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ECO 610-401

ECO 610-401. Monday, September 29 Topics: Costs & Decision Making: Level of Production & Mix of Resources Readings: Brickley et. al, Chapters 5,7; Chapter 19:562-574 Hoyt, Lecture 3:103-126 Handouts Extended Assignment 1 Notes and Examples

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ECO 610-401

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  1. ECO 610-401 • Monday, September 29 • Topics: • Costs & Decision Making: Level of Production & Mix of Resources • Readings: • Brickley et. al, Chapters 5,7; Chapter 19:562-574 • Hoyt, Lecture 3:103-126 • Handouts • Extended Assignment 1 • Notes and Examples • Reading “Changing the Formula: Seeking Perfect Prices, CEO Tears Up the Rules…” (WSJ, March 27, 2007)

  2. Assignment for Monday, October 6th • Topics: • Decision Making: Make or Buy and Transfer Pricing • Double Marginalization and Vertical Integration • Relevant Costs • Review for Exam 1 • Readings: • Brickley et. al, Chapter 19:562-574; • Hoyt, Lecture 3:115-126 • Extended Assignment 1 Due

  3. Some Terminology for Production • Total Product or Total Output(TP or Q) • Q • Total output produced by L workers • Average Product (AP) • TP/L • The amount produced by L workers divided by the number of workers‑‑"output per worker". • Marginal Product (MP) • ΔQ/ΔL • the increase in output with an increase in labor

  4. Total Product

  5. Marginal and Average Product

  6. Short Run Costs -- Some Terminology • Fixed Costs (FC) • Costs independent of the level of output • cost of capital‑‑ machinery or rent of a building. • Average Fixed Cost (AFC) • FC/Q • “Overhead per unit” • Total Variable Costs (TVC) • The total variable costs of producing Q units of output • variable costs usually being labor and raw materials • Average Variable Costs (AVC) • TVC/Q • “labor costs per unit".

  7. Cost Terminology (continued) • Total Cost (TC) • FC+TVC • Average Total Cost (ATC) • TC/Q=TVC/Q+FC/Q • cost per unit. • Marginal Cost (MC) • Δ TVC/ Δ Q or Δ TC/ Δ Q • the increase in costs with an increase in output at Q units of output • ”the wages paid to the additional workers hired to produce the additional output".

  8. Total Costs

  9. Unit Costs

  10. Relationship between Cost and Productivity • The cost curves appear to be “flipped” depictions of the product curves. Why? • MC = Δ VC/ΔQ = ΔwL/ΔQ =w(Δ L/ΔQ) = w/MPL • AVC = VC/Q = wL/Q =w(L/Q) = w/APL

  11. Lesson in Cost Theory 1: • MC and AVC are determined by productivity of the variable inputs, generally labor. • Decreasing MC reflects increasing MPL • Increasing MC reflects declining MPL. • From trends in MC and AVC we can infer trends in the productivity of labor

  12. Productivity & Costs(Let Wage = $10 hour) 10/4=2.50 4 6 10/6=1.67 10/5=2.00 5 4 10/4=2.50 3 10/3=3.33 2 10/2=5.00

  13. Input Demand (Short Run) • What is the profit-maximizing demand for inputs? • Let =P(Q)Q(L,K) - wL - rK Q(L,K)= production function. • K is fixed (short run). Choose L to maximize  • MRMPL =w or MRPL = w • MRPL is the “marginal revenue product of labor”

  14. Profit-Maximization and Labor Demand • Lesson in Cost Theory 2: • At profit-maximizing amount of input: • additional revenue from Q associated with an additional unit of the input (MRPL) = • additional cost of hiring that input (w). • If MRPL > w then more labor should be employed; • if MRPL < w, less labor should be employed.

  15. Production in the Long Run • What is long run? • No fixed inputs • Both capital and labor can be adjusted to: • increase output • decrease the cost of producing a given level of output. • More generally all inputs used in production are variable. • Flexible Production Processes • For any level of output there are numerous combinations of inputs to produce it.

