Cost Economics

1. Cost Economics AAE 320 Paul D. Mitchell

2. Goal of Section • Overview what economists mean by Cost • (Economic) Cost Functions • Derivation of Cost Functions • Concept of Duality • What it all means

3. 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

4. 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)

5. 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

6. Economic Cost vs Accounting Cost • Accounting Profit = Revenue – Explicit Cost • Economic Profit = Revenue – Explicit Cost – Implicit Cost + Benefits • Economic analysis includes implicit costs and benefits that accounting does not include • Zero economic profit does not mean you are not making money, but that you are making as much money as you should

7. Opportunity Cost • Implicit 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 resources and money • Think of the Counterfactual • Opportunity Cost of attending UW • What would I be doing if not going to UW?

8. Accounting Cost of Attending UW • Tuition and Fees $10,609 • Books and Supplies $1,200 • Room and Board $8,354 • Travel $800 • Miscellaneous $3,241 • Estimated Total $24,204 = $24,000 • Summer Work = $5,000 (~ $10/hr x 40 hrs x 13 wks) Source: http://www.admissions.wisc.edu/costs.php for 2012-2013

9. Economic Cost of Attending UW • What are your opportunity costs of attending UW? • Opportunity cost of your time • Opportunity cost of your capital

10. Opportunity Cost of Time • What’s your next best alternative? • Assume you’d have a job making $12/hr x 40 hrs x 50 weeks = $24,000/year • Note: you earn $5,000 each summer as a UW student • Opportunity Cost of Your Time while attending UW is $24,000/year – $5,000 in lost wages, for a net opportunity cost of $19,000

11. Opportunity Cost of Your Capital • How much money do you give up to attend UW each year? • Accounting cost = $24,000/year, including $8,000 for Room and Board • You must live somewhere and eat, so assume Room and Board = $8,000 for your next best alternative also • Final cost = $24,000 – $8,000 = $16,000 • What else could you do with the money? • Assume invest money at going interest rate, say 2% • Opportunity Cost of Your Capital: $16,000/year that could earn 2% interest = $320/year • UW costs you $320/year in lost use of your money

12. Economic Cost to Attend UW • $16,000 in Tuition, Books, etc. • $19,000 in lost wages • If you did not attend UW, you’d earn $19,000 at your job (opportunity cost of your time) • $320 in lost return on your money • If you did not attend UW, you’d have $16,000 that you could have put in a bond and earned $320 (opportunity cost of your money) • Room and Board is not a cost, since you’d pay it whether or not you attended UW

13. Economic Benefits • Economic profit 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

14. Economic Profit • Tuition, Books, (Direct Cost) – $16,000 • Lost Wages (Opportunity Cost) – $19,000 • Lost Interest (Opportunity Cost) – $320 • Current Value of Future Income ???? • Value of the UW Experience ???? • Your Net Profit ????

15. Opportunity Cost • Assume you make $50,000 and your next best job pays $45,000 • Typical way of thinking: Make more money with $50,000 job than with $45,000 job, so keep the higher paying job • Economic way of thinking: looks at the difference in pay • Treat $45,000 as an “opportunity cost” and subtract it from you current salary, leaving you $5,000 • Your economic profit = $5,000: You are making $5,000 more with current job than you could in your next best opportunity • If your economic profit is zero, you are making as much money as you can—no better opportunities out there

16. 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?

17. Opportunity Cost of Farm Capital • You have equity in your farm—you own part of it—it is your money invested in the farm • If you gave the money to John Deere, Alliant Energy, Monsanto, you would own stock in the company and they would pay you a dividend • You could buy bonds or precious metals, etc. or put it in the bank in a CD or similar. • These are ways to estimate the opportunity cost of your money—you could make XX% rate of return • What are you making by keeping it in the farm? • We do this later: how to calculate rates of return on equity, assets and such

18. Think Break #8 • You operate a farm with market value of $600,000 in land, buildings, machinery, etc. Your debt is $300,000 with an annual interest payment of $15,000 this year. Annual revenue averages $400,000 with operating costs of $320,000. If you sold the farm, you expect to earn a 5% return if you invested the money. You think you could work for the farm co-op 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?

19. Main point of this section • “Cost” in economics is more comprehensive than accounting cost • Exposure to concept of opportunity cost • We will come back to opportunity costs when we do budgeting • Start New Section: Cost Functions

20. 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

21. 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

22. 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 seen: VMPx = rx and MPx/MPy = rx/ry • Duality implies that a cost function with standard properties implies a production function with standard properties

23. 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

24. 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

25. 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

26. Cost Function Graphics TC VC Cost FC Output

27. TC Average Costs = slope of line through the origin to the point on the function Cost Output

28. TC VC Cost ATC AVC Minimum ATC Minimum AVC Output

29. Cost Function Graphics TC VC Cost FC MC ATC AVC Output

30. Cost Function Graphics MC Cost ATC AVC Output

31. 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.

32. Production Function Beef (cwt) Marginal Product (cwt) Steers

33. Think Break #9 (Review) How 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?

35. Why aren’t these FC, VC and TC curves? Costs $ Steers

36. Because MP decreases, TC and VC increase more and more rapidly as output increases (that’s duality) TC VC Costs $ FC Beef Produced (cwt)

37. ATC MC Costs $ AVC Beef Produced (cwt)

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

40. 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

41. 30 steers = 225 beef marginal cost increases since marginal product decreases

42. 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

43. Think Break #10 (VC = $3350/cow) • Fill in the missing MC’s • If the milk price is $14/cwt, what is the optimal milk output and farm size?

44. MC = Output Supply Curve • Maximize p = PQ – TC(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

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

46. MC = ATC at min ATC • ATC = TC(Q)/Q, use quotient rule to get first derivative, then set = 0 and solve • d(TC(Q)/Q)/dQ = (MC x Q – TC(Q))/Q2 = 0 • Rearrange to get MC x Q = TC(Q), and then MC = TC(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

47. 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

48. Profit and min AVC • Profit at min AVC: p = PQ – VC(Q) – FC • P = MC = AVC at min AVC, so rewrite as p = MC x Q – VC(Q) – FC • VC(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)) – FC • MC = AVC at min AVC, so MC – AVC = 0, so that p = – FC • Produce at P ≥ min AVC because, though lose money, still pay part of FC

49. Cost Functions and Supply Green: P ≥ min ATC and p ≥ 0 Yellow: min AVC ≤ P ≤ min ATC and – FC ≤ p ≤ 0 MC ATC AVC

50. Cost Function and Supply Green is complete supply schedule MC Cost or Price ATC AVC Output