Cost Concepts and Relationships, Microeconomic Theory Ch. 7 – Study Notes

Source: Seminar Practice Questions, Texas A&M University

Tags: cost theory, average cost, marginal cost, variable cost, fixed cost, AVC, ATC, AFC, MC, total cost, cost curves, microeconomics, Chapter 7


TL;DR

Chapter 7 covers how firms measure and break down production costs. The core skill is understanding the algebra connecting total cost, average cost, marginal cost, and their fixed/variable components, and knowing how changes in one measure constrain the behaviour of the others.


Key Terms

Total cost (TC)

The sum of all costs a firm incurs to produce a given quantity. TC = FC + VC, where FC is fixed cost and VC is variable cost.

Fixed cost (FC)

Costs that do not change with the level of output (e.g. rent, equipment leases). Present even when output is zero.

Variable cost (VC)

Costs that change with the level of output (e.g. raw materials, hourly wages).

Average cost (AC / ATC)

Total cost per unit of output. AC = TC / q. Sometimes written ATC (average total cost) to distinguish from AVC.

Average variable cost (AVC)

Variable cost per unit of output. AVC = VC / q. Equivalent to AVC = w / AP_L (wage divided by the average product of labour), and also AVC = wage × L / q.

Average fixed cost (AFC)

Fixed cost per unit of output. AFC = FC / q. Since FC is constant, AFC falls continuously as output rises. Also: AFC = AC − AVC.

Marginal cost (MC)

The additional cost of producing one more unit of output. MC = ΔTC / Δq = ΔVC / Δq (fixed costs drop out of the change).

Average product of labour (AP_L)

Output per unit of labour. AP_L = q / L. Appears in the AVC identity: AVC = w / AP_L.

Marginal product of labour (MP_L)

The extra output from one additional unit of labour. When MP_L is rising, MC is falling, and vice versa.


Core Content

Identities Linking Cost Measures

  • TC = FC + VC

  • AC = TC / q = AFC + AVC

  • AFC = AC − AVC

  • AVC = VC / q = w / AP_L = wage × L / q

  • MC = ΔVC / Δq (since fixed costs do not change with output)

A common exam trap: the statement C = MC + VC is not a valid identity. Total cost equals FC + VC, not MC + VC. Marginal cost is a rate of change, not a level that sums into total cost in that way.

Calculating Average Cost from a TC Function

Given TC = 50 + 2q:

  • FC = 50 (the constant term)

  • VC = 2q

  • AC at q = 10: AC = (50 + 20) / 10 = 7

The average cost of the 10th T-shirt is 7, not 2 (which is just the marginal/variable cost per unit) and not 50 (which is only fixed cost).

Marginal Cost from Variable Cost Data

When VC at 1 unit = $10 and VC at 2 units = $16:

  • MC of the 2nd unit = ΔVC / Δq = (16 − 10) / (2 − 1) = $6

MC measures the change in variable cost between output levels, not the average.

Relationship Between MC and AVC

  • When MC < AVC, average variable cost is falling.

  • When MC > AVC, average variable cost is rising.

  • When MC = AVC, average variable cost is at its minimum.

Knowing that average cost is positive tells you nothing by itself about whether MC is above, below, or equal to AC. The direction of AC depends on whether MC is pulling it up or down.

Falling MC and Rising MP_L

If marginal cost is decreasing as output rises, marginal product of labour must be rising. The two move inversely: MC = w / MP_L (with a single variable input). So when MP_L climbs, each extra unit of output costs less.

A falling MC does not mean AVC is rising, nor that MC = AVC, nor that AFC is rising (AFC always falls with output).

What Shifts the Marginal Cost Curve

MC is driven by variable input costs per unit of output. For the MC curve to shift, something must change the per-unit variable cost of production.

  • A per-unit tax (e.g. $1 per pack) raises the variable cost of each unit produced, so MC shifts up.

  • A lump-sum penalty (e.g. $5 million fine) is a fixed cost. It shifts AFC and AC, but not MC.

  • An advertising campaign by a third party affects demand, not the firm's production costs. MC does not shift.

Only the per-unit tax shifts MC. "All of the above" is the common wrong answer here.


Formulas / Diagrams

Formula

Meaning

TC = FC + VC

Total cost breakdown

AC = TC / q

Average (total) cost

AVC = VC / q = w / AP_L

Average variable cost

AFC = FC / q = AC − AVC

Average fixed cost

MC = ΔVC / Δq

Marginal cost

MC = w / MP_L

MC-MP inverse relationship (single input)


Why It Matters / Exam Flags

⚠️ C = MC + VC is a false identity. TC = FC + VC is correct. This is a favourite "which is NOT true" question.

⚠️ Average cost of the qth unit means TC(q) / q, not the marginal cost of that unit. Do not confuse AC with MC.

⚠️ "Average cost is positive" tells you nothing about the MC vs AC relationship. The answer is "not enough information."

⚠️ MC is the change in VC between consecutive output levels, not VC divided by q (that would be AVC).

⚠️ Only per-unit cost changes shift MC. Lump-sum charges are fixed costs. Demand-side changes do not affect cost curves at all.


Practice Q&A

Q: Which statement is NOT true: (a) AVC = w/AP_L, (b) C = MC + VC, (c) AVC = wage×L/q, (d) AFC = AC − AVC?

A: (b). Total cost is FC + VC, not MC + VC.

Q: If TC = 50 + 2q, what is the average cost of the 10th T-shirt?

A: 7. AC = (50 + 20)/10 = 7.

Q: If average cost is positive, what can we say about marginal cost relative to average cost?

A: Not enough information. A positive AC could coexist with MC above, below, or equal to AC.

Q: VC is $10 at 1 unit and $16 at 2 units. What is the MC of the 2nd unit?

A: $6. MC = (16 − 10) / 1 = 6.

Q: If MC is falling as output rises, which must be true: MP_L rising, MC = AVC, AVC rising, or AFC rising?

A: MP_L is rising. MC and MP_L are inversely related.

Q: Which shifts the MC curve for cigarettes: a third-party ad campaign, a $1/pack tax, or a $5 million lump-sum penalty?

A: Only the $1/pack tax. It raises variable cost per unit. The ad campaign affects demand, not costs. The lump-sum penalty is a fixed cost.


Related Terms / Search Tags

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