Difficulty: Intermediate | Prerequisites: Production Theory notes (isoquants, MRTS, returns to scale)
Cost theory translates production functions into cost curves by adding input prices. Firms minimise cost where the isocost line is tangent to the isoquant. In perfectly competitive markets, firms are price takers who maximise profit by producing where MC = MR = P, and long-run equilibrium drives economic profit to zero. Government interventions (price supports, tariffs, quotas) create deadweight loss.
Accounting cost
Actual expenses plus depreciation charges for capital equipment.
Economic cost (opportunity cost)
The cost to a firm of utilising resources in production, including the value of the next-best alternative foregone.
Sunk cost
An expenditure that has been made and cannot be recovered. It should have no bearing on current decisions.
Marginal cost (MC)
Change in total cost / change in quantity. With diminishing marginal returns, MC increases; with increasing marginal returns, MC decreases.
Isocost line
A graph showing all combinations of labour and capital that can be purchased for a given total cost. Slope = -(w/r), where w is the wage rate and r is the rental rate of capital.
Expansion path
The curve passing through points of tangency between a firm's isocost lines and its isoquants.
Economies of scale
Output can be doubled for less than a doubling of cost. Cost-output elasticity EC = MC/AC < 1.
Diseconomies of scale
Doubling output requires more than a doubling of cost. EC > 1.
Economies of scope
Joint output of a single firm is greater than the combined output of two separate firms each producing one product. The product transformation curve is bowed outward (concave).
User cost of capital
Annual cost of owning and using a capital asset = economic depreciation + (interest rate * value of capital). In a competitive market, the rental rate should equal user cost.
Perfectly competitive market
A market with many buyers and sellers, homogeneous products and free entry/exit. Each firm is a price taker.
Profit
Total revenue minus total cost. Economic profit = revenue minus labour cost minus capital cost.
Zero economic profit
The firm is earning a normal return on its investment, doing as well as it could by investing its money elsewhere.
Producer surplus
Revenue minus variable cost. In the long run, it equals economic rent from all scarce inputs.
Economic rent
The amount a firm is willing to pay for an input less the minimum amount necessary to obtain it. Positive even when economic profit is zero.
Deadweight loss
The net loss of total (consumer + producer) surplus from a market distortion.
Price support
Prices set by government above the free-market level, maintained by government purchases of excess supply.
Tariff
A tax on an imported good.
Import quota
A limit on the quantity of a good that can be imported.
Economic efficiency
Maximisation of aggregate consumer and producer surplus.
Market failure
When an unregulated competitive market is inefficient because prices fail to provide proper signals. Occurs because of externalities and lack of information.
Given TC = 4000 + 5Q + 10Q^2:
Total fixed cost (TFC) = 4000
Average fixed cost (AFC) = 4000 / Q
Total variable cost (TVC) = 5Q + 10Q^2
Average variable cost (AVC) = 5 + 10Q
Average total cost (ATC) = 4000/Q + 5 + 10Q
Marginal cost (MC) = 5 + 20Q
Average total cost always equals average variable cost plus average fixed cost.
Cost-curve relationships: whenever AVC is falling as output rises, MC is below AVC (but MC need not also be falling). Whenever ATC is rising as output rises, AVC must also be rising (Statement I is false, Statement II is true).
An isocost line reveals the input combinations that can be purchased for a given total cost. Its slope equals -(w/r).
Cost is minimised where the isocost line is tangent to the isoquant. At that point, MRTS = w/r, or equivalently MPl/w = MPk/r. Any expression that omits the wage and rental rate is not a valid cost-minimisation condition.
If MRTS = 3 and w/r differs from 3, the firm can reduce cost by adjusting inputs. With MRTS = 3 (when K is vertical, L horizontal), the marginal product of labour is 3 times the marginal product of capital, and the firm should employ more labour and less capital if w/r < 3.
