Cost Economics AAE 320 Paul D. Mitchell - PowerPoint Presentation

1. Cost EconomicsAAE 320Paul D. Mitchell

2. Goal of SectionOverview what economists mean by Cost(Economic) Cost FunctionsDerivation of Cost FunctionsConcept of DualityWhat it all means

3. Economic CostEconomic Cost: Value of what is given up whenever an exchange or transformation of resources takes placeFor an exchange of resources (a purchase) not only is money given up, but also the opportunity to do some thing else with that moneyFor a transformation of resources (including time), the opportunity to do other things with those resources is given up

4. Economic Cost vs Accounting CostEconomics includes these implicit costs in the analysis that standard accounting methods do not includeAccountants ask: What did you pay for it? Explicit CostEconomists also ask: What else could you do with the money? Explicit Cost, plus Implicit Cost (Opportunity Cost)

5. Economic Cost vs Accounting CostEconomic cost ≠ accounting costAccounting Cost: Used for financial reporting (balancing the books, paying taxes, etc.)Typically uses reported prices, wages and interest rates (explicit costs)Economic Costs: Used for decision making (resource allocation, developing strategy)Includes opportunity costs (implicit costs) in the analysis and calculates depreciation differently

6. Economic Cost vs Accounting CostAccounting Profit = Revenue – Explicit CostEconomic Profit = Revenue – Explicit Cost – Implicit Cost + Implicit BenefitsEconomic analysis includes implicit costs and implicit benefits that accounting does not includeZero economic profit does not mean you are not making money, but that you are making as much money as you should, a “normal” rate of return

7. Opportunity CostImplicit Costs = “Opportunity Costs”Value of the best opportunity given up because resources are used for the given transaction or transformation“Value of the next best alternative”Value of what you could do with your time & moneyOpportunity Cost of Farming: Think of the Counter-factual: What would you be doing if not farming?Opportunity cost of your timeOpportunity cost of your assets and capital

8. Opportunity CostWhat’s your next best alternative?Opportunity Cost of TimeUsually assume a different job and estimate the implied lost wagesOpportunity Cost of CapitalUsually assume a low risk investment alternative like bonds or CD and estimate the implied lost returns on capitalOpportunity Cost of Asset (land)Usually assume rental rate

9. Opportunity Cost of TimeAssume you make $50,000 as a farmerYour next best job pays $45,000 = Opportunity Cost of your Time as a farmerTypical way of thinking: Accounting profit = $50,000Economic way of thinking: look at difference in payTreat $45,000 as an “opportunity cost” and subtract it from your current salaryEconomic profit = $50,000 – $45,000 = $5,000You are making $5,000 more with current job than in your next best opportunity

10. Opportunity Cost of CapitalYou have equity in your farm, your money invested in the farmIf you invest the money in a company (owned stock), bought bonds, or a CD, they would pay you a dividend We will use returns on these investments as a way to estimate the opportunity cost of capital: you give up X% rate of return What rate of return are you making by keeping your money in the farm? Covered later in semesterTypical way of thinking: you have $100,000 equity in a farm, earning 5% return = $5,000 annuallyEconomic way of thinking: treat the potential investment income as an opportunity cost of capital: you could have earned 3% in the bond market, so opportunity cost is $3,000Economic profit = $5,000 – $3,000 = $2,000

11. Opportunity Cost of Working AssetsYou have land and other “working assets” on a farm as well, not just capital invested as equityInstead of using them to farm, you could rent them out to someone else at market rates, but still own themAlternative opportunity to consider instead of the conversion to “cash” in a hypothetical saleThis is the opportunity cost for you to use these assets to farmLand, buildings, tractors, machinery, milk cows, breeding livestock (bulls, cows, …)You earn $300/acre growing crops, land rents for $200 in areaAccounting profit is $300/A, economic profit is $100/A

12. Economic Profit vs Accounting ProfitAccounting profit is the “normal” way of thinking: I make $50,000 as a farmer, I earn a 5% rate of return on my farm equity, I make $300/A growing cropsEconomic profit: How do these compare to what else you could make with these? Alternatives: $45,000 salary, $100,000 at 3% = $3,000 investment, and $200/A land rentYou are making a positive economic profit: very good$5000 more in salary, 2% more than market rates, $100/acre more in return to landIf economic profit is zero, you are making as much as you can—no better opportunities exist for you

13. Economic BenefitsEconomic profit includes benefits accounting methods do notAccounting Profit = Revenue – Explicit CostEconomic Profit = Revenue – Explicit Cost – Implicit Cost + Implicit BenefitsWhat benefits do you get from an activity besides money? Economics develops ways to estimate these types of benefits or values based on available dataIf you accept a below market salary/rate of return for a job, you must be getting other economic benefits

14. Main point of this section“Cost” in economics is more comprehensive than accounting costExposure to concept of opportunity costStart New Section: Cost Functions

