CMA Foundation · Fundamentals of Business Economics and Management

Cost of Production: formula sheet

Full chapter guide

Key formulas

Economic cost: Economic cost = Explicit cost + Implicit cost; Accounting cost equals explicit cost only.
Opportunity cost: Opportunity cost = Value of the next best alternative foregone; It is the single best alternative given up, not the sum of all alternatives.
Social cost: Social cost = Private cost + External cost; External cost falls on third parties, such as pollution or congestion.
Economic profit: Economic profit = Total revenue − (Explicit cost + Implicit cost); Accounting profit = Total revenue − Explicit cost.
Total cost: TC = TFC + TVC; The basic relation. Use it to find any one of the three when the other two are given.
Total variable cost: TVC = TC − TFC; Also equals the sum of variable costs of all units produced.
Total fixed cost: TFC = TC − TVC; At zero output, TFC = TC because TVC = 0.
Fixed cost at any output: TFC is constant for all outputs; The TFC curve is a horizontal line. Do not multiply it by output.
Gap between TC and TVC: TC − TVC = TFC at every output; The vertical distance between the two curves is constant.
Total cost: TC = TFC + TVC; TFC stays constant at every level of output, including zero output.
Average fixed cost: AFC = TFC ÷ Q; Falls continuously as Q rises. It never touches zero.
Average variable cost: AVC = TVC ÷ Q; U-shaped in the short run.
Average total cost: ATC (AC) = TC ÷ Q = AFC + AVC; The gap between ATC and AVC is AFC, and it narrows as output rises.
Marginal cost: MC = ΔTC ÷ ΔQ = TCn − TC(n−1); When output rises by one unit at a time, MC is simply the difference between successive TC values. It also equals ΔTVC ÷ ΔQ.
AC-MC relationship: MC < AC → AC falls; MC = AC → AC is minimum; MC > AC → AC rises; MC cuts both AVC and ATC at their minimum points, coming from below.
Long-run average cost: LAC = Long-run total cost ÷ Output; All inputs are variable, so there is no fixed cost in the long run.
Envelope rule: LAC ≤ SAC at every output level; LAC touches each SAC curve at one point and lies on or below all of them.
Tangency position: Falling LAC: tangent to the left of SAC minimum. Rising LAC: tangent to the right. At LAC minimum: SAC minimum.; Holds for U-shaped LAC with SAC curves of different plant sizes.
Scale and cost link: Economies of scale: LAC falls as output rises. Diseconomies: LAC rises as output rises.; Constant LAC means constant returns to scale in the cost sense.
Minimum efficient scale: Output at which LAC is lowest; This is the optimum size of the firm.
Total revenue: TR = P × Q; Price multiplied by quantity sold.
Average revenue: AR = TR ÷ Q = P; AR is the same as price, so the AR curve is the demand curve.
Marginal revenue: MR = ΔTR ÷ ΔQ = TRn − TRn−1; Extra revenue from one more unit. Use the difference of TR when Q rises by 1.
Perfect competition: AR = MR = P; Horizontal AR and MR curve at the market price.
Imperfect competition: MR < AR; When AR falls as output rises, MR is below AR. For a straight-line demand, MR falls twice as fast as AR.
Profit: Profit = TR − TC; Positive means profit, negative means loss.
Break-even: TR = TC; Profit is zero. Equivalent: AR = AC.
Profit-maximising output: MC = MR, with MC rising; The slope of MC must be greater than the slope of MR at that point (second-order condition).

Quick revision

TC = TFC + TVC; TFC stays the same at every output level, including zero output.
AFC = TFC ÷ Q and it keeps falling as output rises.
AVC = TVC ÷ Q, ATC = TC ÷ Q, and ATC = AFC + AVC.
MC is the extra cost of producing one more unit: MC = change in TC ÷ change in Q.
MC is not affected by fixed cost, because fixed cost does not change when output changes.
MC cuts AVC and ATC from below at their lowest points.
When MC is below average cost, average cost falls; when MC is above it, average cost rises.
Explicit cost is an actual payment; implicit cost is the value of the owner's own resources used.
Opportunity cost is the value of the next best alternative given up.
The long-run average cost curve is U-shaped because of economies and then diseconomies of scale.
TR = P × Q, AR = TR ÷ Q, and MR is the change in TR from one more unit sold.
Profit = TR − TC; AR equals price.

Common mistakes

Treating implicit cost as a cash payment. Fix: Remember implicit cost involves no outflow. It is the owner's own resource valued at what it could earn elsewhere.
Adding all alternatives to find opportunity cost. Fix: Opportunity cost is only the value of the best alternative given up.
Thinking TFC rises with output. Fix: Total fixed cost never changes in the short run. Only average fixed cost falls.
Starting the TVC curve on the cost axis above zero. Fix: TVC is zero when nothing is produced, so it starts at the origin. Only TC starts at TFC.
Treating MC as TC ÷ Q. Fix: MC is the extra cost of the last unit. Always subtract successive TC values.
Thinking fixed cost affects MC. Fix: TFC cancels out when you subtract. MC depends only on change in variable cost.
Saying the LAC is the sum of SAC curves or joins their minimum points. Fix: LAC is tangent to each SAC at the output where that plant is the cheapest choice. It joins minimum points only at its own minimum.
Explaining the U-shape of LAC with the law of variable proportions. Fix: Short-run U-shape comes from variable proportions. Long-run U-shape comes from economies and diseconomies of scale.
Thinking AR and price are different things. Fix: Remember AR = TR ÷ Q = (P × Q) ÷ Q = P. AR is the demand curve.
Calculating MR as TR ÷ Q. Fix: MR is the change in TR for an extra unit. Always subtract successive TR values.

Exam tips

Most questions are definition or classification MCQs. Learn the one-line difference for each pair.
In numerical MCQs, check whether the question asks for accounting or economic profit before calculating.
Watch for options that give explicit cost alone when economic cost is asked.
Words like 'foregone', 'next best' and 'sacrificed' point to opportunity cost.
Pollution, congestion and noise examples point to social cost.
Questions often ask which curve starts at the origin. The answer is TVC, not TC or TFC.
When a table is given, the TC at zero output is your TFC. Find it first.
Watch for options that say TFC rises with output. These are wrong, but may be right for average fixed cost only if the word 'average' is used.