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Economic Analysis for Business Session XI: The Costs of Production

Economic Analysis for Business Session XI: The Costs of Production. Instructor Sandeep Basnyat 9841892281 Sandeep_basnyat@yahoo.com. Objectives of the firms. Varieties of objectives: Profit maximization Sales Revenue maximization Utility maximization Corporate growth maximization Etc….

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Economic Analysis for Business Session XI: The Costs of Production

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  1. Economic Analysis for BusinessSession XI: The Costs of Production InstructorSandeep Basnyat 9841892281 Sandeep_basnyat@yahoo.com

  2. Objectives of the firms Varieties of objectives: • Profit maximization • Sales Revenue maximization • Utility maximization • Corporate growth maximization • Etc…

  3. the amount a firm receives from the sale of its output the market value of the inputs a firm uses in production Most Important economic Objective- Profit Maximization • The economic goal of the firm is to maximize profits. Profit = Total revenue – Total cost

  4. Sequence of Presentation • Understanding Costs, Production functions and their relationship • Derive various cost curves • A concept of Revenue • How firms behave if they are in different market structures?

  5. 0 Costs: Explicit vs. Implicit • Explicit costs – require an outlay of money,e.g. paying wages to workers Accounting profit = total revenue minus total explicit costs • Implicit costs (Opportunity Costs) – do not require a cash outlaye.g. the cost of the owner’s time • Economic profit • = total revenue minus total costs (including explicit and implicit costs)

  6. 0 The Production Function • A production function shows the relationship between the quantity of inputs used to produce a good, and the quantity of output of that good. • It can be represented by a table, equation, or graph.

  7. L(no. of workers) Q(bushels of wheat) 3,000 2,500 0 0 2,000 1 1000 1,500 Quantity of output 2 1800 1,000 3 2400 500 4 2800 0 0 1 2 3 4 5 5 3000 No. of workers 0 Simple Example: Production Function

  8. Properties of Production Functions: Returns to Scale • Increasing Returns to Scale When inputs are increased by m, output increases by more than m. Eg: A 10% increase in labour/capital increases the output by more than 10% • Constant Returns to Scale When inputs are increased by m, output increases by exactly m. • Decreasing Returns to Scale When inputs are increased by m, output increases by less than m. Note: Assuming that the value of multiplier >1 (positive)

  9. Properties of Production Functions: Returns to Scale Find if the followings production functions have increasing, constant or decreasing returns to scale. (i) Q = 3L (ii) Q = L0.5 (iii) Q = L2 • Q = 3L = 3 (mL) = m . 3L = m. Q (Constant) • Q = L0.5 = (mL)0.5 = m0.5L0.5 = m0.5Q (Decreasing) • Q = L2 = (mL)2 = m2L2 = m2Q (Increasing)

  10. ∆Q ∆L 0 Marginal Product • The marginal productof any input is the increase in output arising from an additional unit of that input, holding all other inputs constant. • Marginal product of labor (MPL) = ∆Q = change in output, ∆L = change in labor

  11. L(no. of workers) Q(bushels of wheat) 0 0 ∆Q = 1000 ∆L = 1 1 1000 ∆Q = 800 ∆L = 1 2 1800 ∆L = 1 ∆Q = 600 3 2400 ∆Q = 400 ∆L = 1 4 2800 ∆L = 1 ∆Q = 200 5 3000 0 EXAMPLE :Marginal Product MPL 1000 800 600 400 200

  12. 3,000 2,500 2,000 Quantity of output 1,500 1,000 500 0 0 1 2 3 4 5 No. of workers 0 Relationship between Production Function and MPL L(no. of workers) Q(bushels of wheat) MPL 0 0 1000 1 1000 800 2 1800 600 3 2400 400 4 2800 200 5 3000 Diminishing MPL: This property explains why Production Function flatters as output increases.

