1. Slide 1 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Production Economics Managers must decide not only what to produce for the market, but also how to produce it in the most efficient or least cost manner. Economics offers widely accepted tools for judging whether the production choices are least cost. A production function relates the most that can be produced from a given set of inputs. »Production functions allow measures of the marginal product of each input.

2. Slide 2 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. A Production Function is the maximum feasible quantity from any amounts of inputs If L is labor and K is capital, one popular functional form is known as the Cobb-Douglas Production Function The Production Function

3. Slide 3 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Q =  K   L   is a Cobb- Douglas Production Function The number of inputs is typically greater than just K & L. But economists simplify by suggesting some, like materials or labor, is variable, whereas plant and equipment is fairly fixed in the short run. The Production Function (con’t)

4. Slide 4 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Short Run Production Functions: »Max output, from a n y set of inputs »Q = f ( X1, X2, X3, X4, X5... ) FIXED IN SR VARIABLE IN SR _ _ Q = f ( K, L) for two input case, where K is Fixed The Short Run Production Function

5. Slide 5 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. The Short Run Production Function (con’t) A Production Function with only one variable input is easily analyzed. The one variable input is labor, L. Q = f( L )

6. Slide 6 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Average Product = Q / L »output per labor Marginal Product =  Q/  L =  Q/  L = dQ/dL »output attributable to last unit of labor applied Similar to profit functions, the Peak of MP occurs before the Peak of average product When MP = AP, this is the peak of the AP curve

7. Slide 7 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Law of Diminishing Returns INCREASES IN ONE FACTOR OF PRODUCTION, HOLDING ONE OR OTHER FACTORS FIXED, AFTER SOME POINT, MARGINAL PRODUCT DIMINISHES. A SHORT RUN LAW point of diminishing returns Variable input MP

8. Slide 8 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Bottlenecks in Production Plants Boeing found diminishing returns in ramping up production. It sought ways to adopt lean production techniques, cut order sizes, and outsourced work at bottlenecked plants.

9. Slide 9 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Increasing Returns and Network Effects There are exceptions to the law of diminishing returns. When the installed base of a network product makes efforts to acquire new customers increasing more productive, we have network effects »Outlook and Microsoft Office

10. Slide 10 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Table 7.2: Total, Marginal & Average Products

11. Slide 11 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Total, Marginal & Average Products Marginal Product 3 4 5 6 7 8 Average Product The maximum MP occurs before the maximum AP

12. Slide 12 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. When MP > AP, then AP is RISING »IF YOUR MARGINAL GRADE IN THIS CLASS IS HIGHER THAN YOUR GRADE POINT AVERAGE, THEN YOUR G.P.A. IS RISING When MP < AP, then AP is FALLING »IF YOUR MARGINAL BATTING AVERAGE IS LESS THAN THAT OF THE NEW YORK YANKEES, YOUR ADDITION TO THE TEAM WOULD LOWER THE YANKEE’S TEAM BATTING AVERAGE When MP = AP, then AP is at its MAX »IF THE NEW HIRE IS JUST AS EFFICIENT AS THE AVERAGE EMPLOYEE, THEN AVERAGE PRODUCTIVITY DOESN’T CHANGE

13. Slide 13 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Three stages of production

14. Slide 14 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Three stages of production Stage 1: average product rising. »Increasing returns Stage 2:average product declining (but marginal product positive). »Decreasing returns Stage 3:marginal product is negative, or total product is declining. »Negative returns L

15. Slide 15 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Determining the Optimal Use of the Variable Input HIRE, IF GET MORE REVENUE THAN COST HIRE if  TR/  L >  TC/  L HIRE if the marginal revenue product > marginal factor cost: MRP L > MFC L AT OPTIMUM, MRP L = W  MFC MRP L  MP L P Q = W optimal labor MP L MRP L W W  MFC L wage

16. Slide 16 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Optimal Input Use at L = 6 Table 7.3

17. Slide 17 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Production Functions with multiple variable inputs Suppose several inputs are variable »greatest output from any set of inputs Q = f( K, L ) is two input example MP of capital and MP of labor are the derivatives of the production function »MP L =  Q/  L =  Q/  L MP of labor declines as more labor is applied. Also the MP of capital declines as more capital is applied.

