Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics in a Global Economy Chapter 6 Production Theory and Estimation

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University  The production function with one variable  Inputs  Labor, Capital, Land …etc.  Fixed Inputs  Variable Inputs  Short Run  At least one input is fixed  Long Run  All inputs are variable

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University  Total Product TP = Q = f(L)  Average Product The total product divided by the amount of the input used.  Marginal Product The addition to total output resulting from the addition of the last unit of the input. - Marginal product = negative when TP is decreasing - Marginal product = zero when TP is at its maximum - Marginal output = Average product when AP reaches maximum AP L = TP L MP L =  TP  L

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University   Production or Output Elasticity E L = MP L AP L The production function is a table, graph, or an equation showing the maximum output from inputs. The following table is an example (where there is one variable input, the remaining are constant).

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University

 The Law of Diminishing Returns. If equal increments of an input are added, and the quantities of other inputs are held constant, the resulting increments of product will decrease beyond some point; that is, the marginal product of the input will diminish. Note: - The law is an empirical generalization - Technology is assumed to be constant - There is a change in one input and the others are held constant

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Stages of Production

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University  The Optimal Level of Utilization of an Input.  How much of the variable input should we utilize?. The answer: we have to compare between the marginal revenue product MRP of the input and the marginal expenditure on the input i.e., the marginal resource cost MRC.  The Marginal Revenue Product: The amount that an additional unit of the variable input (Y) adds to the firm’s total revenue: MRP L = (  TR/  Q). (  Q/  L) (marginal revenue × marginal product), Or: MRPL = MR. MPL

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University  The Marginal Resource Cost  The amount that an additional unit of the variable input adds to the firms total costs. MRCL =  TC/  L; (wage level in a competitive labor market)  To maximize its profits, the firm should utilize the amount of input where the marginal revenue product equals the marginal expenditures. Optimal Use of Labor  MRPL = MRCL

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Optimal Use of the Variable Input Look at the table. The use of Labor is Optimal When L = 3.50

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Optimal Use of the Variable Input

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University  The Production Function with Two Variable Inputs. Q = f ( X1, X2 );  production function Capital Labor

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University  Isoquants  A curve showing all possible (efficient) combinations of (two) inputs that are capable of producing a certain quantity of output Production With Two Variable Inputs

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University  Isoquants slope is negative, but it may also have positively sloped segments. Positive slope implies that increases in both capital and labor are required to maintain a certain output rate. In this case the marginal product of one or the other input must be negative.  Economic Region of Production  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  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.

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Hence output will increase if less quantities of the input were used. profit maximizing firms will produce on the negatively slopped curves only.

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Marginal Rate of Technical Substitution MRTSMarginal Rate of Technical Substitution MRTS  The rate at which an input can be substituted for another input if output remains constant Q = f ( X1, X2 )  MRTS = - dX2 / dX1; the slope of the isoquant  Since MRTS = - dX2 / dX1, it follows that (given capital and labor are the two inputs)  MRTS = -  K/  L = MPL/MPK

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University MRTS = -(-2.5/1) = 2.5

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Perfect Substitutes Perfect Complements

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University  Optimal Combination of Inputs  Input combinations that can be obtained from a total outlay M is: M =PL. L + PK. K;  The various combinations of capital and labor can be represented by a straight line. This line is called the isocost curve. Its slope is: -PL / PK. -PL / PK.   Isocost lines represent all combinations of two inputs that a firm can purchase with the same total cost. C = total costW = wage rate r = cost of capital

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University  Isocost Lines  ABC = $100, w = r = $10  A’B’C = $140, w = r = $10  A’’B’’C = $80, w = r = $10  AB*C = $100, w = $5, r = $10

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University To determine the optimal combination of inputs, we superimpose the isocost on the isoquant map.

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University  The firm should pick the point on the isocost that is on (tangent) the highest isoquant. i.e, MPL / MPK = PL / PK  Or MPL / PL = MPK / PK ( maximization condition )  If we use more than two inputs the optimal combination of inputs is: MPa / Pa = MPb / Pb =... = MPn / Pn

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Effect of a Change in Input Prices

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University  Returns to Scale  How output responds in the long run to changes in the scale of the firm. Suppose that the firm increases inputs by the same proportion; what will happen to output. a - output may increase by a larger proportion of each input. This is the case of increasing returns to scale. b - output may increase by a smaller proportion than each of the inputs. This is the case of decreasing returns to scale. c - output may increase by the same proportion of each of the inputs. This is the case of constant returns to scale.

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Production Function Q = f (L, K) Q = f (hL, hK) 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  If < h, the f has decreasing returns to scale. Constant Returns Increasing Decreasing Returns to Scale Returns to Scale to Scale

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University  Causes of increasing returns to scale. - geometric relations (technical characteristics of tools) - specialization - probabilistic considerations, the greater the number of customers, customer behavior tends to be more stable, the firm’s inventory may not need to increase in proportion to its sales  Causes of decreasing returns to scale - the difficulty of coordinating a large scale enterprise. large teams seem to be less effective than small teams

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University  The output elasticity ε  To measure whether there are increasing or decreasing returns or constant returns to scale, the output elasticity can be computed.  The output elasticity is the percentage change in output resulting from one percentage change in all inputs.  If ε > 1  increasing returns to scale  If ε < 1  decreasing returns to scale  If ε = 1  constant returns to scale

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University  Cobb-Douglas Production Function Q = AK a L b  Estimated using Natural Logarithms ln Q = ln A + a ln K + b ln L  If a+b = 1constant returns  If a+b > 1increasing returns  If a+b < 1decreasing returns

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University 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 Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University

e.g. Q = 0.8L 0.3 K 0.8 multiply both inputs by 1.01 Q = 0.8(1.01L).3 ( 1.01K).8 = 0.8(1.01) 1.1 L.3 K.8 = 0.8(1.01) 1.1 L.3 K.8 = (1.01) 1.1 (.8L.3 K.8 ) = (1.01) 1.1 (.8L.3 K.8 ) = (1.01) 1.1 Q = (1.01) 1.1 Q = Q = Q  if the quantity of both inputs increases by 1% output will increase by 1.1%.

Managerial Economics Prof. M. El-Sakka CBA. Kuwait University Managerial Economics Prof. M. El-Sakka CBA. Kuwait University