  16. Why study long run? • Characterize conditions that ensure cost-minimization in production? • Develop a framework to explain changes in production processes when: • prices of inputs change • output increases or decreases • productivity of inputs changes

  17. Conditions for Cost-Minimization • What characterizes cost minimization in long run? • MPl/w –”additional productivity of an additional $ spent on labor • MPk/r –”additional productivity of an additional $ spent on capital • So cost minimization --> • MPL/w = MPk/r • Q per additional $ in L = Q per additional $ in K • Or MPL/MPK = w/r • relative productivity = relative cost

  18. Example • Worker costs $150 per day. Hiring (dismissing) at a print shop will increase (decrease) revenues by $200 per day through special orders • Leasing another copy machines at $50 will increase revenues by $75. • Does the shop have the correct mix of labor and capital (copy machines)?

  19. The Impact of Changes in Input Prices on Input Use • At w=$10 & r=$20 • cost minimizing at K= 7 and L=14 • total cost of producing 100 units is $280. • Suppose w increases to $20. • Then the cost of K=7 & L=14 is 20(14) + 20(7) = $420. • Is this the new cost of producing 100 units of output? • Answer: No.

  20. Input Price Changes and Cost Changes • Lesson in Cost Theory 4: • Increases in costs based on current mix of inputs will always overestimate the cost increase. • With flexible production, a firm can substitute away from the input that has increased in price.

  21. Production with Multiple Plants and Products • Issues: • Multi-plant Production • Given multiple plants how should you allocate production between the plants? • When is it profitable to open another plant? • How does having multiple plants affects costs of production and output decisions? • Multiple Products • How do we allocate inputs between products? • How do we make production decisions when production is joint?

  22. Example: Allocation of Production among Plants • A manufacturer has a work force of 1,000 to allocate between the production of a single product produces in 2 plants. • How should it allocate the workers to maximize output?

  23. Multiple Products • A firm produces 2 products with labor of 5 • Product A • Price = $10 • Cost of materials, $2 • 1st worker give 5 units an hour per worker • 2nd worker give 4 units • 3rd worker gives 3 units • 4th worker gives 2 units • 5th worker gives 2 units • Product B • Price = $7 • Cost of materials, $1 • 1st worker give 8 units an hour per worker • 2nd worker give 6 units • 3rd worker gives 4 units • 4th worker gives 2 units • 5th worker gives 1 units

  24. Rules for Allocating Inputs • For plants (A & B) we allocate the inputs so that • For products we allocate the inputs so that

  25. Allocation of Scarce Inputs • Lesson in Cost Theory . • With limited inputs to be allocated in the production of a single product among a number of plants, the profit-maximizing allocation of the input requires that the marginal product of the input be equal in all plants. • For allocation of a limited input among a number of products it must be the case that the marginal contribution of the input to profits, marginal revenue product less the marginal cost of product, should be equal for all products.

  26. Multiple Plant Production • Lesson in Cost Theory. • A firm with multiple plants can always minimize its costs by allocating the production so that marginal cost is equal in all plants.

  27. Opportunity Costs • Notice: Fixed supplies of labor & material in examples with 2 plants, 2 products. Then no costs for these? Correct? • What is meant by Opportunity Cost? • Opportunity Cost of an action is value of the foregone alternative, the “benefits” sacrificed. • Explicit costs are opportunity costs as price of input reflects its value in alternative use. • But use of any input (labor, capital) that has no explicit cost may have opportunity cost

  28. Opportunity Costs: Some Examples • Sole Proprietorship: Owner/Manager of Retail Outlet • Explicit Costs: • Rent: $20,000 • Direct Labor: 60,000 • Utilities: 3,000 • Merchandise: 140,000 • Total: $227,000

  29. Sole Proprietorship • Revenues: $260,000 • Is profit = $260,000 - $227,000 = $33,000 • Yes if we mean Accounting Profit • No if we mean Economic Profit. • Why? Did not include the opportunity cost of owners time & effort. • Suppose that Owner could earn $50,000 as manager of similar retail operation. Then full cost is explicit cost + opportunity cost = $267,000 • Economic Profit = $260,000 - $277,000 = (17,000)

  30. Planting a Crop • Agribusiness plants corn in a field that it owns. Costs include: • labor • storage, shipping • fertilizer, irrigation, seed • depreciation of machinery (due to use) • What else should be included? • Foregone profits (contribution) on alternative crop. • Foregone rent from sale of land

