies.

• The total product curve is similar to the production possibilities frontier (PPF), separating attainable from unattainable output levels.

Table: Total Product, Marginal Product, and Average Product

Labour (workers/day)	Total product (sweaters/day)	Marginal product (sweaters/additional worker)	Average product (sweaters/worker)
0	0	-	-
1	4	4	4.00
2	10	6	5.00
3	13	3	4.33
4	15	2	3.75
5	16	1	3.20

Marginal and Average Product Curves

• Marginal product curve passes through the midpoints of the bars representing marginal product for each additional worker.

• Average product curve shows the average output per worker.

• Relationship:

  • When MP > AP, AP increases.

  • When MP < AP, AP decreases.

  • When MP = AP, AP is at its maximum.

Law of Diminishing Returns

• Initially, firms experience increasing marginal returns due to specialization and division of labor.

• Eventually, diminishing marginal returns occur as additional workers have less access to capital and space.

• Law of diminishing returns: As a firm uses more of a variable input with a given quantity of fixed inputs, the marginal product of the variable input eventually diminishes.

Short-Run Cost

Types of Cost

• Total cost (TC): Cost of all resources used.

• Total fixed cost (TFC): Cost of fixed inputs (does not change with output).

• Total variable cost (TVC): Cost of variable inputs (changes with output).

• Relationship: $TC = TFC + TVC$

Cost Curves

• TFC is constant at all output levels.

• TVC increases as output increases.

• TC increases as output increases.

• The shape of the AVC curve is derived from the TP curve.

Table: Short-Run Cost Example

Labour (workers/day)	Output (sweaters/day)	Total variable cost (TVC, $/day)	Total fixed cost (TFC, $/day)	Total cost (TC, $/day)
1	4	25	25	50
2	10	50	25	75
3	13	75	25	100
4	15	100	25	125
5	16	125	25	150

Marginal and Average Cost

• Marginal cost (MC): Increase in total cost from a one-unit increase in output. $MC = \frac{\Delta C}{\Delta q}$

• Average fixed cost (AFC): $AFC = \frac{TFC}{q}$

• Average variable cost (AVC): $AVC = \frac{TVC}{q}$

• Average total cost (ATC): $ATC = AFC + AVC = \frac{TC}{q}$

Shape of Cost Curves

• AFC falls as output increases (spreading fixed cost).

• AVC and ATC are typically U-shaped due to diminishing returns and spreading fixed costs.

• MC is below AVC/ATC when they are falling, and above when they are rising. MC equals AVC/ATC at their minimum points.

Summary Table: Cost Relationships

Cost Concept	Formula	Behavior
Total Cost (TC)	$TC = TFC + TVC$	Increases with output
Marginal Cost (MC)	$MC = \frac{\Delta TC}{\Delta q}$	Falls then rises as output increases
Average Fixed Cost (AFC)	$AFC = \frac{TFC}{q}$	Falls as output increases
Average Variable Cost (AVC)	$AVC = \frac{TVC}{q}$	U-shaped
Average Total Cost (ATC)	$ATC = AFC + AVC$	U-shaped

Additional info:

• These notes are based on lecture slides and textbook images for Chapter 10 of a college-level Microeconomics course.

• All equations are provided in LaTeX format for clarity and academic rigor.