  13. Why MPL Diminishes • Diminishing marginal product: the marginal product of an input declines as the quantity of the input increases (other things equal) E.g.: Output rises by a smaller and smaller amount for each additional worker. Why? • If the number of workers increased but not land, the average worker has less land to work with, so will be less productive. • In general, MPL diminishes as L rises whether the fixed input is land or capital (equipment, machines, etc.).

  14. $100 $0 $100 100 70 170 100 120 220 100 160 260 100 210 310 100 280 380 100 380 480 100 520 620 0 Deriving Costs curves $800 FC Q FC VC TC VC $700 TC 0 $600 1 $500 2 Costs $400 3 $300 4 $200 5 $100 6 $0 7 0 1 2 3 4 5 6 7 Example: FC = Cost of land VC = Wages to labor Q

  15. MC = ∆TC ∆Q Marginal Cost curve Marginal Cost (MC)is the change in total cost from producing one more unit: Q TC MC 0 $100 $70 1 170 50 2 220 40 3 260 Usually, MC rises as Q rises, due to diminishing marginal product. Sometimes, MC falls before rising. (In rare cases, MC may be constant.) 50 4 310 70 5 380 100 6 480 140 7 620

  16. $2.00 $2.50 $3.33 $5.00 $10.00 EXAMPLE : Rising Marginal Cost Curve Q(bushels of wheat) TC MC 0 $1,000 1000 $3,000 1800 $5,000 2400 $7,000 2800 $9,000 3000 $11,000

  17. n.a. $100 50 33.33 25 20 16.67 14.29 0 Average Fixed Cost curve Average fixed cost (AFC)is fixed cost divided by the quantity of output: AFC = FC/Q Q FC AFC 0 $100 1 100 2 100 3 100 4 100 5 100 6 100 7 100

  18. n.a. $70 60 53.33 52.50 56.00 63.33 74.29 0 Average Variable Cost curve Average variable cost (AVC)is variable cost divided by the quantity of output: AVC = VC/Q Q VC AVC 0 $0 1 70 2 120 3 160 As Q rises, AVC may fall initially. In most cases, AVC will eventually rise as output rises. 4 210 5 280 6 380 7 520

  19. AFC AVC n.a. n.a. n.a. $170 $100 $70 110 50 60 86.67 33.33 53.33 77.50 25 52.50 76 20 56.00 80 16.67 63.33 88.57 14.29 74.29 0 Average Total Cost curve Average total cost (ATC) equals total cost divided by the quantity of output: ATC = TC/Q Q TC ATC 0 $100 1 170 2 220 3 260 Also, ATC = AFC + AVC 4 310 5 380 6 480 7 620

  20. $200 $175 $150 $125 Costs $100 $75 $50 $25 $0 0 1 2 3 4 5 6 7 Q 0 Average Total Cost Curves Q TC ATC Usually, the ATC curve is U-shaped. 0 $100 n.a. 1 170 $170 2 220 110 3 260 86.67 4 310 77.50 5 380 76 6 480 80 7 620 88.57

  21. $200 $175 $150 $125 Costs $100 $75 $50 $25 $0 0 1 2 3 4 5 6 7 Q 0 Why ATC Is Usually U-shaped As Q rises: Initially, falling AFCpulls ATC down. Eventually, rising AVCpulls ATC up.

  22. $200 $175 $150 AFC $125 AVC Costs $100 ATC $75 MC $50 $25 $0 0 1 2 3 4 5 6 7 Q 0 The Various Cost Curves Together

  23. $200 $175 $150 $125 Costs $100 ATC $75 MC $50 $25 $0 0 1 2 3 4 5 6 7 Q 0 Important Economic Relation: ATC and MC When MC < ATC, ATC is falling. When MC > ATC, ATC is rising. The MC curve crosses the ATC curve at the ATC curve’s minimum.