15. Cost DefinitionsCost Function: schedule or equation that gives the minimum cost to produce the given output Q, e.g., C(Q)Cost functions are not the sum of prices times inputs used: C = rxX + ryY C = rxX + ryY is cost as a function of the inputs X and Y, not cost as a function of output Q

16. Cost FunctionsOutput Price = Marginal Cost (P = MC) identifies how much output Q to produceProfit, production function and prices identify inputs to use VMP = r, this gives output QCost depends on inputs used and their prices, but how much of each input to use?Mathematical wonders of duality needed to fully explain how it works

17. Main PointIf you choose Q so that price = marginal cost, the inputs needed to produce this level of output at minimum cost will satisfy the optimality conditions we have already seen: VMPx = rx and MPx/MPy = rx/ryDuality implies that a cost function with standard properties implies a production function with standard properties

18. Fixed Cost (FC)Costs that do not vary with the level of output Q during the planning periodCost of resources committed through previous planningProperty Taxes, Insurance, Depreciation, Interest Payments, Scheduled MaintenanceIn the long run, all costs are variable because you can change assets

19. Variable Cost (VC)Costs that change with the level of output Q that is producedManager controls these costsFertilizer, Seed, Herbicides, Feed, Grain, Fuel, Veterinary Services, Hired LaborVary the relative amounts used as increase output produced

20. Cost DefinitionsTotal Cost TC = fixed cost + variable costAverage Fixed Cost AFC = FC/QAverage Variable Cost AVC = VC/QAverage Total Cost ATC = TC/QMarginal Cost MC = cost of producing the last unit of output = slope of the TC = slope of the VC = dTC/dQ = dVC/dQ

21. Output QCostTCFCVCCost Function Graphics

22. Output QCostAverage Costs = slope of line through the origin to the point on the function TC

23. Output QCostVCAVCMinimum AVCTCATCMinimum ATC

24. Output QCostTCVCFCMCATCAVCCost Function Graphics

25. Output QCostMCATCAVCCost Function Graphics

26. Livestock ExampleSuppose you have pasture and will stock steers over the summer to sell in the fallAs add more steers, eventually the rate of gain decreases as forage per animal falls (diminishing marginal product)Fixed cost = $5,000 in land opportunity costs, depreciation on fences and watering facilities, insurance, property taxes, etc.Variable cost = $495/steer: buying, transporting, vet costs, feed supplements, etc.

27. Steers XBeef QMP 0 0 10 727.2 201487.6 302257.7 402957.0 503606.5 604206.0 704755.5 805255.0 905704.51006104.0SteersBeef (cwt)Marginal Product (cwt)Production Function

28. Think Break #9 (Review)SteersXBeefQMPVMP 0 0 10 727.2648 201487.6684 302257.7693 402957.0630 503606.5 604206.0 704755.5 805255.0450 905704.54051006104.0360How many steers should you stock if the expected selling price is $90/cwt and steers cost $495 each? Hint: What’s the single input optimality condition?

29. Steers XBeef Q F CostV CostTotal CAVCATCMC005,00005,00010725,0004,9509,95068.75138.1968.75201485,0009,90014,90066.89100.6865.13302255,00014,85019,85066.0088.2264.29402955,00019,80024,80067.1284.0770.71503605,00024,75029,75068.7582.6476.15604205,00029,70034,70070.7182.6282.50704755,00034,65039,65072.9583.4790.00805255,00039,60044,60075.4384.9599.00905705,00044,55049,55078.1686.93110.001006105,00049,50054,50081.1589.34123.75

30. Steers XCosts $Why aren’t these FC, VC and TC curves?

31. Beef Produced (cwt) QCosts $TCVCFCBecause MP decreases, TC and VC increase more and more rapidly as output increases (that’s duality)

32. Beef Produced (cwt) QCosts $MCATCAVC

33. Profit Maximization and Cost FunctionsChoose output Q to maximize profitMax p = pQ – C(Q)FOC: dp/dQ = p – MC(Q) = 0Choose output Q so that price equals marginal cost will maximize profitSOC: d2p/dQ2 = – MC’(Q) < 0, or C’’(Q) > 0Need a convex cost function (diminishing marginal product)

34. Steers XBeef Q MPVMPF CostV CostTotal CAVCATCMC005,00005,00010727.26485,0004,9509,95068.75138.1968.75201487.66845,0009,90014,90066.89100.6865.13302257.76935,00014,85019,85066.0088.2264.29402957.06305,00019,80024,80067.1284.0770.71503606.55855,00024,75029,75068.7582.6476.15604206.05405,00029,70034,70070.7182.6282.50704755.54955,00034,65039,65072.9583.4790.00805255.04505,00039,60044,60075.4384.9599.00905704.54055,00044,55049,55078.1686.93110.001006104.03605,00049,50054,50081.1589.34123.75

