Chapter 8: Short-Run Costs and Output Decisions – Principles of Microeconomics

Short-Run Costs and Output Decisions

Introduction

This chapter examines the cost structure of firms in the short run and how these costs influence output decisions, especially in perfectly competitive markets. Understanding these concepts is essential for analyzing firm behavior and market outcomes.

Costs in the Short Run

Types of Costs

• Fixed Cost (FC): Costs that do not depend on the firm's level of output. These are incurred even if the firm produces nothing. There are no fixed costs in the long run.

• Variable Cost (VC): Costs that depend on the level of production chosen. They vary with output.

• Total Cost (TC): The sum of total fixed costs and total variable costs.

Formula:

$TC = TFC + TVC$

Fixed Costs

• Total Fixed Cost (TFC): The total of all costs that do not change with output, even if output is zero.

• Average Fixed Cost (AFC): Total fixed cost divided by the number of units of output; a per-unit measure of fixed costs.

• Spreading Overhead: As output increases, AFC declines because the fixed cost is spread over more units.

Formula:

$AFC = \frac{TFC}{q}$

Table: Short-Run Fixed Cost (Total and Average) of a Hypothetical Firm

q	TFC	AFC
0	$100	–
1	$100	$100
2	$100	$50
3	$100	$33
4	$100	$25
5	$100	$20

Variable Costs

• Total Variable Cost (TVC): The total of all costs that vary with output in the short run.

• Total Variable Cost Curve: Shows the relationship between TVC and the level of a firm's output.

Table: Derivation of Total Variable Cost Schedule from Technology and Factor Prices

Units of Output	Units of Input (K)	Units of Input (L)	Total Variable Cost
1	10	7	$27
2	16	8	$40
3	19	15	$53
3	18	22	$58

Additional info: TVC is calculated as $TVC = (K \times P_K) + (L \times P_L)$, where $P_K$ and $P_L$ are input prices.

Marginal Cost (MC)

• Marginal Cost: The increase in total cost resulting from producing one more unit of output. Marginal costs reflect changes in variable costs.

Formula:

$MC = \frac{\Delta TC}{\Delta q}$

Table: Derivation of Marginal Cost from Total Variable Cost

Units of Output	Total Variable Cost ($)	Marginal Cost ($)
0	0	–
1	20	20
2	38	18
3	53	15

The Shape of the Marginal Cost Curve in the Short Run

• Firms are constrained by some fixed input, leading to diminishing returns to variable inputs and limiting capacity.

• As capacity is approached, producing additional output becomes increasingly costly.

• Marginal costs ultimately increase with output in the short run.

Graphing Total Variable Costs and Marginal Costs

• Total variable costs always increase with output.

• Marginal cost is the cost of producing each additional unit.

• The marginal cost curve shows how TVC changes with single-unit increases in output.

Formula:

$\text{Slope of TVC} = \frac{\Delta TVC}{\Delta q} = \Delta TVC = MC$

Average Variable Cost (AVC)

• Average Variable Cost: TVC divided by the number of units of output; a per-unit measure of variable costs.

Formula:

$AVC = \frac{TVC}{q}$

Table: Short-Run Costs of a Hypothetical Firm

q	TVC	MC	AVC	TFC	TC	AFC	ATC
0	$0.00	–	–	$100.00	$100.00	–	–
1	$20.00	$20.00	$20.00	$100.00	$120.00	$100.00	$120.00
2	$35.00	$15.00	$17.50	$100.00	$135.00	$50.00	$67.50
3	$45.00	$10.00	$15.00	$100.00	$145.00	$33.33	$48.33
4	$55.00	$10.00	$13.75	$100.00	$155.00	$25.00	$38.75
5	$70.00	$15.00	$14.00	$100.00	$170.00	$20.00	$34.00

Graphing Average Variable Costs and Marginal Costs

• When MC is below AVC, AVC is declining.

• When MC is above AVC, AVC is increasing.

