Cost Economics - Cost Economics AAE 320 Paul D Mitchell...

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Unformatted text preview: Cost Economics AAE 320 Paul D. Mitchell Goal of Section Overview what economists mean by Cost (Economic) Cost Functions Derivation of Cost Functions Concept of Duality What it all means Economic Cost Economic Cost: Value of what is given up whenever an exchange or transformation of resources takes place For an exchange of resources (a purchase) not only is money given up, but also the opportunity to do some thing else with that money For a transformation of resources (including time), the opportunity to do other things with those resources is given up Economic Cost vs Accounting Cost Economics includes these implicit costs in the analysis that standard accounting methods do not include Accountants ask: What did you pay for it? Explicit Cost Economists also ask: What else could you do with the money? Explicit Cost, plus Implicit Cost (Opportunity Cost) Economic Cost vs Accounting Cost Economic cost accounting cost Accounting 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 Economic Cost vs Accounting Cost Accounting Profit = Revenue Explicit Cost Economic Profit = Revenue Explicit Cost Implicit Cost Economic analysis includes implicit costs that accounting does not include Zero economic profit does not mean you are making no money, but that you are making as much money as you should Accounting Cost of Attending UW Tuition and Fees Books and Supplies Room and Board Miscellaneous Transportation Estimated Total $6,220 $860 $6,500 $1,920 $430 $15,930 = $16,000 ($7.50/hr x 40 hrs x 13 wks) Summer Work = $3,900 Source: http://www.admissions.wisc.edu/costs.php for 2006 Opportunity Cost 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 resources and money Think of the Counterfactual Opportunity Cost of attending UW What would I be doing if not going to UW? Economic Cost of Attending UW What are your opportunity costs of attending UW? Opportunity cost of your time Opportunity cost of your capital Opportunity Cost of Time What's your next best alternative? Assume you'd have a job making $10/hr x 40 hrs x 50 weeks = $20,000/year Note: you earn $3,900 each summer as a UW student Opportunity Cost of Your Time while attending UW is $20,000/year $3,900 in lost wages, for a net opportunity cost of $16,100 Opportunity Cost of Your Capital How much money do you give up to attend UW each year? Accounting cost = $16,000/year, including $6,500 for Room and Board You must live somewhere and eat, so assume Room and Board = $6,500 for your next best alternative too Final cost = $16,000 - $6,500 = $9,500 What else could you do with the money? Assume invest money at going interest rate, say 10% Opportunity Cost of Your Capital: $9,500/year that could earn 10% interest = $950/year UW costs you $950/year in lost use of your money Economic Cost to Attend UW $9,500 in Tuition, Books, etc. $16,100 in lost wages If you did not attend UW, you'd earn $16,100 at your job (opportunity cost of your time) If you did not attend UW, you'd have $9,500 that you could have put in a bond and earned $950 (opportunity cost of your money) $950 in lost return on your money Room and Board is not a cost, since you'd pay it whether or not you attended UW Economic Profit Economics includes benefits accounting methods do not Besides increased income due to attending UW Value of UW Education better education than a directional school, connection into alumni networks, friends made while here, UW's international prestige and reputation giving better jobs, the UW experience, Bucky Badger, greater satisfaction in life, etc. Your Net Profit = ??? Economic Costs and Benefits harder to quantify A Simple Example A store owner/operator earns $50,000 Opportunity Costs: She could earn $35,000 managing for a national chain and rent her store for $25,000 Opportunity Costs = $35,000 + $25,000 = $60,000 Economic Profit = $50,000 $60,000 + benefit Including opportunity costs show that she is losing $10,000 per year, but we have not included the value of all the intangibles (being her own boss, etc.) Value of intangibles = How much would she need to quit She must value owning and operating her own store vs working for a national chain by at least $10,000 per year What if the national chain job included health insurance and the peace of mind it offers? Think Break #8 You operate a farm with market value of $1 million in land, buildings, machinery, etc. Your debt is $800,000 with an annual interest payment of $80,000 this year. Annual revenue averages $1.5 million with operating costs of $1.35 million. If you sold the farm, you expect to earn a 10% return if you invested the money. You think you could work for the coop in town