MANAGERIAL ECONOMICS 11 th Edition By Mark Hirschey

Production Analysis and Compensation Policy Chapter 8

Chapter 8 OVERVIEW Production Functions Total, Marginal, and Average Product Law of Diminishing Returns to a Factor Input Combination Choice Marginal Revenue Product and Optimal Employment Optimal Combination of Multiple Inputs Optimal Levels of Multiple Inputs Returns to Scale Production Function Estimation Productivity Measurement

Chapter 8 KEY CONCEPTS production function discrete production function continuous production function returns to scale returns to a factor total product marginal product average product law of diminishing returns isoquant technical efficiency input substitution marginal rate of technical ridge lines marginal revenue product economic efficiency net marginal revenue isocost curve (or budget line) constant returns to scale expansion path increasing returns to scale decreasing returns to scale output elasticity power production function productivity growth labor productivity multifactor productivity

Production Functions Properties of Production Functions Production functions are determined by technology, equipment and input prices. Discrete production functions are lumpy. Continuous production functions employ inputs in small increments.

Returns to Scale and Returns to a Factor Returns to scale measure output effect of increasing all inputs. Returns to a factor measure output effect of increasing one input.

Total, Marginal, and Average Product Total Product Total product is total output.

Marginal Product Marginal product is the change in output caused by increasing input use. If MP X =∂Q/∂X> 0, total product is rising. If MP X =∂Q/∂X< 0, total product is falling (rare). Average product AP X =Q/X.

Law of Diminishing Returns to a Factor Diminishing Returns to a Factor Concept MP X tends to diminish as X use grows. If MP X grew with use of X, there would be no limit to input usage. MP X < 0 implies irrational input use (rare). Illustration of Diminishing Returns to a Factor

Input Combination Choice Production Isoquants Technical efficiency is least-cost production. Input Factor Substitution Isoquant shape shows input substitutability. C-shaped isoquants are common and imply imperfect substitutability.

Marginal Rate of Technical Substitution MRTS XY =-MP X /MP Y Rational Limits of Input Substitution MP X <0 or MP Y <0 are never observed.

Marginal Revenue Product and Optimal Employment Marginal Revenue Product MRP L is the revenue gain after all variable costs except labor costs. MRP L = MP L x MR Q = ∂TR/∂L. Optimal Level of a Single Input Set MRP L =P L to get optimal employment. Illustration of Optimal Employment

Optimal Combination of Multiple Inputs Budget Lines Least-cost production occurs when MP X /P X = MP Y /P Y and P X /P Y = MP X /MP Y Expansion Path Shows efficient input combinations as output grows. Illustration of Optimal Input Proportions Input proportions are optimal when no additional output could be produce for the same cost. Optimal input proportions is a necessary but not sufficient condition for profit maximization.

Optimal Levels of Multiple Inputs Optimal Employment and Profit Maximization Profits are maximized when MRP X = P X for all inputs. Profit maximization requires optimal input proportions plus an optimal level of output. Illustration of Optimal Levels of Multiple Inputs

Returns to Scale Evaluating Returns to Scale Returns to scale show the output effect of increasing all inputs. Output Elasticity and Returns to Scale Output elasticity is ε Q = ∂Q/Q ÷ ∂X i /X i where X i is all inputs (labor, capital, etc.) ε Q > 1 implies increasing returns. ε Q = 1 implies constant returns. ε Q < 1 implies decreasing returns. Returns to Scale Estimation

Production Function Estimation Cubic Production Functions Display variable returns to scale. First increasing, then decreasing returns are common. Power Production Functions Allow marginal productivity of each input to vary with employment of all inputs.

Productivity Measurement How Is Productivity Measured? Productivity measurement is the responsibility of the Bureau of Labor Statistics (since 1800s). Productivity growth is the rate of change in output per unit of input. Labor productivity is the change in output per worker hour. Data Uses and Limitations of Productivity Data Quality changes make productivity measurement difficult. Quality changes make productivity measurement difficult.