1. Production Theory and Estimation Department of Business Administration FALL 20 10 - 11 by Assoc. Prof. Sami Fethi

2. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 2 The Production Function  Production refers to the transformation of inputs or resources into outputs of goods and services. In other words, production refers to all of the activities involved in the production of goods and services, from borrowing to set up or expand production facilities, to hiring workers, purchasing row materials, running quality control, cost accounting, and so on, rather than referring merely to the physical transformation of inputs into outputs of goods and services.

3. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 3 For example  A computer company hires workers to use machinery, parts, and raw materials in factories to produce personal computers.  The output of a firm can either be a final commodity or an intermediate product such as computer and semiconductor respectively.  The output can also be a service rather than a good such as education, medicine, banking etc.

4. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 4 The Organization of Production  Inputs Labor, Capital, Land  Fixed Inputs  Variable Inputs  Short Run At least one input is fixed  Long Run All inputs are variable

5. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 5 The Organization of Production  Inputs: are the sources used in the production of goods and services and can be broadly classified into labour, capital, land, natural resources, and entrepreneurial talent.  Fixed input: are those that cannot be readily changed during the time period under consideration such as a firm’s plant and specialized equipment.

6. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 6 The Organization of Production  Variables Inputs: are those can be varied easily and on very short notice such as raw materials and unskilled labour.  The time period during which at least one input is fixed called the short-run and if all inputs are variable, we are in the long-run.

7. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 7 The Production Function  A production function is an equation, tables, or graph showing the maximum output of a commodity that a firm can produce per period of time with each set of inputs.  Both inputs and outputs are measured in physical rather than in monetary units. Here technology is assumed to remain constant during the period of the analysis.

8. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 8 The Production Function  The general equation of the production function of a firm using labour (L) and capital (K) to produce a good or service (Q) or shows the maximum amount of output (Q) that can be produced within a given time period with each combination of (L) and (K). This can be defined as follows: Q= f (L,K)

9. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 9 Production Function With Two Inputs Q = f(L, K) The table shows that by using 1 unit of labour (1L) and 1 unit of capital (1K), the firm would produce 3 units of o/p (3Q).

10. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 10 Production Function With Two Inputs Discrete Production Surface The previous table are shown graphically in this figure. The height of bars refers to the max o/p that can be produced with each combination of labour and capital shown on the axes.

11. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 11 Production Function With Two Inputs Continuous Production Surface In this figure, If we assume that i/p’s and o/p’s are continuously divisibly, we would have the continuous production surface. This indicates that by increasing L 2 with K 1 of capital, the firm produces the o/p by height of cross section K 1 AB. Increasing L 1 with K 2, we have cross section K 2 CD.

12. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 12 Production Function With One Variable Input When discussing production in the short run, three definitions are important:  Total product  Marginal product  Average product

13. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 13 Production Function With One Variable Input Total Product Marginal Product Average Product Production or Output Elasticity TP = Q = f(L) MP L =  TP  L AP L = TP L E L = MP L AP L

14. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 14 Total Product Total product (TP) is another name for output in the short run. TP = Q = f (L)

15. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 15 Marginal Product The marginal product (MP) of a variable input is the change in output (or TP) resulting from a one unit change in the input. MP tells us how output changes as we change the level of the input by one unit. Consider the two input production function Q=f (L,K) in which input L is variable and input K is fixed at some level. The marginal product of input L is defined as holding input K constant. MP L =  TP  L

16. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 16 Average Product The average product (AP) of an input is the total product divided by the level of the input. AP tells us, on average, how many units of output are produced per unit of input used. The average product of input L is defined as holding input K constant. AP L = TP L

17. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 17 Production Function With One Variable Input-Example Total, Marginal, and Average Product of Labor, and Output Elasticity

18. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 18 Production Function With One Variable Input

19. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 19 The Law of Diminishing Returns As additional units of a variable input are combined with a fixed input, after a point the additional output (marginal product) starts to diminish. This is the principle that after a point, the marginal product of a variable input declines.

20. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 20 The Law of Diminishing Returns X MP Increasing Returns Diminishing Returns Begins MP

21. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 21 The Three Stages of Production

22. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 22 The Three Stages of Production Stage I: The range of increasing average product of the variable input.  From zero units of the variable input to where AP is maximized Stage II: The range from the point of maximum AP of the variable i/p to the point at which the MP of i/p is zero.  From the maximum AP to where MP=0 Stage III: The range of negative marginal product of the variable input.  From where MP=0 and MP is negative.

23. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 23 The Three Stages of Production

24. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 24 The Three Stages of Production  In the short run, rational firms should only be operating in Stage II.  Why Stage II?  Why not Stage I and III?  In Stage III- MP L is negative  In Stage I- MP K is negative  In Stage II- MP L and MP K are both positive but decline

25. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 25 The Three Stages of Production-Example Stage II

26. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 26 The Three Stages of Production-Example What level of input usage within Stage II is best for the firm? Is there a precise point.  The answer depends upon how many units of output the firm can sell, the price of the product, and the monetary costs of employing the variable input.

27. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 27 Optimal Use of the Variable Input How much labor or the variable input should the firm use in order to maximize profit. The firm should employ an additional unit of labor as long as the extra revenue genereted until the extra revenue equals the extra cost. Where MRP=MLC.

28. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 28 Optimal Use of the Variable Input Marginal Revenue Product of Labor MRP L = (MP L )(MR) Marginal Resource Cost of Labor MRC L =  TC  L Optimal Use of Labor MRP L = MRC L

29. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 29 Optimal Use of the Variable Input-Example Use of Labor is Optimal When L = 3.50 MRP L =MRxMP L --------MRC=W

30. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 30 Optimal Use of the Variable Input

31. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 31 Production With Two Variable Inputs - -In the long run, all inputs are variable. Isoquants show combinations of two inputs that can produce the same level of output. -In other words, Production isoquant shows the various combination of two inputs that the firm can use to produce a specific level of output. -Firms will only use combinations of two inputs that are in the economic region of production, which is defined by the portion of each isoquant that is negatively sloped. -A higher isoquant refers to a larger output, while a lower isoquant refers to a smaller output.

32. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 32 Production With Two Variable Inputs Isoquants

33. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 33 Production Isoquant Economic region of production: Negatively sloped portions of the isoquants within the ridge lines represents the relevant economic region of production. Ridge lines: The lines that separate the relevant (i.e., negatively sloped) from the irrelevant ( or positively sloped) portions of the isoquant. This refers to stage II where the MP L and MP K are both positive but declining and producers never want to operate outside this region.

34. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 34 Production With Two Variable Inputs Economic Region of Production

35. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 35 Production With Two Variable Inputs Marginal Rate of Technical Substitution: The absolute value of the slope of the isoquant. It equals the ratio the marginal products of the two inputs. Slope of isoquant indicates the quantity of one input that can be traded for another input, while keeping output constant. MRTS = -  K/  L = MP L /MP K Substitution among inputs

36. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 36 Production With Two Variable Inputs MRTS = -(-2.5/1) = 2.5

37. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 37 Production With Two Variable Inputs Perfect Substitutes Perfect Complements When an isoquant is straight line or MRTS is constant, inputs are perfect substitutes whilst an isoquant is right angled, inputs are perfect complements.

38. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 38 Optimal Combination of Inputs To determine the optimal combination of labor and capital, we also need an isocost line. Isocost lines represent all combinations of two inputs that a firm can purchase with the same total cost. Slope of isocost Vertical intercept of isocost

39. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 39 Optimal Combination of Inputs

40. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 40 Example: Isocost Lines AB Total Cost = c = $100 w=r=$10 c/r = $100/$10 = $10k (vertical intercept) -w/r = -$10/$10 = -1(slope) A’B’ Total Cost = c = $140 w=r=$10 c/r = $140/$10 = $14k-w/r = -$10/$10 = -1 A’’B’’ Total Cost = c = $80 w=r=$10 c/r = $80/$10 = $8k -w/r = -$10/$10 = -1 AB* C = $100, w = $5, r = $10 c/r = $100/$10 =$10k -w/r = -$10/$5 = -1/2 MRTS = w/r; since MRTS = MPL/ MPK, condition for optimal combination of inputs as MPL/ MPK= w/r

41. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 41 Expansion Path Expansion path: joinning points of tangency of isoquants and isocost of optimal input combination. The optimal input combination required to minimize the cost of producing a given level of maximum output that the firm can produce at the tangency of an isoquant and an isocost.

42. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 42 Optimal Combination of Inputs If the price of an input declines, the firm will substitute the cheaper input for another inputs in production in order to reach a new optimal input combination.

43. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 43 Returns to Scale How does output vary with the scale of production? Production Function Q = f(L, K) Q = f(hL, hK) If = h, then f has constant returns to scale. If > h, then f has increasing returns to scale. If < h, the f has decreasing returns to scale. Returns to scale describes what happens to total output as all of the inputs are changed by the same proportion.

44. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 44 Returns to Scale  Graphically, the returns to scale concept can be illustrated using the following graphs.  The long run production process is described by the concept of returns to scale. Q X,Y IRTS Q X,Y CRTS Q X,Y DRTS

45. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 45 If all inputs into the production process are doubled, three things can happen:  output can more than double increasing returns to scale (IRTS)  output can exactly double constant returns to scale (CRTS)  output can less than double decreasing returns to scale (DRTS ) Returns to Scale

46. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 46 Constant Returns to Scale Increasing Returns to Scale Decreasing Returns to Scale Returns to Scale

47. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 47 Empirical Production Functions Several Useful Properties : 1. The Marginal Product of capital and the marginal Product of labor depend on both the quantity of capital and the quantity of labor used in production, as is often the case in the real world. 2. K and L are represents the output elasticity of labor and capital and the sum of these exponents gives the returns on scale. a + b = 1 Constant return to scale a + b > 1 Increasing return to scale a + b <1 Decreasing return to scale

48. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 48 Empirical Production Functions Cobb-Douglas Production Function Q = AK a L b Estimated using Natural Logarithms ln Q = ln A + a ln K + b ln L

49. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 49 Empirical Production Functions-Example A bus ltd in a district has estimated the following Cobb-Douglas production function using monthly observations for the past four years: ln Q = ln A + a ln K + b ln L+ c Ln G Ln Q = 2.303+ 0.40 ln K + 0.60 Ln L+ 0.20 ln G (3.40) (4.15) (3.05) R 2 =0.94DW=2.20F= 25.6 Q is the number of bus miles driven, K is the number of buses the firm operates, L is the number of bus drives it employes each day, and G is the gallons of gasoline it uses.

50. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 50 Innovations and Global Competitiveness  Product Innovation  Process Innovation  Product Cycle Model  Just-In-Time Production System  Competitive Benchmarking  Computer-Aided Design (CAD)  Computer-Aided Manufacturing (CAM)

51. Ch 6 Production Theory © 2010/11, Sami Fethi, EMU, All Right Reserved. © 2004, Managerial Economics, Dominick Salvatore 51 The End Thanks