making $40,000. What are the accounting profits you obtain for owning and operating the farm? What are the economic profits you obtain from owning and operating the farm? Main point of this section Cost in economics is more comprehensive than accounting cost First exposure to concept of opportunity cost We will come back to opportunity costs when we do budgeting Cost Definitions Cost 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 Cost Functions Cost depends on inputs used and their prices, but how much of each input to use? Output price = marginal cost (P = MC) identifies how much output Q to produce Production function and prices identify input combinations to use to produce Q Mathematical wonders of duality needed to fully explain how it works Main Point If 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 seed: VMPx = rx and MPx/MPy = rx/ry Duality implies that a cost function with standard properties implies a production function with standard properties Fixed Cost (FC) Costs that do not vary with the level of output Q during the planning period Cost of resources committed through previous planning Property Taxes, Insurance, Depreciation, Interest Payments, Scheduled Maintenance In the long run, all costs are variable because you can change assets Variable Cost (VC) Costs that change with the level of output Q produced Manager controls these costs Fertilizer, Seed, Herbicides, Feed, Grain, Fuel, Veterinary Services, Hired Labor Vary the relative amounts used as increase output Cost Definitions Total Cost TC = fixed cost + variable cost Average Fixed Cost AFC = FC/Q Average Variable Cost AVC = VC/Q Average Total Cost ATC = TC/Q Marginal Cost MC = cost of producing the last unit of output = slope of the TC = slope of the VC = dTC/dQ = dVC/dQ Cost Function Graphics TC VC Cost FC Output Average Costs = slope of line through the origin to the point on the function Cost TC Output TC VC Cost ATC AVC Minimum AVC Minimum ATC Output Cost Function Graphics TC VC Cost FC 0 0 MC ATC AVC 0 0 Output Cost Function Graphics MC Cost ATC AVC 0 0 Output Livestock Example Suppose you have pasture and will stock steers over the summer to sell in the fall As 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. Steers 0 10 20 30 40 50 60 70 80 90 100 Beef 0 72 148 225 295 360 420 475 525 570 610 MP Beef (cwt) Production Function 700 600 500 400 300 200 100 0 0 20 40 60 80 100 7.2 7.6 7.7 7.0 6.5 6.0 5.5 5.0 4.5 4.0 Marginal Product (cwt) 90 80 70 60 50 40 30 20 10 0 0 20 40 60 80 100 Steers Think Break #9 (Review) Steers Beef MP VMP 0 10 0 72 7.2 648 20 30 148 7.6 225 7.7 684 693 How many steers should you stock if the expected selling price is $90/cwt and steers cost $495 each? 40 50 60 295 7.0 360 6.5 420 6.0 630 Hint: What's the single input optimality condition? 70 80 475 5.5 525 5.0 450 90 100 570 4.5 610 4.0 405 360 Steers Beef F Cost V Cost Total C 0 10 20 30 40 50 60 70 80 90 100 0 72 148 225 295 360 420 475 525 570 610 5,000 5,000 5,000 0 4,950 5,000 AVC ATC MC 68.75 65.13 64.29 70.71 76.15 82.50 90.00 99.00 9,950 68.75 138.19 88.22 84.07 82.64 82.62 83.47 84.95 9,900 14,900 66.89 100.68 5,000 14,850 19,850 66.00 5,000 19,800 24,800 67.12 5,000 24,750 29,750 68.75 5,000 29,700 34,700 70.71 5,000 34,650 39,650 72.95 5,000 39,600 44,600 75.43 5,000 44,550 49,550 78.16 5,000 49,500 54,500 81.15 86.93 110.00 89.34 123.75 Why aren't these FC, VC and TC curves? 60,000 50,000 Costs $ 40,000 30,000 20,000 10,000 0 0 20 40 Steers 60 80 100 Because MP decreases, TC and VC increase more and more rapidly as output increases (that's duality) 60,000 50,000 TC Costs $ 40,000 30,000 20,000 10,000 0 0 100 200 300 400 500 VC FC 600 Beef Produced (cwt) 140 120 100 ATC MC Costs $ 80 60 40 20 0 0 100 200 300 400 500 AVC 600 Beef Produced (cwt) Profit Maximization and Cost Functions Choose output to maximize profit Max = pQ C(Q) FOC: d /dQ = p MC(Q) = 0 Choose output Q so that price equals marginal cost will maximize profit SOC: d2 /dQ2 = MC'(Q) < 0, or C''(Q) > 0 Need a convex cost function (diminishing marginal product) Steers 0 10 Beef MP VMP F Cost V Cost Total C 0 72 7.2 648 5,000 5,000 0 4,950 5,000 AVC ATC MC 9,950 68.75 138.19 68.75 20 30 40 50 60 70 80 90 100 148 7.6 225 7.7 295 7.0 360 6.5 420 6.0 475 5.5 525 5.0 570 4.5 610 4.0 684 693 630 585 540 495 450 405 360 5,000 9,900 14,900 66.89 100.68 88.22 84.07 82.64 82.62 83.47 84.95 65.13 64.29 70.71 76.15 82.50 90.00 99.00 5,000 14,850 19,850 66.00 5,000 19,800 24,800 67.12 5,000 24,750 29,750 68.75 5,000 29,700 34,700 70.71 5,000 34,650 39,650 72.95 5,000 39,600 44,600 75.43 5,000 44,550 49,550 78.16 5,000 49,500 54,500 81.15 86.93 110.00 89.34 123.75 P = MC and VMP = r Cost Function based optimality condition P = MC identifies Q = 475 cwt as the profit maximizing