35. P = MC and VMP = rCost Function based optimality condition P = MC identifies Q = 475 cwt as the profit maximizing outputTo produce Q = 475 cwt requires 70 steersProduction Function based optimality condition VMP = r identifies Steers = 70 as the profit maximizing input useBuying 70 steers produces Q = 475 cwtOptimality conditions are consistent with each other because of duality

36. marginal cost increases because marginal product decreases

37. Think Break #10You work for UWEX and have data on several farms in your seven county districtYou look at all farms with similar sized milking parlors and a similar number of workersYou calculate the average production per cow as the number of cows varies among the farmsUse these data in the table to recommend the optimal milk output and herd size

38. Think Break #10Cows XMilk Q cwt FCVCTCMC0010000010000020480010000670007700013.964096401000013400014400013.846014490100002010002110008019320100002680002780001002410010000335000345000120288241000040200041200014.18140334881000046900047900014.37160380961000053600054600014.54180426241000060300061300014.80200470601000067000068000015.10(VC = $3350/cow)Fill in the missing MC’sIf the milk price is $14/cwt, what is the optimal milk output and farm size?

39. MC = Output Supply CurveMaximize p = PQ – TC(Q) gives P = MC(Q)P = MC(Q) defines the supply curve — for any price P, how much output Q to supplyProfit changes along the MC curve, but for the given price, the maximum is on the MC curveThink of MC curve as a line defining the peak of a long ridge, with the elevation of the peak (profit) changing along the line

40. ATC defines Zero ProfitWith free entry and exit and competition, long run economic profit is zero—everyone earns a fair return for their time & assetsSet profit to zero and rearrange PQ – TC(Q) = 0 becomes PQ = TC(Q), then P = TC(Q)/Q = ATCP = ATC defines zero profitThink of ATC curve as line defining sea level, below ATC means p < 0

41. MC = ATC at min ATCATC = TC(Q)/Q, use quotient rule to get first derivative, then set = 0 and solved(TC(Q)/Q)/dQ = (MC x Q – TC(Q))/Q2 = 0Rearrange to get MC x Q = TC(Q), and then MC = TC(Q)/Q = ATCFOC implies MC = ATC at min ATCIntersection between MC and ATC occurs when ATC is at a minimumMin ATC: where profit max ridge hits the sea

42. MC = AVC at min AVCRepeat process with AVCd(VC(Q)/Q)/dQ = (MC x Q – VC(Q))/Q2 = 0Rearrange to get MC x Q = VC(Q), and then MC = VC(Q)/Q = AVCFOC implies MC = AVC at min AVCIntersection between MC and AVC occurs when AVC is at a minimum

43. Profit and min AVCProfit at min AVC: p = PQ – VC(Q) – FCP = MC = AVC at min AVC, so rewrite as p = MC x Q – VC(Q) – FCVC(Q) = (VC(Q)/Q) x Q = AVC(Q) x Q, so rewrite as p = MC x Q – AVC(Q) x Q – FC, or p = Q(MC – AVC(Q)) – FCMC = AVC at min AVC, so MC – AVC = 0, so that p = – FCProduce at P ≥ min AVC because, though lose money, still pay part of FC

44. Cost Functions and SupplyMCATCAVCGreen: P ≥ min ATC and p ≥ 0Yellow: min AVC ≤ P ≤ min ATC and – FC ≤ p ≤ 0Output QCost or Price

45. Cost Function and SupplyOutput QCost or PriceMCGreen is complete supply scheduleAVCATC

46. Think Break #11CowsMilkVCTCMCATCAVC00010000204800670007700013.9616.0413.9640964013400014400013.8414.9413.90601449020100021100013.8114.56801932026800027800013.871002410033500034500014.021202882440200041200014.1813.951403348846900047900014.3714.3014.011603809653600054600014.5414.3314.071804262460300061300014.8014.3814.152004706067000068000015.1014.4514.24These are the Think Break #10 data (FC = $10,000)Fill in the missing costsWhat do you recommend for farms this size if the milk price is $13/cwt?

47. What if P < min AVC?Remember economic profit includes opportunity costs, so negative economic profit means better opportunities elsewhereYour money/assets and time would get better returns in other activitiesChoices when p < min AVC for long term1) Quit and convert resources 2) Find new way to produce with lower average production costs (new technology)

48. Other Cost Terms UsedFixed Cost synonyms: Overhead, Ownership Costs Variable Costs synonyms : Operating Costs, Out-of-Pocket CostsDirect vs Indirect: direct costs are linked to a specific enterprise (dairy), indirect are not (pickup truck, tractors). Both can be fixed and variableCash vs Non-Cash: Cash costs paid from farm income, while non-cash costs include depreciation, returns to equity, labor, management (opportunity costs). Both can be fixed and variable

49. SummaryOpportunity CostCost FunctionsDefinitionsGraphicsProfit Maximization and Cost FunctionsOptimality conditionsGraphicsOutput supply