BUSS1040 · Economics For Business Decision Making
Firm Behaviour: Production & Costs
Topic 2 builds the short-run cost structure every later firm chapter depends on: TC = FC + VC, the average curves AFC/AVC/ATC, and the marginal cost MC = ΔTC/Δq. The signature geometric fact — that MC cuts AVC and ATC at their minimum points from below — underpins the perfect-competition shut-down rule and the monopoly DWL diagram. It is examined as calculation (differentiate a cost function, evaluate the curves at a quantity) and as 'which curve is which' MCQs.
What this chapter covers
- 011. Cost identities: TC = FC + VC; ATC = TC/q; AVC = VC/q; AFC = FC/q
- 022. AFC = ATC − AVC and falls continuously as q rises
- 033. Marginal cost MC = ΔTC/Δq = dTC/dq
- 044. MC from a quadratic cost: if TC = F + aq + bq² then MC = a + 2bq
- 055. Curve geometry: MC cuts AVC and ATC at their minimum points from below
- 066. The U-shaped ATC and the falling AFC gap between ATC and AVC
- 077. Short run (at least one fixed input, FC > 0) vs long run (all inputs variable)
- 088. Reading the cost-curve family for later rules (shut-down, profit-max)
Short-run cost curves from a quadratic cost function
- 2 marksFC is the constant term: FC = 90. Variable cost VC = 6q + 3q². Differentiate total cost for marginal cost: MC = dTC/dq = 6 + 6q.
- 1 markAt q = 5: MC = 6 + 6(5) = 36.
- 2 marksVC at q = 5 = 6(5) + 3(25) = 30 + 75 = 105, so AVC = 105/5 = 21. TC = 90 + 105 = 195, so ATC = 195/5 = 39. AFC = 90/5 = 18 (and 39 − 21 = 18 ✓).
- 1 markAVC = 6 + 3q rises from q = 0, so MC = 6 + 6q lies above AVC for all q > 0 — consistent with MC cutting AVC at its minimum from below.
Key terms
- Total, fixed and variable cost (TC, FC, VC)
- TC = FC + VC. Fixed cost FC does not change with output (it exists even at q = 0); variable cost VC rises with output. In a quadratic cost TC = F + aq + bq², F is the fixed cost and aq + bq² is the variable cost.
- Average costs (ATC, AVC, AFC)
- ATC = TC/q, AVC = VC/q, AFC = FC/q. They satisfy AFC = ATC − AVC. AFC falls continuously toward zero; ATC and AVC are U-shaped, with ATC lying above AVC by the AFC gap.
- Marginal cost (MC)
- The change in total cost from one more unit, MC = ΔTC/Δq = dTC/dq. For TC = F + aq + bq², MC = a + 2bq. MC is the curve the firm's output decisions are made on.
- MC cuts AVC and ATC at their minima
- When MC is below an average curve it pulls the average down; when above, it pulls it up. So MC must intersect each U-shaped average curve exactly at its lowest point, from below — a fact used directly in the shut-down and profit-max rules.
- Short run vs long run
- In the short run at least one input is fixed, so FC > 0 and the firm can shut down but not exit. In the long run all inputs are variable (no fixed cost is unavoidable) and the firm can enter or exit the industry.
- U-shaped ATC
- Average total cost first falls (spreading fixed cost and rising productivity) then rises (diminishing returns), tracing a U. Its minimum is the most cost-efficient scale and is where MC crosses it.
Firm Behaviour: Production & Costs FAQ
How do I get MC from a total-cost function?
Differentiate total cost with respect to quantity: MC = dTC/dq. For the standard intro form TC = F + aq + bq², MC = a + 2bq. Two common errors lose marks: forgetting the factor of 2 on the bq² term (the derivative of bq² is 2bq, not bq), and differentiating the fixed cost F to something other than zero — F is constant, so it disappears from MC entirely.
Why does MC always cut AVC and ATC at their minimum points?
It is the average-marginal relationship. Whenever the marginal value is below the average, it drags the average down; whenever it is above, it pulls the average up. So the average can only stop falling and start rising — its minimum — at the exact quantity where marginal equals average. That is why MC passes through the bottom of both the AVC and ATC curves, and it crosses from below.
What is the difference between fixed cost and sunk cost in this course?
Fixed cost (FC) is any cost that does not vary with output in the short run, like rent or a leased machine. It matters for ATC but NOT for the short-run produce-or-shut-down decision, because you pay it whether you produce or not. The intro framing is: in the short run the firm decides on variable costs (compare price to AVC); fixed cost only re-enters in the long-run exit decision (compare price to ATC).
How is Topic 2 examined?
As calculation and identification. You will be given a cost function and asked to find FC, MC, AVC, ATC and AFC at a quantity (differentiate, then divide), or shown a graph and asked which curve is MC/AVC/ATC and where they cross. The cost family then feeds straight into Topic 5 (perfect competition) — the shut-down point is AVC-min and the break-even point is ATC-min, both read off this same diagram.
Exam move
Drill two moves until they are automatic: (1) from TC = F + aq + bq², write MC = a + 2bq by differentiation, and (2) build a small table of q, TC, VC, FC, then divide to get the three average curves — and check AFC = ATC − AVC as a self-test. Memorise the geometry rather than re-deriving it under time pressure: AFC falls forever, ATC and AVC are U-shaped, and MC slices through the minimum of each from below. Sketch the whole family once cleanly and label the AVC-min (future shut-down point) and ATC-min (future break-even point) — that single diagram is reused in Topic 5 and Topic 6, so the time you invest here pays off three chapters later.