Worked example: A firm employs 100 workers at $10/hour and 50 capital units at $21/hour. MPl = 3, MPk = 5. MPl/w = 3/10 = 0.3, MPk/r = 5/21 = 0.238. Since MPl/w > MPk/r, the firm could reduce costs by employing more labour and less capital.
Worked example (Acme): Q = 25L^0.6 * K^0.4, w = $10, r = $25. Cost minimisation requires MRTS = w/r. MRTS = (0.6K) / (0.4L) = 1.5K/L. Setting 1.5K/L = 10/25 = 0.4, so K/L = 0.4/1.5 = 4/15. The optimal capital-labour ratio is 4/15.
Three Guys From Nowhere has C(q,K) = 0.5q^2/K + 0.25K with K = 4 ovens. ATC of 10 pizzas = (0.5 * 100/4 + 0.25 * 4) / 10 = (12.5 + 1) / 10 = 1.35. With 9 ovens: (0.5 * 100/9 + 0.25 * 9) / 10 = (5.56 + 2.25) / 10 = 0.78.
Marvel Studios: C(q,K) = 15q^2/K + 12K with K = 15. LTC(q) = 26.8q, so long-run ATC = 26.8 (constant). With 4 fewer green screens (K = 11), short-run ATC of 10 units = (15 * 100/11 + 12 * 11)/10 = (136.4 + 132)/10 = 26.84, which is higher than with 15 screens. Short-run ATC increases. The long-run cost curve exhibits constant returns to scale.
For fixed-proportion production (one pilot per plane), the optimal capital-labour ratio remains the same even if relative input prices change.
Economies of scale: EC = MC/AC < 1.
Degree of economies of scope: SC = [C(Q1) + C(Q2) - C(Q1,Q2)] / C(Q1,Q2). When Bubba Burgers discovers economies of scope, the likely response is to add grilled chicken sandwiches.
Q = 4L^0.5 * K^0.5 (constant returns to scale). To double output from 200 to 400, the firm must exactly double its inputs.
Constantine bought IBM shares at $150; they are now $55. His refusal to sell below $150 is incorrect because the original purchase price is a sunk cost and should have no bearing on whether to hold or sell.
Farmer Jones's farm cost $75,000 in 1975 and is now worth $500,000 at 10% interest. ABC offers $500,000 today; XYZ offers $530,000 in one year. Farming nets $15,000 this year. Selling to ABC today yields $500,000 * 1.10 = $550,000 next year, versus $530,000 + $15,000 = $545,000 from waiting. He should sell to ABC.
Characteristics: price taker, product homogeneity, free entry and exit. The demand curve facing an individual firm is perfectly horizontal.
A perfectly competitive firm sets MC(Q*) = MR = P. In the long run, LR MC = P.
A firm should shut down when P < AVC in the short run. In long-run equilibrium, all firms earn zero economic profit, no firm has incentive to enter or exit, and Qs = Qd.
Price supports: consumers lose (area -A - B), producers gain (A + B + D), government cost = (Q2 - Q1) * Ps. Net welfare = consumers + producers - government cost.
Tariffs: gain to domestic producers = A, loss to consumers = A + B + C + D, net domestic loss = B + C.
Quotas: net domestic loss = B + C + D (larger than tariff because the government does not collect tariff revenue).
Positive analysis describes cause and effect. Normative analysis examines what ought or should be.
Total cost: TC = TFC + TVC
Average total cost: ATC = TC / Q = AFC + AVC
Marginal cost: MC = dTC / dQ
Isocost line slope: -(w / r)
Cost minimisation condition: MRTS = w / r, or equivalently MPl / w = MPk / r
Profit: Total revenue - total cost
Shutdown rule (short run): Shut down if P < AVC
Long-run profit maximisation: LR MC = P
Cost-output elasticity: EC = MC / AC (< 1 = economies of scale, > 1 = diseconomies)
Degree of economies of scope: SC = [C(Q1) + C(Q2) - C(Q1,Q2)] / C(Q1,Q2)
Elasticity of market supply: Es = (Change in Q / Q) / (Change in P / P)
Producer surplus: Revenue - variable cost
Welfare from price support: Consumers + producers - government cost
Tariff net domestic loss: B + C
Quota net domestic loss: B + C + D
The sunk cost fallacy is everywhere: people hold losing investments because they paid a high price, or finish a bad film because they already paid for the ticket. In business, the cost-minimisation condition drives decisions about automation vs hiring, since MRTS = w/r tells the firm how to balance labour and capital at current prices. Tariff and quota analysis is central to trade policy debates.