18. Slide 18 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Isoquants & LR Production Functions In the LONG RUN, ALL factors are variable Q = f ( K, L ) ISOQUANTS -- locus of input combinations which produces the same output »Points A & B are on the same isoquant SLOPE of ISOQUANT from A to B is ratio of Marginal Products, called the MRTS, the marginal rate of technical substitution = -  K /  L ISOQUANT MAP B A C Q1 Q2 Q3 K L

19. Slide 19 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. The objective is to minimize cost for a given output ISOCOST lines are the combination of inputs for a given cost, C 0 C 0 = C L ·L + C K ·K K = C 0 /C K - (C L /C K )·L Optimal where: » MP L /MP K = C L /C K · »Rearranged, this becomes the equimarginal criterion Optimal Combination of Inputs

20. Slide 20 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Optimal Combination of Inputs Equimarginal Criterion: Produce where MP L /C L = MP K /C K where marginal products per dollar are equal at D, slope of isocost = slope of isoquant

21. Slide 21 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Q: Is the following firm EFFICIENT? Suppose that: »MP L = 30 »MP K = 50 »W = 10 (cost of labor) »R = 25 (cost of capital) Labor: 30/10 = 3 Capital: 50/25 = 2 A: No! Use of the Equimarginal Criterion

22. Slide 22 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Use of the Equimarginal Criterion A dollar spent on labor produces 3, and a dollar spent on capital produces 2. USE RELATIVELY MORE LABOR! If spend $1 less in capital, output falls 2 units, but rises 3 units when spent on labor Shift to more labor until the equimarginal condition holds. That is peak efficiency.

23. Slide 23 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Production Processes and Process Rays under Fixed Proportions If a firm has five computers and just one person, typically only one computer is used at a time. You really need five people to work on the five computers. The isoquants for processes with fixed proportions are L-shaped. Small changes in the prices of input may lead to no change in the process. M is the process ray of one worker and one machine people computers 1 2 3 4 5 6 7 8 9 5432154321 M

24. Slide 24 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Allocative & Technical Efficiency Allocative Efficiency – asks if the firm using the least cost combination of input »It satisfies: MP L /C L = MP K /C K Technical Efficiency – asks if the firm is maximizing potential output from a given set of inputs »When a firm produces at point T rather than point D on a lower isoquant, that firm is not producing as much as is technically possible. Q (1) D Q (0) T

25. Slide 25 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Overall Production Efficiency Suppose a plant produces 93% of what the technical efficient plant (the benchmark) would produce. Suppose a plant produces 85.7% of what an allocatively efficient plant would produce, due to a misaligning the input mix. Overall Production Efficiency = (technical efficiency)*(allocative efficiency) In this case: overall production efficiency = (.93)(.857) = 0.79701 or about 79.7%.

26. Slide 26 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Returns to Scale If multiplying all inputs by (lambda) increases the dependent variable by  the firm has constant returns to scale (CRS). »Q = f ( K, L) »So, f(  K, L) = Q is Constant Returns to Scale »So if 10% more all inputs leads to 10% more output the firm is constant returns to scale. Cobb-Douglas Production Functions are constant returns if  + 

27. Slide 27 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Cobb-Douglas Production Functions Q = A K  L  is a Cobb-Douglas Production Function IMPLIES: Can be CRS, DRS, or IRS if  +  1, then constant returns to scale if  +  < 1, then decreasing returns to scale if  +  > 1, then increasing returns to scale Suppose: Q = 1.4 K.35 L.70 Is this production function constant returns to scale? No, it is Increasing Returns to Scale, because 1.05 > 1.

28. Slide 28 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Reasons for Increasing & Decreasing Returns to Scale Some Reasons for IRS The advantage of specialization in capital and labor – become more adept at a task Engineering size and volume effects – doubling the size of motor more than doubles its power Network effects Pecuniary advantages of buying in bulk Some Reasons for DRS Problems with coordination and control – as a organization gets larger, harder to get everyone to work together Shirking increases Bottlenecks appear – a form of the law of diminishing returns appears CEO can’t oversee a gigantically complex operation

29. Slide 29 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Interpreting the Exponents of the Cobb-Douglas Production Functions The exponents  and  are elasticities   is the capital elasticity of output  The  is [% change in Q / % change in K]  is the labor elasticity of output  The  is a [% change in Q / % change in L] These elasticities can be written as E K and E L Most firms have some slight increasing returns to scale.

