Output and Cost – Microeconomics Study Notes (Chapter 10)

Output and Cost

Introduction

This chapter explores how firms make production decisions and incur costs 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 and Its Goal

• 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.

• Sum of costs for resources:

  • Bought in the market

  • Owned by the firm

  • Supplied by the firm's owner

Types of Resources and Their Costs

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

• Resources Owned by the Firm: Opportunity cost arises because the firm could sell the capital and rent it from another firm. 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 an opportunity cost.

  • Interest forgone: The return on funds used to acquire capital. Example: If $300,000 is used to buy capital instead of earning $15,000 in interest, that $15,000 is an opportunity cost.

• Resources Supplied by the Firm's Owner:

  • Entrepreneurship: The expected average profit is called normal profit, which is an opportunity cost.

  • Labour: If the owner does not take a wage, the opportunity cost is the wage income forgone from the best alternative job.

Economic Accounting: A Summary

Economic profit equals total revenue minus total opportunity cost of production.

Item	Amount
Total Revenue	$400,000
Cost of Resources Bought in Market
Wood	$80,000
Utilities	$20,000
Wages	$120,000
Computer lease	$5,000
Bank interest	$5,000
Subtotal	$230,000
Cost of Resources Owned by Firm
Economic depreciation	$25,000
Forgone interest	$15,000
Subtotal	$40,000
Cost of Resources Supplied by Owner
Cindy's normal profit	$45,000
Cindy's forgone wages	$55,000
Subtotal	$100,000
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 (labour, materials) can be varied. Decisions are easily reversed.

• Long Run: Time frame in which all resources, including plant size, can be varied. 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 (managers, skilled and less-skilled workers).

  • Capital (K): Long-lived inputs (land, buildings, 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 (diminishing returns).

  • 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

• Total Product Curve: Shows how total product changes with labor employed; separates attainable from unattainable output levels.

• Marginal Product Curve: Shows the change in output from hiring additional workers; passes through midpoints of marginal product bars.

• Average Product Curve: Shows average output per worker; reaches maximum when marginal product equals average product.

Law of Diminishing Returns

• Increasing Marginal Returns: Initially, each additional worker adds more output than the previous one due to specialization.

• Diminishing Marginal Returns: Eventually, each additional worker adds less output due to limited capital and workspace.

• Law of Diminishing Returns: As a firm uses more of a variable input with a fixed input, 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

• Total Fixed Cost: Constant at all output levels.

• Total Variable Cost: Increases as output increases.

• Total Cost: Sum of TFC and TVC; increases with output.

• Shape of Curves: AVC curve gets its shape from the TP curve; TVC curve becomes steeper at high output levels.

Labour (workers/day)	Output (sweaters/day)	Total variable cost ($/day)	Total fixed cost ($/day)	Total cost ($/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 and Relationships of Cost Curves

• AFC Curve: Falls as output increases.

• AVC and ATC Curves: U-shaped; fall to a minimum then rise.

• MC Curve: Falls when marginal returns are increasing, rises when diminishing returns set in.

• When MC is below AVC or ATC, those averages are falling; when MC is above, they are rising. MC equals AVC or ATC at their minimum points.

Why ATC Curve Is U-Shaped

• ATC is the vertical sum of AFC and AVC.

• U-shape arises from two forces:

  1. Spreading fixed cost over more output (AFC falls).

  2. Diminishing returns (AVC rises faster than AFC falls at high output).

Shifts in Cost Curves

• Cost curves shift due to changes in technology or factor prices.

• Technological improvement shifts product curves up and cost curves down.

• Increase in factor prices shifts TC, ATC, and MC curves upward.

Long-Run Cost

Production Function in the Long Run

• All inputs are variable; all costs are variable.

• 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. $f(2L, 2K) = 2f(L, K) = 2q$

• Increasing Returns to Scale (IRS): Output increases by more than the percentage increase in inputs. $f(2L, 2K) > 2f(L, K)$

• Decreasing Returns to Scale (DRS): Output increases by less than the percentage increase in inputs. $f(2L, 2K) < 2f(L, K)$

Short-Run vs. Long-Run Cost

• Average cost of producing a given output depends on plant size.

• Each plant size has its own short-run ATC curve.

• The firm chooses the plant size that minimizes cost for each output level.

Long-Run Average Cost Curve (LRAC)

• Shows the lowest attainable average total cost for each output when both plant and labor are varied.

• Serves as a planning curve for firms to choose optimal plant size.

Economies and Diseconomies of Scale

• Economies of Scale: Features of technology that lead to falling LRAC as output increases.

• Diseconomies of Scale: Features that lead to rising LRAC as output increases.

• Constant Returns to Scale: LRAC remains constant as output increases.

Minimum Efficient Scale

• The smallest quantity of output at which LRAC reaches its lowest level.

• If LRAC is U-shaped, the minimum point identifies the minimum efficient scale.

Additional info: These notes expand on the brief points in the slides, providing definitions, formulas, and examples for clarity and completeness. Tables have been recreated and equations are presented in LaTeX format for academic rigor.