  24. ACTIVE LEARNING 3: Costs Fill in the blank spaces of this table. Q VC TC AFC AVC ATC MC 0 $50 n.a. n.a. n.a. $10 1 10 $10 $60.00 2 30 80 30 3 16.67 20 36.67 4 100 150 12.50 37.50 5 150 30 60 6 210 260 8.33 35 43.33 24

  25. ACTIVE LEARNING 3: Answers Q VC TC AFC AVC ATC MC 0 $0 $50 n.a. n.a. n.a. $10 1 10 60 $50.00 $10 $60.00 20 2 30 80 25.00 15 40.00 30 3 60 110 16.67 20 36.67 40 4 100 150 12.50 25 37.50 50 5 150 200 10.00 30 40.00 60 6 210 260 8.33 35 43.33 25

  26. Numerical Problem on Costs Given the cost function: TC = 1000 + 10Q - 0.9Q2 + 0.04Q3 Find: 1) MC, TVC, AVC functions 2) Discarding the previous TC function, consider that the existing AVC function became the ATC function for the firm. Find Q when AVC is minimum.

  27. Worked out Problem TC = 1000 + 10Q - 0.9Q2 + 0.04Q3 1) MC = ΔTC / ΔQ = d(TC) / dQ = 10-1.8Q+ 0.12Q2 2) TVC = TC –TFC = 1000 + 10Q - 0.9Q2 + 0.04Q3 – 1000 = 10Q - 0.9Q2 + 0.04Q3 3) AVC = TVC / Q =(10Q - 0.9Q2 + 0.04Q3 )/Q = 10 - 0.9Q + 0.04Q2 4) Since AVC function is the ATC function, Q at Minimum AVC when: AVC = MC 10 - 0.9Q + 0.04Q2 = 10-1.8Q+ 0.12Q2 Or, - 0.08Q2 + 0.9Q = 0 Or, Q(- 0.08Q+ 0.9) = 0 Or, Q =0 and - 0.08Q+ 0.9 = 0 i.e, Q = 11.25 (Minimum AVC)

  28. Costs in the Short Run & Long Run • Short run: Some inputs are fixed (e.g., factories, land). The costs of these inputs are FC. • Long run: All inputs are variable (e.g., firms can build more factories, or sell existing ones)

  29. AvgTotalCost ATCM ATCS ATCL Q LRATC with 3 Factory Sizes Firm can choose from 3 factory sizes: S, M, L. Each size has its own SRATC curve. The firm can change to a different factory size in the long run, but not in the short run.

  30. AvgTotalCost ATCM ATCS ATCL Q QA QB EXAMPLE 3: LRATC with 3 Factory Sizes To produce less than QA, firm will choose size Sin the long run. To produce between QAand QB, firm will choose size Min the long run. To produce more than QB, firm will choose size Lin the long run. LRATC

  31. ATC LRATC Q A Typical LRATC Curve In the real world, factories come in many sizes, each with its own SRATC curve. So a typical LRATC curve looks like this:

  32. ATC LRATC Q How ATC Changes as the Scale of Production Changes Economies of scale: ATC falls as Q increases. Constant returns to scale: ATC stays the same as Q increases. Diseconomies of scale: ATC rises as Q increases.

  33. = P AR = ∆TR TR ∆Q Q MR = The Revenue of a Competitive Firm TR = P x Q • Total revenue (TR) • Average revenue (AR) • Marginal Revenue (MR):The change in TR from selling one more unit.

  34. How do firms behave in different market structures? • Perfectly Competitive Market • Monopoly Market • Oligopoly Market • Monopolistically Competitive Market

  35. Perfectly Competitive Market 1. Many buyers and many sellers 2. The goods offered for sale are largely the same. 3. Firms can freely enter or exit the market. • Because of 1 & 2, each buyer and seller is a “price taker” – takes the price as given.

  36. MR = TR AR = Q $0 $10 ∆TR $10 ∆Q $10 Notice that MR = P $20 $10 $10 $30 $10 $10 $10 $10 Sample Data Q P TR= P x Q 0 $10 n.a. 1 $10 $10 2 $10 3 $10 4 $10 $40 $10 5 $10 $50 36

  37. MR = P for a Competitive Firm • A competitive firm can keep increasing its output without affecting the market price. • So, each one-unit increase in Q causes revenue to rise by P, i.e., MR = P. MR = P is only true for firms in competitive markets.

