MBA201a: Economic Costs & Costs of ProductionEconomic categorizations of costs: cost functionsT-shirt factory exampleCategorizing the costsThe Average Cost FallacyWe will talk about 6 types of cost functionsA total cost function graphicallyThe average total cost functionMarginal costsT-shirts: costsT-shirt factory cost functionsMarginal and average cost curves: generic shapeMore average cost and marginal cost in ExcelEconomies of scaleT-shirt factory profitsWhat if Fruit-of-the-LoomTM offers a lower price?General lessons on output decisionsOutput decisions in the generic caseSlide 19Supply curveSupply curve for a competitive (price-taking) firmNext weekTakeawaysMBA201a: Economic Costs & Costs of ProductionProfessor Wolfram MBA201a - Fall 2009 Page 2Economic categorizations of costs: cost functions•We have seen how economic costs include opportunity costs and exclude sunk costs.•Once we’ve got the right costs, what do we do with them?Cost functions–Cost functions relate some cost to the quantity a firm produces.–Cost functions represent ideal rather than actual costs.–A firm’s cost function may change over time.Professor Wolfram MBA201a - Fall 2009 Page 3T-shirt factory exampleYou run a t-shirt factory for Fruit-of-the-Loom.You’re currently producing 45 t-shirts a week, and selling them to headquarters for $1.80 each, for total revenues of $80/week.Your division manager tells you that if you’re making 45 t-shirts a week, your total costs are $71/week, so your average cost per t-shirt is $1.58.Are you happy?Professor Wolfram MBA201a - Fall 2009 Page 4Categorizing the costsUpon further investigation, you learn that your cost structure looks like this:To produce t-shirts:•You must lease one machine at $20 / week.•The machine requires one worker.•The machine, operated by the worker, produces one t-shirt per hour.•Worker is paid $1/hour on weekdays (up to 40 hours), $2/hour on Saturdays (up to 8 hours), $3 on Sundays (up to 8 hours).Are you still happy?Professor Wolfram MBA201a - Fall 2009 Page 5The Average Cost Fallacy•The first 40 t-shirts cost: C(n) = F + V(n) = $20 + $1*40 = $60At a price of $1.80, profits on these is $12.•The next 5 t-shirts cost:$2*5 = $10At a price of $1.80, they generate revenue of $9.You’re losing $1 by producing up to 45! You should have stopped at 40.fixedvariableProfessor Wolfram MBA201a - Fall 2009 Page 6We will talk about 6 types of cost functionsTotal cost (C): total cost of inputs the firm needs to produce output q. Denoted C(q). Fixed cost (FC): the cost that does not depend on the output level, C(0) [or really C(0.00001)]Variable cost (VC): that cost which would be zero if the output level were zero, C(q) – C(0) [or really C(q) – C(0.00001)].Average total cost (ATC) (aka simply “average cost” (AC)): total cost divided by output level, C(q)/q. Average variable cost (AVC): variable cost divided by output level, VC(q)/q. Marginal cost (MC): the unit cost of a small increase in output. –Derivative of cost with respect to output, dC/dq–Approximated by C(q)-C(q-1), e.g. C(40)-C(39)Professor Wolfram MBA201a - Fall 2009 Page 7A total cost function graphicallyAn example: C(Q) = 10 + .5QProfessor Wolfram MBA201a - Fall 2009 Page 8The average total cost functionATC(Q) = C(Q)/Q = 10/Q + .5Professor Wolfram MBA201a - Fall 2009 Page 9Marginal costsMC(Q) = dC(Q)/dQ = .5Professor Wolfram MBA201a - Fall 2009 Page 10T-shirts: costsSuppose output level is 40 t-shirts per week. Then,–Fixed cost: FC = $20. –Variable cost: VC = 40 x $1 = $40.–Average total cost: ATC = (20+40)/40 = $1.5–Average variable cost: AVC = (40)/40 = $1–Marginal cost: MC = $1.(Note that producing an extra T-shirt would imply working on Saturday, which costs more: MC(41) = $2.) Similar calculations can be made for other output levels, leading to the cost functions …Professor Wolfram MBA201a - Fall 2009 Page 11T-shirt factory cost functionsCost ($)ATC103120 30 40 501.52MC48T-shirtsProfessor Wolfram MBA201a - Fall 2009 Page 12Marginal and average cost curves: generic shapeCost ($)ATCq1MCq2p1p2Marginal cost always crosses average cost at its minimum.Professor Wolfram MBA201a - Fall 2009 Page 13More average cost and marginal cost in ExcelC(Q) = 10 + .2Q2; ATC = 10/Q +.2Q; AVC= .2Q; MC = .4QProfessor Wolfram MBA201a - Fall 2009 Page 14Economies of scaleEconomies of scale describe how the firm’s average costs change as output increases.–ATC  with quantity = “diseconomies of scale”–ATC  with quantity = “economies of scale”Note: a cost function can exhibit economies of scale at some output levels and diseconomies of scale at other output levels.Professor Wolfram MBA201a - Fall 2009 Page 15T-shirt factory profitsCost ($)ATC103120 30 40 501.52MC48T-shirts1.8ProfitsProfessor Wolfram MBA201a - Fall 2009 Page 16What if Fruit-of-the-LoomTM offers a lower price?Scenario B: Fruit-of-the-Loom™ offers p = $1.3 per t-shirt.No matter how much factory produces, price is below per-unit cost; i.e., no matter how much factory produces, it will lose money: p < AC implies q x p < q x ACimplies Revenue < CostOptimal decision is not to produce at all.Professor Wolfram MBA201a - Fall 2009 Page 17General lessons on output decisionsThere is a general lesson from the factory example.What to produce: Firms should produce every unit for which the income on that unit (in this case the price) is greater than the cost.What not to produce: Firms should not produce any unit for which the income on that unit is less than the cost.Note that AC(q) is not playing a role in determining how much to produce, only whether to produce at all.Marginal cost: how much to produceAverage Cost: whether to produceProfessor Wolfram MBA201a - Fall 2009 Page 18Output decisions in the generic caseCost ($)ATCq1MCp1p2Professor Wolfram MBA201a - Fall 2009 Page 19Output decisions in the generic caseCost ($)q1MCq2p2 = lost profitsProfessor Wolfram MBA201a - Fall 2009 Page 20Supply curveSupply curve: how much a firm produces at each price. Generalizing from previous example: Firm can sell all it wants at given price (we say market is “perfectly competitive”). If price is below minimum average cost, p0, then firm is better off by shutting down.If price is greater than P0, say P’, then firm should sell output q’ such that MC=P’.Supply curve is given by MC curve for values of P greater than the minimum of AC, zero for