  31. Machine Time • 2 Product Lines share limited machine time • Product Line 1: • Unit Costs:DM (Direct Machine):2, DL(Direct Labor):1 • 1 Machine hour per unit • Price = 5 • Product Line 2 • Unit Costs: DM: 3 DL: 4 • 2 Machine hours per unit • Price = 10

  32. Machine Time (continued) • What is the economic cost of each product line (per unit)? • 1 MH for product line 1 yields contribution of 5-2-1=2 • 2 MH for product line 2 yields contribution of 10-3-4=3 or 1.5 per 1 MH • Then economic cost is • For 1, 2 + 1+ 1.5 = 4.5 • For , 3 + 4 + 2 = 9

  33. Vertical Integration • The modern corporation is often organized into a number of different divisions that are vertically integrated. • Vertical integration implies a structure in which the product developed in the "upstream" division is an input in production in a "downstream" division. • Examples: • Automobile production • Engines are produced in one division of GM and then purchased by another a division that assembles the automobile.

  34. An Example with External Market • Company produces electronic control devices and specialty microchips. • ATC is $300 and Pc = 550. • Company uses chips in control devices. • ATC of device (ATCd) is $500 + 2*ATCc = $1100 and Pd = $1,500. Assume the $500 is variable. • Should the company produce control devices? • Consider 2 alternative situations: • Outside orders for chips were insufficient to keep capacity utilized. • Suppose that $200 of the devices costs are fixed and capacity could be fully-utilized by outside orders. Should the firm produce chips in the short run?

  35. Why have vertical integration? • Enables a corporation to monitor and reward production more easily by rewarding division based on the "profits" generated by that division. • Upstream division that "sells" its products to downstream division needs a price for its product. Reasons: • To accurately measure division profit and evaluate the overall success of the firm. • To motivate divisions by giving them a chance to earn profits based on their performance. • To ensure the proper production and allocation of "upstream" products to "downstream" divisions or external markets. • To minimize international tax liabilities.

  36. Choosing the Transfer Price • Example: 2 divisions “upstream" and downstream. • The upstream produces a component by the downstream division for sale on an external market. • What should the price of the component (pC) be? • To answer -- the overall objective of the corporation is to maximize its profits, not the profits of any single division. • Assume that each division operates independently given the component price: • upstream division can decided how much to produce • downstream can decide how much to purchase and from whom (possibly outside the firm). • There are two general cases:

  37. No External Market • Price of the components (pc) should be set at the marginal cost of producing the component. • If at the pc = MC, the division is not earning positive profits because of fixed costs, then the corporation must subsidize the division by providing a payment to cover these fixed costs but it should not change pc from MC.

  38. No External Market: An Example • 2 divisions (downstream (d) and upstream (u)): • Demand for downstream (d) given by • Pd = 20 - (1/50)Q • MCd = 6 • Mcu = 4 (1 unit of u for each unit of d)

  39. No External Market: An Example D MCd+Mcu=MCd+PT MCd MR

  40. An External Market for the Upstream Component • In the case of perfect competition, the price of the component equal to what the price is on the external market. • If the upstream division cannot produce them at that price then it is more profitable for the corporation to purchase externally and not have internal production.

  41. External Sales and Purchases • Upstream division may also want to sell externally as well. • If demand for component by the downstream division is less than Q at which pe = MC then: • Upstream division can increase its profits by selling components on the external market. • If demand is greater than Q at which pc = MC then: • Upstream division will not be willing to supply the entire demand for downstream division and it will need to purchase the component externally.

  42. External Markets: An Example • 2 cases: • Low Demand for downstream product in firm • Pd= 14 - (1/50)Qd • High Demand for downstream product in firm • Pd= 20 - (1/50)Qd • MCd = 6 • Mcu = 2.5 + (1/100)Q • Pe=4 (external price for component)

  43. Example A: External Sales/Low Demand MCu+MCu 4 Pe D 0 MCd External Sales MRd

  44. Example B: External Purchases/High Demand D MCu+MCu 4 Pe 0 MCd MRd External Purchases

  45. An Example Problem (5.5) • Manufacturer of Toys has 2 lines (A&B) • Also produces chip used in both lines • Has capacity of 10,000 • Chip can be sold externally (line C) • External price is $20 • Additional costs for external sale

  46. Demand for 3 products

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