  38. Profit Maximization • What Q maximizes the firm’s profit? • If increase Q by one unit,revenue rises by MR,cost rises by MC. • If MR > MC, then increase Q to raise profit. • If MR < MC, then reduce Q to raise profit.

  39. –$5 $5 $4 $6 1 9 6 4 5 15 8 2 7 23 10 0 7 33 12 –2 5 45 Profit Maximization (continued from earlier exercise) Q TR TC Profit MR MC Profit = MR–MC At any Q with MR > MC,increasing Q raises profit. 0 $0 $10 1 10 10 2 20 10 At any Q with MR < MC,reducing Q raises profit. 3 30 10 4 40 10 5 50

  40. Costs MC P1 MR Q Q1 Qa Qb MC and the Firm’s Supply Decision Rule: MR = MC at the profit-maximizing Q. At Qa, MC < MR. So, increase Qto raise profit. At Qb, MC > MR. So, reduce Qto raise profit. At Q1, MC = MR. Changing Qwould lower profit.

  41. MC P2 MR2 P1 MR Q2 Q1 MC and the Firm’s Supply Decision If price rises to P2, then the profit-maximizing quantity rises to Q2. The MC curve determines the firm’s Q at any price. Hence, Costs the MC curve is the firm’s supply curve. Q

  42. Market Structure Problems Assume the cost function: TC = 1000 + 2Q + 0.01Q2 and Price is $10 per unit for a firm in the competitive market. Calculate the profit maximizing output (Q) and economic profit.

  43. Market Structure Problems Assume the cost function: TC = 1000 + 2Q + 0.01Q2 and Price is $10 per unit for a firm in the competitive market. Calculate the profit maximizing output (Q) and economic profit. Solution: MC = dTC /dQ = 2+0.02Q In a perfectly competitive market, profit maximizing output is at where MR = P = MC 10 = 2+0.02Q Therefore, Q = 400 Economic Profit = TR –TC = 10(400) – (1000 + 2(400) + 0.01(4002)) =$600

  44. When would the firms Shutdown, Exit or Enter? • Shutdown: A short-run decision not to produce anything because of market conditions. • Exit: A long-run decision to leave the market. • A firm that shuts down temporarily must still pay its fixed costs. A firm that exits the market does not have to pay any costs at all, fixed or variable.

  45. A Firm’s Short-Run Decision to Shut Down • If firm shuts down temporarily, • revenue falls by TR • costs fall by VC • So, the firm should shut down if TR < VC. • Divide both sides by Q: TR/Q < VC/Q • So we can write the firm’s decision as: Shut down if P < AVC

  46. Costs MC If P > AVC, then firm produces Q where P = MC. ATC AVC If P < AVC, then firm shuts down (produces Q = 0). Q A Competitive Firm’s SR Supply Curve The firm’s SR supply curve is the portion of its MC curve above AVC.

  47. A Firm’s Long-Run Decision to Exit • If firm exits the market, • revenue falls by TR • costs fall by TC • So, the firm should exit if TR < TC. • Divide both sides by Q to rewrite the firm’s decision as: Exit if P < ATC

  48. A New Firm’s Decision to Enter the Market • In the long run, a new firm will enter the market if it is profitable to do so: if TR > TC. • Divide both sides by Q to express the firm’s entry decision as: Enter if P > ATC

  49. Costs, P MC P = $10 MR ATC $6 Q 50 Identifying a firm’s profit or Loss A competitive firm Determine if this firm’s total has profit/Loss? Identify the area on the graph that represents the firm’s profit or Loss. 49

  50. Costs, P MC P = $10 MR ATC profit $6 Q 50 Answers A competitive firm profit per unit = P – ATC= $10 – 6 = $4 Total profit = (P – ATC) x Q = $4 x 50= $200 50

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