Production Theory and Estimation Department of Business Administration FALL by Asst. Prof. Sami Fethi

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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)

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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).

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 12 Production Function With One Variable Input When discussing production in the short run, three definitions are important:  Total product  Managerial product  Average product

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 14 Total Product Total product (TP) is another name for output in the short run. TP = Q = f (L)

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 17 Production Function With One Variable Input Example Total, Marginal, and Average Product of Labor, and Output Elasticity

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 18 Production Function With One Variable Input

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 20 The Law of Diminishing Returns X MP Increasing Returns Diminishing Returns Begins MP

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 21 The Three Stages of Production

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 23 The Three Stages of Production

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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?

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 25 The Three Stages of Production Example Stage II

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 26 The Three Stages of Production Example What level of input usage within Stage II is best for the firm?  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.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 27 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 LaborMRP L = MRC L

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 28 Optimal Use of the Variable Input A profit-maximizing firm operating in perfectly competitive output and input markets will be using the optimal amount of an input at the point at which the monetary value of the input’s marginal product is equal to the additional cost of using that input. Where MRP=MLC.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 29 Optimal Use of the Variable Input Example Use of Labor is Optimal When L = 3.50

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 30 Optimal Use of the Variable Input

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 32 Production With Two Variable Inputs Isoquants

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 34 Production With Two Variable Inputs Economic Region of Production

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 36 Production With Two Variable Inputs MRTS = -(-2.5/1) = 2.5

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 37 Production With Two Variable Inputs Perfect SubstitutesPerfect Complements When an isoquant is straight line or MRTS is constant, inputs are perfect substitutes whilst an isoquant is right angled, inputs are perfect comlements.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 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

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 39 Optimal Combination of Inputs

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 40 Example: Example: Isocost Lines AB Total Cost = c = $100 w=r=$10 c/r = $100/$10 = $10k -w/r = -$10/$10 = -1 A’B’ Total Cost = c = $140 w=r=$10 c/r = $140/$10 = $14k (vertical intercept) -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

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 41 Optimal Input Combination for Minimizing Cost or Maximizing Output Cost-Minimization Simply by changing the proportions of factors K and L, it may be able to decrease total costs without affecting total revenue - and thus increase profits. Thus, we first begin with analyzing the cost-minimizing choice of technique for a firm which seeks to produce a particular level of output.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 42 Con’t It is important to note that this story is not the whole story behind the producer's profit-maximizing decision. In cost- minimization, we leave the decision on the level of output out of the picture. The full, profit-maximization story would require that output level enter as a variable and not as a given. We shall consider this later.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 43 Con’t Where C is total factor costs and w and r are the rental rates for labor and capital respectively. Notice that this cost equation defines a function in L-K space of the following linear form, L = C/w - (r/w)K. This is known as an isocost curve and is depicted as a downward- sloping straight line, as we see in Figure 1.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 44 Con’t Any factor input combination on a particular isocost curve has the same total costs, C. The vertical intercept of the isocost curve is C/w and the slope of the isocost curve is - (r/w). The horizontal intercept is obviously C/r. Thus, for different levels of costs, C, there will be different (but parallel) isocost curves. The isocost curves closest to the origin represent relatively low total costs, those furthest away represent relatively high total costs. Thus, referring to the isocost curves, C < C* < C’. Note that a change in the factor prices, r or w, will change the slopes of all the isocost curves.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 45 Con’t In order for the cost minimizing firm, is then to minimize cost given that a certain level of output must be reached. This is stated as follows: min C = wL + rK Y* = F(K, L) In other words, as the output level Y* is given, then the consraint is the isoquant Y* depicted in previous Figure. What the firm seeks to do is thus find the factor combination, (K, L), which has the lowest total cost and yet still produces output Y*.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 46 Con’t Diagramatically, this is represented as the tangency of the given isoquant Y* and the lowest İsocost curve, C*. This will be at point e* in Figure 1, which represents factor input combination K*, L*. Notice that point e is unattainable: although the factor combination corresponding to e yields a lower cost (as it lies on isocost curve C which is below isocost curve C*), it does not produce Y* and thus will not be considered.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 47 Con’t In contrast, point e` is attainable as it lies on the isoquant Y*, but obviously, as it also lies on the higher isocost curve C`, it is more costly than the combination e*. Thus, point e* - and thus capital employment K* and labor employment L* - will be the optimal choice of inputs for a firm which seeks to minimize the costs of producing Y*. We can obtain this tangency solution from the cost- minimization problem via simple mathematical programming. Setting up in Lagrangian form, we have: E = rK + wL + λ(Y* - f(K, L))

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 48 Con’t Where λ is the Lagrangian multiplier. This yields the following first order conditions for a maximum are (we are assuming an interior solution): E/ dK = r - λfK = 0 E/dL = w - λfL = 0 E/dλ = Y* - λf(K, L) = 0 Combining the first two yield: r/w = fK/fL

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 49 Con’t Thus, for a minimum, the (negative of the) slope of the lowest isocost curve must equal the ratio of marginal products, or MRTS, which, as we know, is the (negative of the) slope of the isoquant Y*. So, minimum cost is achieved by finding the factor combination which yields a tangency between the isoquant and the lowest isocost curve.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 50 Output-Maximization In our cost-minimization problem, we assumed that the producer was trying to find the input combinations that would produce a given level of output at minimum cost. An alternative way of thinking about the producer's decision on factor inputs is to ask him to find the highest amount of output he can produce for a given total cost. Such an exercise could be expressed as the following: max Y = f (K, L) C* = wL + rK

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 51 Output-Maximization Notice that now the constraint is now a given level of costs. This is analogous to a consumer case: the entrepreneur is now given a "budget" (the maximum amount of costs he is allowed to incur, C*) and will thus try to achieve as much output as he can out of this by choosing the appropriate factor input combinations.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 52 Output-Maximization Diagramatically, we impose on the producer a particular isocost curve and then ask to choose factor inputs such that output is maximized. In the Figure, we see that the maximimum output is represented by the isoquant Y* which is tangent to the given isocost curve, C*, at point e*. Point e’ is not output-maximizing as that factor combination produces a lower level of output Y’< Y*), while point e’’ is not available, as costs at e’’ would be greater than C*, thus our constraint would be violated.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 53 Optimal Combination of Inputs MRTS = w/r; since MRTS = MP L / MP K, condition for optimal combination of inputs as MPL/ MPK= w/r

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 54 Optimal Combination of Inputs Effect of a Change in Input Prices

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 55 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.

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 56 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

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 57 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)

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 58 Returns to Scale Constant Returns to Scale Increasing Returns to Scale Decreasing Returns to Scale

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 59 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

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 60 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

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 61 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)

Managerial Economics © 2006/07, Sami Fethi, EMU, All Right Reserved. Production Theory 62 The End Thanks