Chapter 5 Production Chapter 5 Production analysis and policy analysis and policy

Chapter 5 Production Chapter 5 Production analysis and policy 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.

MPX=∂Q/∂X

***If MPX> 0, TP↑

If MPX< 0, TP↓

3. Average product APX=Q/X.

四 . Law of Diminishing Returns to a Factor

1. Definition: MPX tends to diminish as X use grows.

2.Illustration

– If MPX ↑, then ?

– MPX< 0 then ?

五 . Input Combination Choice

• 1. Production Isoquants**Technical efficiency is least-cost

production.

• 2. Input Factor SubstitutionIsoquant shape ←→ input substitutability.C-shaped isoquants: common ( imperfect substitutability)

3. Marginal Rate of Technical Substitution

MRTSXY=-MPX/MPY

4.Ridge lines: Rational Limits of Input Substitution

六 . Optimal Combination of Multiple Inputs

• Budget Lines– Least-cost production occurs when MPX/PX = MPY/PY and

PX/PY = MPX/MPY

• 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 MRPX = PX 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 εQ = ∂Q/Q ÷ ∂Xi/Xi where Xi is all inputs (labor, capital, etc.) • εQ > 1 implies increasing returns.• εQ = 1 implies constant returns.• εQ < 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.