30. Slide 30 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Empirical Production Elasticities Table 7.4: Most are statistically close to CRS or have IRS such as management or other staff personnel.

31. Slide 31 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Cost Analysis The Importance of Cost Analysis »Managers seek to produce the highest quality products at the lowest possible cost. »Firms that are merely satisfied with the status quo find that competitors arise that produce at lower costs and drive them out of business. »The advantages once assigned to being a large firm (economies of scale and scope) have not provided the advantages of flexibility and agility found in some smaller companies. »Cost analysis is helpful in the task of finding the lowest cost methods to produce goods and services.

32. Slide 32 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Meaning and Measurement of Cost There are many cost concepts used in business. One example is distinctions between: Accounting vs. Economic Cost Accounting costs involve explicit historical costs. They attempt to use the same rules for different firms to be able to compare firm performance. Economic costs are based on making decisions. These costs can be both implicit and explicit. A chief example is that economic costs include the opportunity costs of owner-supplied resources such as time and money, which are implicit costs.

33. Slide 33 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. »A chief example is that economic costs include the opportunity costs of owner-supplied resources such as time and money, which are implicit costs. Economic Profit = Total Revenues - Explicit Costs - Implicit Costs »Implicit costs make economic profit lower than accounting profit Three Contrasts between Accounting & Economic Cost: 1.Depreciation Cost Measurement. Accounting depreciation (e.g., straight-line depreciation) tends to have little relationship to the actual loss of value »To an economist, the actual loss of value is the true cost of using machinery, though it is often hard to measure.

34. Slide 34 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 2.Inventory Valuation. Accounting valuation depends on its acquisition cost »Economists view the cost of inventory as the cost of replacement. 3.Sunk Costs of Unutilized Facilities. Empty space may appear to have "no cost” »Economists view its alternative use (e.g., rental value) as its opportunity cost. »Sunk Costs -- already paid for, or there already exists a contractual obligation to pay

35. Slide 35 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Meaning and Measurement of Cost There a number of cost concepts in business. Opportunity Cost – value of next best alternative use. Explicit vs. Implicit Cost – actual prices paid vs. opportunity cost of owner-supplied resources.

36. Slide 36 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. SHORT RUN COST FUNCTIONS 1.TC = FC + VC total cost (TC) is the sum of Fixed Cost (FC) and Variable Cost (VC) 2.AFC = FC/Q average fixed cost is FC divided by Q 3.AVC = VC/Q average variable cost is VC divided by Q 4.ATC = TC/Q = AFC + AVC average total cost is the sum of AFC and AVC. 5.MC =  TC/  Q =  TC/  Q marginal cost is the cost of the last item produced  Incremental cost is the extra cost of implementing a decision =  TC of a decision, such as adding a 2 nd shift’s incremental cost

37. Slide 37 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Figure 8.1 FC is $150 Adding FC to VC is an upward shift of cost to make TC An S-shaped VC gives an S- shaped TC

38. Slide 38 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Short Run Cost Graphs using AFC & AVC AFC Q Q 1. 2. AVC 3. Q AFC AVC ATC MC MC intersects lowest point of AVC and lowest point of ATC. When MC < AVC, AVC declines When MC > AVC, AVC rises

39. Slide 39 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Suppose we have found that: TC = 100 + 60Q -3Q 2 +.1Q 3 What is FC? »100 »Not a function of Q What is VC? »VC = 60Q -3Q 2 +.1Q 3 What is MC? »MC = dTC/dQ = 60 - 6Q +.3Q 2 Notice TC is cubic or S-shaped Notice the MC is quadratic, which is U-shaped. Notice also that VC is quadratic, which also U-shaped Q AVC MC

40. Slide 40 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Long Run Cost Functions All inputs are variable in the long run LAC is long run average cost »ENVELOPE of SAC curves LMC is FLATTER than SMC curves The optimal plant size for a given output Q 2 is plant size 1 (A SR concept.) However, the optimal plant size occurs at Q 3, which is the lowest cost point overall. (A LR concept.)