Students think "zero economic profit" means the firm is failing. It means the firm is earning a normal return, doing exactly as well as its next-best alternative.
A common mistake is including sunk costs in decision-making. The original price of an asset is irrelevant to whether you should sell it today.
Students often assume that whenever AVC is falling, MC must also be falling. MC can be rising while still below AVC.
The shutdown condition is P < AVC, not P < ATC. A firm can operate at a loss in the short run as long as it covers variable costs.
⚠️ TC decomposition problems are very common. Given a TC function, be ready to extract TFC, TVC, AFC, AVC, ATC and MC.
⚠️ Cost minimisation: know that MRTS = w/r and be able to determine whether a firm should use more labour or more capital.
⚠️ The sunk cost fallacy appears regularly as a true/false or scenario question.
⚠️ Welfare area calculations (consumer surplus, producer surplus, deadweight loss) for tariffs and quotas are exam staples. Know which areas are A, B, C, D.
⚠️ The shutdown rule (P < AVC in the SR) vs long-run exit condition (zero economic profit) are frequently tested.
True or false: ATC = AVC + AFC always. (True.)
Fill in the blank: A firm should shut down in the short run when P < ______. (AVC)
True or false: In long-run competitive equilibrium, economic profit is positive. (False, it is zero.)
Fill in the blank: The isocost line's slope equals ______. (-(w/r))
True or false: The deadweight loss from a quota is larger than from a tariff with the same price effect. (True, by area D.)
Q: TC = 4000 + 5Q + 10Q^2. Find TFC, TVC, AVC, ATC and MC.
A: TFC = 4000. TVC = 5Q + 10Q^2. AVC = 5 + 10Q. ATC = 4000/Q + 5 + 10Q. MC = 5 + 20Q.
Q: A firm has 100 workers ($10/hr), 50 capital units ($21/hr). MPl = 3, MPk = 5. Is the firm minimising cost?
A: No. MPl/w = 0.3 > MPk/r = 0.238. The firm should use more labour and less capital.
Q: Constantine bought IBM shares at $150; they are now $55. He refuses to sell below $150. Is his reasoning correct?
A: No. The original price is a sunk cost and should not influence the decision to hold or sell.
Q: Farmer Jones can sell his farm to ABC for $500,000 today or to XYZ for $530,000 in one year. Interest rate is 10%. Farming this year nets $15,000. What should he do?
A: Sell to ABC. $500,000 today grows to $550,000 in a year at 10%. Waiting yields $530,000 + $15,000 = $545,000.
Q: TGFN has C(q,K) = 0.5q^2/K + 0.25K, K = 4. What is the ATC of producing 10 pizzas?
A: TC = 0.5(100)/4 + 0.25(4) = 12.5 + 1 = 13.5. ATC = 13.5/10 = 1.35.
Q: Bubba Burgers discovers economies of scope. What is the most likely response?
A: Adding grilled chicken sandwiches (producing a related product jointly reduces costs).
cost theory, total cost, fixed cost, variable cost, marginal cost, average total cost, ATC, AVC, AFC, MC, isocost line, cost minimisation, economies of scale, diseconomies of scale, economies of scope, sunk cost, sunk cost fallacy, perfect competition, price taker, profit maximisation, shutdown rule, producer surplus, economic rent, deadweight loss, price support, tariff, quota, welfare analysis, economic efficiency, market failure, intermediate microeconomics, FIU