Chapter 5 Production analysis and policy

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 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

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

一.Production Functions 1.Properties of Production Functions 2.Discrete production functions and Continuous production functions

二. Returns to Scale and Returns to a Factor Returns to scale: all inputs ↑→ output effect Returns to a factor: one input ↑→ output effect

三.Total, Marginal, and Average Product 1.Total Product –Total product is total output.

2. Marginal product: the change in output caused by increasing input use. MP X =∂Q/∂X ***If MP X > 0, TP ↑ If MP X < 0, TP ↓ 3. Average product AP X =Q/X.

四. Law of Diminishing Returns to a Factor 1. Definition: MP X tends to diminish as X use grows. 2.Illustration

–If MP X ↑, then ? –MP X < 0 then ?

五. Input Combination Choice 1. Production Isoquants **Technical efficiency is least-cost production. 2. Input Factor Substitution Isoquant shape ←→ input substitutability. C-shaped isoquants: common ( imperfect substitutability)

3. Marginal Rate of Technical Substitution MRTS XY =-MP X /MP Y 4.Ridge lines: Rational Limits of Input Substitution

六. 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

七. 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

八. 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.

九. 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. Uses and Limitations of Productivity Data –Quality changes make productivity measurement difficult.