Chapter The Theory and Estimation of Production Chapter Outline • The production function • Short-run analysis of total, average and marginal products • Long-run production function • Estimation of the production function • Importance of production functions in managerial decision making Copyright ©2014 Pearson Education, Inc All rights reserved 6-2 Learning Objectives • Define the production function • Distinguish between the short-run and longrun production functions • Explain the “law of diminishing returns” and how it relates to the Three Stages of Production • Define the Three Stages of Production and explain why a rational firm always tries to operate in Stage II Copyright ©2014 Pearson Education, Inc All rights reserved 6-3 Learning Objectives • Provide examples of types of inputs that might go into a production function • Describe the various forms of production functions that are used business analysis • Briefly describe the Cobb-Douglas function and its application Copyright ©2014 Pearson Education, Inc All rights reserved 6-4 Production Function • Production function: defines the relationship between inputs and the maximum amount that can be produced within a given period of time with a given level of technology Q = f(X1, X2, , Xk) Q = level of output X1, X2, , Xk = inputs used in production Copyright ©2014 Pearson Education, Inc All rights reserved 6-5 Production Function • Additional key assumptions – A given ‘state of the art’ production technology – Whatever input or input combinations are included in a particular function, the output resulting from their utilization is at the maximum level – The measure of quantity is not a measure of accumulated output, but the inputs and output for a specific period of time Copyright ©2014 Pearson Education, Inc All rights reserved 6-6 Production Function • For simplicity we will often consider a production function of two inputs: Q=f(X, Y) Q = output X = labor Y = capital Copyright ©2014 Pearson Education, Inc All rights reserved 6-7 Production Function • Short-run production function: the maximum quantity of output that can be produced by a set of inputs – Assumption: the amount of at least one of the inputs used remains unchanged • Long-run production function: the maximum quantity of output that can be produced by a set of inputs – Assumption: the firm is free to vary the amount of all the inputs being used Copyright ©2014 Pearson Education, Inc All rights reserved 6-8 Short-run Analysis of Total, Average, and Marginal Product • Alternative terms in reference to inputs – – – – ‘inputs’ ‘factors’ ‘factors of production’ ‘resources’ • Alternative terms in reference to outputs – – – – ‘output’ ‘quantity’ (Q) ‘total product’ (TP) ‘product’ Copyright ©2014 Pearson Education, Inc All rights reserved 6-9 Short-run Analysis of Total, Average, and Marginal Product • Marginal product (MP) = change in output (Total Product) resulting from a unit change in a variable input Q MPX X • Average product (AP) = Total Product per unit of input used Q APX X Copyright ©2014 Pearson Education, Inc All rights reserved 6-10 Long-run Production Function • Graphically, the returns to scale concept can be illustrated using the following graphs Q IRTS Q X,Y Copyright ©2014 Pearson Education, Inc All rights reserved DRTS CRTS Q X,Y X,Y 6-27 Estimation of Production Functions • Production function examples • short run: one fixed factor, one variable factor Q = f(L)K • cubic: increasing marginal returns followed by decreasing marginal returns Q = a + bL + cL2 – dL3 • quadratic: diminishing marginal returns but no Stage I Q = a + bL - cL2 Copyright ©2014 Pearson Education, Inc All rights reserved 6-28 Estimation of Production Functions • Production functions examples • power function: exponential for one input Q = aLb if b > 1, MP increasing if b = 1, MP constant if b < 1, MP decreasing Advantage: can be transformed into a linear (regression) equation when expressed in log terms Copyright ©2014 Pearson Education, Inc All rights reserved 6-29 Estimation of Production Functions • Production function examples • Cobb-Douglas function: exponential for two inputs Q = aLbKc if b + c > 1, IRTS if b + c = 1, CRTS if b + c < 1, DRTS Copyright ©2014 Pearson Education, Inc All rights reserved 6-30 Estimation of Production Functions Cobb-Douglas production function advantages: • • • • • can investigate MP of one factor holding others fixed elasticities of factors are equal to their exponents can be estimated by linear regression can accommodate any number of independent variables does not require constant technology Copyright ©2014 Pearson Education, Inc All rights reserved 6-31 Estimation of Production Functions Cobb-Douglas production function shortcomings: • cannot show MP going through all three stages in one specification • cannot show a firm or industry passing through increasing, constant, and decreasing returns to scale • specification of data to be used in empirical estimates Copyright ©2014 Pearson Education, Inc All rights reserved 6-32 Estimation of Production Functions • Statistical estimation of production functions – inputs should be measured as ‘flow’ rather than ‘stock’ variables, which is not always possible – usually, the most important input is labor – most difficult input variable is capital – must choose between time series and crosssectional analysis Copyright ©2014 Pearson Education, Inc All rights reserved 6-33 Estimation of Production Functions • Aggregate production functions: whole industries or an economy – Gathering data for aggregate functions can be difficult: • for an economy: GDP could be used • for an industry: data from Census of Manufactures or production index from Federal Reserve Board • for labor: data from Bureau of Labor Statistics Copyright ©2014 Pearson Education, Inc All rights reserved 6-34 Importance of Production Functions in Managerial Decision Making • Careful planning can help a firm to use its resources in a rational manner – Production levels not depend on how much a company wants to produce, but on how much its customers want to buy – There must be careful planning regarding the amount of fixed inputs that will be used along with the variable ones Copyright ©2014 Pearson Education, Inc All rights reserved 6-35 Importance of Production Functions in Managerial Decision Making • Capacity planning: planning the amount of fixed inputs that will be used along with the variable inputs Good capacity planning requires: – accurate forecasts of demand – effective communication between the production and marketing functions Copyright ©2014 Pearson Education, Inc All rights reserved 6-36 Importance of Production Functions in Managerial Decision Making • The intensity of current global competition often requires managers to go beyond these simple production function curves • Being competitive in production today mandates that today’s managers also understand the importance of speed, flexibility, and what is commonly called “lean manufacturing” Copyright ©2014 Pearson Education, Inc All rights reserved 6-37 Importance of Production Functions in Managerial Decision Making • Textbook example: Zara • Spanish fashion retailer • Factories located close to stores • Quick response time of 2-4 weeks compared with competitors’ 4-12 months, which is a significant competitive advantage Copyright ©2014 Pearson Education, Inc All rights reserved 6-38 Global Application • Application: call centers • service activity • production function is Q = f(X,Y) where Q = number of calls X = variable inputs Y = fixed input Copyright ©2014 Pearson Education, Inc All rights reserved 6-39 Global Application • What does this mean for the US? • China: the world’s factory India: the worlds back office Copyright â2014 Pearson Education, Inc All rights reserved 6-40 Summary • The firm’s production function relationship is the relationship between the firm’s inputs and the resulting output • In the short run, at least one of the firm’s inputs is fixed • Production is subject to the law of diminishing returns • In the long-run, a firm is able to vary all its inputs • A firm will try to operate in Stage II Copyright ©2014 Pearson Education, Inc All rights reserved 6-41 ... Total, Average, and Marginal product • Summary of relationship between demand for output and demand for a single input: A profit-maximizing firm operating in perfectly competitive output and input... accumulated output, but the inputs and output for a specific period of time Copyright ©2014 Pearson Education, Inc All rights reserved 6-6 Production Function • For simplicity we will often consider... Short-run Analysis of Total, Average, and Marginal Product • Total revenue product (TRP) = market value of the firm’s output, computed by multiplying the total product by the market price TRP = Q · P