Output and Cost: Microeconomics Study Notes (Chapter 10)

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Output and Cost

Introduction

This chapter explores how firms make production decisions and incur costs in both the short run and long run. Understanding these concepts is essential for analyzing firm behavior and market outcomes 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 its decisions, focusing on economic profit.
Economic profit is defined as total revenue minus total cost, where total cost is measured as the opportunity cost of production.
Formula:

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 could have been used to buy other resources for alternative production.
Owned by the Firm: Using owned capital incurs an opportunity cost, as the firm could have sold the capital and rented it instead.
Implicit Rental Rate of Capital: The opportunity cost of using owned capital, consisting of:
- 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 an opportunity cost.
- Interest forgone: The return the firm could have earned by investing funds elsewhere. Example: $300,000 invested in bonds could earn $15,000 in interest, which is forgone if used to buy capital.
Supplied by the Firm's Owner: Includes entrepreneurship and labor. The return to entrepreneurship is normal profit, which is an opportunity cost. If the owner supplies labor without taking a wage, the opportunity cost 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

Short Run vs. Long Run

Short Run: Time frame in which the quantity of at least one resource (usually capital/plant) is fixed. Other resources (labor, materials) can be varied. Short-run decisions are easily reversed.
Long Run: Time frame in which all resources, including plant size, can be varied. Long-run decisions are not easily reversed.
Sunk Cost: A cost that has already been incurred and cannot be changed. Sunk costs are 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.
Inputs:
- 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 the quantities of inputs used and the maximum quantity of output that can be produced, given current technology and organization.
Mathematical Form: where is output, is labor, and 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.
3. Average Product of Labor (APL): Total product divided by quantity of labor employed.

Product Schedules and Curves

As labor increases:
- Total product increases.
- Marginal product increases initially, then decreases.
- Average product decreases.

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

Product Curves

Total Product Curve: Shows how total product changes with labor employed. Similar to the production possibilities frontier (PPF), it separates attainable from unattainable output levels.
Marginal Product Curve: Shows the marginal product of labor for each additional worker. The curve passes through the midpoints of the bars representing marginal product.
Average Product Curve: Shows the average product of labor and its relationship with the marginal product curve.

Marginal Returns

Increasing Marginal Returns: Initially, each additional worker adds more output than the previous one due to specialization and division of labor.
Diminishing Marginal Returns: Eventually, each additional worker adds less output than the previous one due to limited capital and workspace.
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.

Relationship Between Marginal and Average Product

When marginal product exceeds average product, average product increases.
When marginal product is below average product, average product decreases.
When marginal product equals average product, average product is at its maximum.

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:

Cost Curves

Total Fixed Cost Curve: Remains constant at all output levels.
Total Variable Cost Curve: Increases as output increases.
Total Cost Curve: Sum of TFC and TVC; increases as output increases.
Average Variable Cost (AVC): U-shaped; falls to a minimum then rises as output increases.
Average Total Cost (ATC): U-shaped for similar reasons.

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 Cost

Marginal Cost (MC): The increase in total cost from a one-unit increase in output.
MC falls when marginal returns are increasing, and rises when diminishing returns set in.

Average Cost Measures

Average Fixed Cost (AFC):
Average Variable Cost (AVC):
Average Total Cost (ATC):

Shape of Cost Curves

AFC falls as output increases (spreading fixed cost).
AVC and ATC are U-shaped due to the law of diminishing returns and the spreading of fixed costs.
MC intersects AVC and ATC at their minimum points.

Relationship Between Product and Cost Curves

The shapes of cost curves are determined by the technology used.
MC is at its minimum when MP is at its maximum.
AVC is at its minimum when AP is at its maximum.

Shifts in Cost Curves

Cost curves shift due to changes in technology or prices of factors of production.
Technological improvements shift product curves upward and cost curves downward.
Increases in input prices shift cost curves upward.

Long-Run Cost

All Inputs Variable

In the long run, all inputs and costs are variable.
The behavior of long-run cost depends on the firm's production function.

Returns to Scale

Constant Returns to Scale (CRS): Output increases by the same percentage as all inputs.
Increasing Returns to Scale (IRS): Output increases by more than the percentage increase in inputs.
Decreasing Returns to Scale (DRS): Output increases by less than the percentage increase in inputs.

Long-Run Average Cost Curve

The long-run average cost curve shows the lowest attainable average total cost for each output level when both plant and labor are varied.
It is a planning curve for firms to choose the optimal plant size for a given output range.
Each plant size has its own short-run ATC curve; the long-run curve is the envelope of these curves.

Economies and Diseconomies of Scale

Economies of Scale: Features of technology that lead to falling long-run average cost as output increases.
Diseconomies of Scale: Features that lead to rising long-run average cost as output increases.
Constant Returns to Scale: Long-run average cost remains constant as output increases.

Minimum Efficient Scale

The smallest quantity of output at which long-run average cost reaches its lowest level.
If the long-run average cost curve is U-shaped, the minimum point identifies the minimum efficient scale.

Summary Table: Returns to Scale and Long-Run Costs

Scale	Input Increase	Output Change	Long-Run Average Cost
Economies of Scale	All inputs doubled	Output more than doubled	Decreases
Constant Returns to Scale	All inputs doubled	Output exactly doubled	Constant
Diseconomies of Scale	All inputs doubled	Output less than doubled	Increases

Example Application

If a firm wants to produce 13 sweaters per day, it should choose the plant size (number of knitting machines) that yields the lowest average total cost for that output.
Long-run planning involves selecting the plant size and input mix that minimizes cost for the expected output level.

Additional info: These notes expand on the brief points in the slides, providing definitions, formulas, and context for key microeconomic concepts related to production and cost.