41. Slide 41 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Long Run Cost Function (LRAC) Envelope of SRAC curves Q SRAC-small capital SRAC-med. capital SRAC-big capital LRAC--Envelope of SRAC curves Ave Cost Variation of Figure 8.3

42. Slide 42 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Economies and Diseconomies of Scale 1.Product-level Internal Economies of Scale involves declining cost associated a product as a firm increases production or throughput per day due to volume discounts, specialization, mass customization, and learning curve effects. »Mass customization is the trend of making products partially mass produced, and partially customized. »Land’s End sells mass produced clothing in catalogs and in stores such as Sears, but it also offers the service of stitching initials or names in shirts or duffle bags – this makes the product at the same time mass produced and customized. » Economies offered in the mass production of items helps to offset the expense of individually designed products.

43. Slide 43 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Learning Curve Relationship “Learning by doing" has wide application in production processes. Workers and management become more efficient with experience. The cost of production declines as the accumulated past production, Q =  q t, increases, where q t is the amount produced in the t th period, and Q is the accumulated past production. Airline manufacturing, ship building, and appliance manufacturing have demonstrated the learning curve effect.

44. Slide 44 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Functionally, the learning curve relationship can be written C = a· Q b, where C is the input cost of the Q th unit is a function of accumulated output. Taking the (natural) logarithm of both sides, we get: log C = log a + b·log Q

45. Slide 45 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. The coefficient b tells us the extent of the learning curve effect. »If the b = 0, then costs are at a constant level. » If b > 0, then costs rise in output, which is exactly opposite of the learning curve effect. »If b < 0, then costs decline in output, as predicted by the learning curve effect.

46. Slide 46 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Example Cookie Baskets, Inc., is a local firm that assembles gift baskets. This is a one- owner, one-worker firm. Using data on time it takes to make the tenth, twentieth, and so on accumulated number of baskets, the manager estimates the following regression. Ln T =.4 -.02 Ln Q R 2 =.834 N = 30 (3.1) (2.6) where T is time it took to make a basket and Q is the accumulated number of baskets made, and the parentheses contain t-statistics. Q: Is this firm finding any benefits of Learning by Doing? A:Yes, the coefficient on Q is negative, so it takes less time to make baskets as the number of baskets made grows. The coefficient is statistically significant as the estimated t-value is 2.6.

47. Slide 47 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Percentage of Learning The proportion by which costs are reduced through DOUBLING output is estimated as follows: L = (C 2 /C 1 )·100% »where C 1 is the input or cost for the Q 1 unit of output and C 2 is the input or cost for the Q 2 unit of output (and Q 2 = 2Q 1 ). If the percentage of learning, L = 82%, then input costs decline 18% as output doubles. »The percentage of learning is 100% - L. When L = 100%, there is no percentage of learning.

48. Slide 48 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Economies and Diseconomies of Scale 2.Plant-level Internal Economies of Scale involve producing several products at the same plant. These include economies in overhead, required reserves, investment, or interactions among products (economies of scope). 3.Firm-level Internal Economies of Scale occur in firms with several plants. These include economies in distribution and transportation of a geographically dispersed firm, or economies in marketing, sales promotion, or R&D of multi- product firms.

49. Slide 49 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Figure 8.5:U-shaped LRAC Flat section of the LRAC »Displays constant returns to scale »The minimum efficient scale (MES) is the smallest scale at which minimum per unit costs are attained. 4. Diseconomies of Scale. Costs start to rise a large scale. These include transportation costs, imperfections in the labor market, and problems of coordination and control by management. »The maximum efficient scale (Max ES) is the largest scale before which unit costs begin to rise. »Modern business management offers techniques to avoid diseconomies of scale through profit centers, transfer pricing, and tying incentives to performance.

50. Slide 50 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Figure 8.5

51. Slide 51 © 2011 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Auto Production: Minimum Efficient Scale At Ford, cars made from aluminum have a minimum efficient size of 50,000 (pt A) Cars made from steel have a MES of 300,000 (pt C) Hence, Ford can change its products faster if it uses aluminum, even if 10% more costly.