output Production Function based optimality condition VMP = r identifies Steers = 70 as the profit maximizing input use Optimality conditions are consistent with each other because of duality 90 Marginal Product (Beef cwt) 80 70 60 50 40 30 20 10 0 0 20 40 60 80 100 Input (Steers) 30 steers = 225 beef marginal cost increases since marginal product decreases 140 120 Marginal Cost 100 80 60 40 20 0 0 100 200 300 400 500 600 700 Output (Beef cwt) Think Break #10 You work for UWEX and have data on several farms in your seven county district You look at all farms with similar sized milking parlors and a similar number of workers You calculate the average production per cow as the number of cows varies among the farms Use these data in the table to recommend the optimal milk output and herd size Think Break #10 Cows 0 Milk cwt FC VC 0 TC 10000 MC 0 (VC = $3350/cow) 0 10000 20 40 60 80 4800 10000 67000 77000 13.96 1) Fill in the missing MC's 2) If the milk price is $14/cwt, what is the optimal milk output and farm size? 9640 10000 134000 144000 13.84 14490 10000 201000 211000 19320 10000 268000 278000 100 120 140 160 24100 10000 335000 345000 28824 10000 402000 412000 14.18 33488 10000 469000 479000 14.37 38096 10000 536000 546000 14.54 180 200 42624 10000 603000 613000 14.80 47060 10000 670000 680000 15.10 MC = Output Supply Curve Maximize = PQ C(Q) gives P = MC(Q) P = MC(Q) defines the supply curve--for any price P, how much output Q to supply Profit changes along the MC curve, but for the given price, the maximum is on the MC curve Think of MC curve as a line defining the peak of a long ridge, with the elevation of the peak (profit) changing along the line ATC defines Zero Profit With free entry and exit and competition, long run economic profit is zero--everyone earning a fair return for their time/assets Set profit to zero and rearrange PQ C(Q) = 0 becomes PQ = C(Q), then P = C(Q)/Q = ATC P = ATC defines zero profit Think of ATC curve as line defining sea level, below ATC means < 0 MC = ATC at min ATC ATC = C(Q)/Q, use quotient rule to get first derivative, then set = 0 and solve d(C(Q)/Q)/dQ = (MC x Q C(Q))/Q2 = 0 Rearrange to get MC x Q = C(Q), and then MC = C(Q)/Q = ATC FOC implies MC = ATC at min ATC Intersection between MC and ATC occurs when ATC is at a minimum Min ATC: where profit max ridge hits the sea MC = AVC at min AVC Repeat process with AVC d(VC(Q)/Q)/dQ = (MC x Q VC(Q))/Q2 = 0 Rearrange to get MC x Q = VC(Q), and then MC = VC(Q)/Q = AVC FOC implies MC = AVC at min AVC Intersection between MC and AVC occurs when AVC is at a minimum Profit and min AVC Profit at min AVC: = PQ VC(Q) FC P = MC = AVC at min AVC, so rewrite as = MC x Q VC(Q) FC VC(Q) = (VC(Q)/Q) x Q = AVC(Q) x Q, so rewrite as = MC x Q AVC(Q) x Q FC, or = Q(MC AVC(Q)) FC MC = AVC at min AVC, so MC AVC = 0, so that = FC Produce at P min AVC because, though lose money, still pay part of FC Cost Functions and Supply Green: P min ATC and 0 Yellow: min AVC P min ATC and FC 0 MC ATC AVC 0 0 Cost Function and Supply Green is complete supply schedule Cost or Price MC ATC AVC 0 0 Output Think Break #11 Cows Milk VC TC MC ATC AVC 0 20 0 4800 0 67000 10000 77000 13.96 16.04 13.96 40 9640 134000 144000 13.84 14.94 13.90 These are the Think Break #10 data (FC = $10,000) 1) Fill in the missing costs 2) What do you recommend for farms this size if the milk price is $13/cwt? 60 14490 201000 211000 13.81 14.56 80 19320 268000 278000 13.87 100 24100 335000 345000 14.02 120 28824 402000 412000 14.18 13.95 140 33488 469000 479000 14.37 14.30 14.01 160 38096 536000 546000 14.54 14.33 14.07 180 42624 603000 613000 14.80 14.38 14.15 200 47060 670000 680000 15.10 14.45 14.24 What if P < min AVC? Remember economic profit includes opportunity costs, so negative economic profit means better opportunities elsewhere Your money/assets and time would get better returns in other activities Choices when p < min AVC for long term 1) Quit and convert resources 2) Find new technology with lower average production costs Other Cost Terms Used Fixed Cost synonyms: Overhead, Ownership Costs Variable Costs synonyms : Operating Costs, Outof-Pocket Costs Direct vs Indirect: direct costs are linked to a specific enterprise (dairy), indirect are not (pickup truck, tractors). Both can be fixed and variable Cash 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 Summary Major Concepts Opportunity Cost Cost Functions Definitions Graphics Optimality conditions Graphics Output supply Profit Maximization and Cost Functions ...
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This note was uploaded on 08/08/2008 for the course AAE 320 taught by Professor Mitchell during the Spring '08 term at University of Wisconsin.

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