• Rising MC intersects AVC at the minimum point of AVC.

Total Costs

Relationship Between TC, TFC, and TVC

• Adding TFC to TVC means adding the same amount of fixed cost to every level of variable cost.

• The TC curve has the same shape as the TVC curve, but is higher by the amount of TFC.

Average Total Cost (ATC)

• Average Total Cost: TC divided by the number of units of output; a per-unit measure of total costs.

Formula:

$ATC = \frac{TC}{q}$

Or, $ATC = AFC + AVC$

Relationship Between ATC and MC

• The relationship between ATC and MC is the same as between AVC and MC.

• If MC is below ATC, ATC will decline toward MC.

• If MC is above ATC, ATC will increase.

• MC intersects ATC at ATC's minimum point.

Short-Run Costs: A Review

Table: Summary of Cost Concepts

Term	Definition	Equation
Accounting costs	Out-of-pocket costs	–
Economic costs	Include opportunity costs of all inputs	–
Total fixed costs (TFC)	Do not depend on output quantity	–
Total variable costs (TVC)	Vary with output	–
Total cost (TC)	Sum of TFC and TVC	$TC = TFC + TVC$
Average fixed cost (AFC)	Fixed cost per unit	$AFC = TFC/q$
Average variable cost (AVC)	Variable cost per unit	$AVC = TVC/q$
Average total cost (ATC)	Total cost per unit	$ATC = TC/q$ or $AFC + AVC$
Marginal cost (MC)	Increase in TC from one more unit	$MC = \Delta TC / \Delta q$

Output Decisions: Revenues, Costs, and Profit Maximization

Perfect Competition

• Perfect Competition: Many firms, identical products, no control over prices, free entry and exit.

• Homogeneous Products: Products are undifferentiated and identical across firms.

Total Revenue and Marginal Revenue

• Total Revenue (TR): The total amount a firm receives from sales: price per unit times quantity.

Formula:

$TR = P \times q$

• Marginal Revenue (MR): The additional revenue from selling one more unit. In perfect competition, $MR = P$.

Formula:

$P = d = MR$

Profit Maximization

• Firms maximize profit by producing up to the point where marginal revenue equals marginal cost.

• In perfect competition, this condition is $P = MC$.

Formula:

$MR = MC$

For perfectly competitive firms: $P = MC$

Table: Profit Analysis for a Simple Firm

q	TFC	TVC	MC	P = MR	TR	TC	Profit
1	$10	$5	–	$15	$15	$15	$0
2	$10	$10	$5	$15	$30	$20	$10
3	$10	$20	$10	$15	$45	$30	$15
4	$10	$35	$15	$15	$60	$45	$15
5	$10	$50	$20	$15	$75	$60	$15
6	$10	$80	$30	$15	$90	$90	$0

The Short-Run Supply Curve

• At any market price, the MC curve shows the output level that maximizes profit.

• The MC curve of a perfectly competitive, profit-maximizing firm is its short-run supply curve, except when price is so low that the firm shuts down.

Economics in Practice: Cost Structure Example

Rock Concert Example

• Output: Number of seats sold.

• Fixed costs: Publicity, booking venue, instruments, etc.

• Variable costs: Additional tickets sold, increased security, etc. These are low relative to fixed costs.

Critical Thinking: Consider other products or services with low marginal costs and high fixed costs (e.g., software, streaming services) and those with high marginal costs and low fixed costs (e.g., custom tailoring).

Key Terms and Formulas

• Average Fixed Cost (AFC): $AFC = TFC/q$

• Average Variable Cost (AVC): $AVC = TVC/q$

• Average Total Cost (ATC): $ATC = TC/q$ or $AFC + AVC$

• Marginal Cost (MC): $MC = \Delta TC / \Delta q$

• Total Revenue (TR): $TR = P \times q$

• Profit Maximizing Output: $MR = MC$ (or $P = MC$ in perfect competition)