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Short-Run Costs and Output Decisions in Perfect Competition

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Short-Run Costs and Output Decisions

Overview

This topic explores the cost structures and output decisions of firms in the short run, focusing on how revenues and costs determine the profit-maximizing output in a perfectly competitive market. The key principle is that, in the short run, a firm maximizes profit by producing the quantity where marginal cost (MC) equals price (P).

Cost Concepts in the Short Run

Fixed Cost (TFC)

  • Definition: Costs that do not depend on the level of output; incurred even when output (q) is zero.

  • Long-Run Context: There are no fixed costs in the long run; all costs become variable.

  • Spreading Overhead: As output increases, average fixed cost (AFC) falls because the fixed cost is spread over more units.

  • Formula:

  • Example: If TFC = $100 and q = 5, then AFC = $20.

Variable Cost (TVC)

  • Definition: Costs that vary directly with the level of output.

  • Total Variable Cost Curve: Shows TVC as a function of output.

  • Formula:

  • Example: If TVC = $75 and q = 5, then AVC = $15.

Total Cost (TC)

  • Definition: The sum of fixed and variable costs.

  • Formula:

  • Shape: The TC curve has the same shape as the TVC curve, but is shifted upward by the amount of TFC.

Average and Marginal Measures

Average Fixed Cost (AFC)

  • Formula:

  • Behavior: AFC declines as output increases.

Average Variable Cost (AVC)

  • Formula:

  • Interpretation: Represents per-unit variable cost.

Average Total Cost (ATC)

  • Formula:

  • Behavior: As AFC shrinks with increasing q, ATC and AVC converge but never meet.

Marginal Cost (MC)

  • Formula:

  • Short-Run Context: When TFC is constant, MC equals the change in TVC.

  • Interpretation: MC reflects the cost of producing one additional unit.

  • Behavior: MC eventually rises due to diminishing marginal product from fixed inputs.

  • Intersection: MC intersects AVC and ATC at their minimum points.

Shapes and Relationships in the Short Run

Diminishing Marginal Product

  • Definition: When a fixed factor is combined with increasing variable inputs, the marginal product of the variable input eventually diminishes.

  • Effect: Causes MC to rise at higher output levels.

Relationship Rules

  • If MC < AVC (or ATC), the respective average cost is declining.

  • If MC > AVC (or ATC), the respective average cost is rising.

  • Rising MC crosses AVC and ATC at their minimum points.

Short-Run Cost Table (Hypothetical Firm)

This table illustrates how TVC and MC change with output. When TFC is known, other cost measures can be calculated.

q (output)

TVC

MC

0

$0.00

—

1

$20.00

$20.00

2

$38.00

$18.00

3

$53.00

$15.00

4

$65.00

$12.00

5

$75.00

$10.00

6

$83.00

$8.00

7

$94.50

$11.50

8

$108.00

$13.50

9

$128.50

$20.50

10

$168.50

$40.00

Additional info: With TFC = $100, students can compute AFC, AVC, ATC, and TC for each output level.

Numerical Profit Example (Perfect Competition)

This table demonstrates how to calculate profit at different output levels for a firm in perfect competition, where price equals marginal revenue (MR).

q

TFC

TVC

MC

P = MR

TR (P×q)

TC (TFC+TVC)

Profit (TR−TC)

0

$10

$0

—

$15

$0

$10

−$10

1

$10

$10

$10

$15

$15

$20

−$5

2

$10

$15

$5

$15

$30

$25

$5

3

$10

$20

$5

$15

$45

$30

$15

4

$10

$30

$10

$15

$60

$40

$20

5

$10

$50

$20

$15

$75

$60

$15

6

$10

$80

$30

$15

$90

$90

$0

  • Profit Maximization: The optimal output occurs where MR = MC. In this example, MR = P = $15; MC crosses MR between q = 4 and q = 5, so the profit-maximizing output is between 4 and 5 units.

Perfect Competition: Revenue Concepts

Market Structure

  • Perfect Competition: Many small firms, homogeneous products, free entry and exit.

  • Demand Curve: Each firm faces a perfectly elastic demand at the market price.

Total Revenue (TR)

  • Formula:

  • Interpretation: Total revenue is the product of price and quantity sold.

Marginal Revenue (MR)

  • Definition: The additional revenue from selling one more unit.

  • Perfect Competition: MR = P; the firm's demand curve is its MR curve.

Profit Maximization Rule

  • General Rule: Firms maximize profit by producing where MR = MC.

  • Perfect Competition: Since MR = P, the rule becomes P = MC.

  • Production Decision: Firms produce additional units as long as MR > MC.

Short-Run Supply Curve

  • Definition: The portion of the MC curve above the shutdown point is the firm's short-run supply curve.

  • Exception: If price falls below the shutdown point (minimum AVC), the firm will cease production in the short run.

Key Terms and Definitions

  • Average Fixed Cost (AFC):

  • Average Variable Cost (AVC):

  • Average Total Cost (ATC):

  • Fixed Cost (TFC): Costs independent of output.

  • Variable Cost (TVC): Costs that vary with output.

  • Total Cost (TC):

  • Marginal Cost (MC):

  • Total Revenue (TR):

  • Marginal Revenue (MR): Additional revenue from one more unit; MR = P in perfect competition.

  • Perfect Competition: Many firms, identical products, price takers.

  • Spreading Overhead: Decline in AFC as output increases.

  • Total Variable Cost Curve: TVC vs. output graph.

Action Items / Next Steps

  • Practice graphing cost curves: TFC, TVC, TC, AFC, AVC, ATC, MC.

  • Use sample tables to compute AVC, AFC, ATC from given TFC and TVC data.

  • Apply MR = MC rule to multiple numerical examples to find profit-maximizing output.

  • Prepare for long-run analysis: understand how fixed costs disappear and supply behavior changes.

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