An Assessment of CES and Cobb-Douglas Production
Functions
1
Eric Miller
E-mail: eric.miller@cbo.gov
Congressional Budget Office
June 2008
2008-05
1 Working
papers in this series are preliminary and are circulated to stimulate discussion and
critical comm

PRESENTED BY:
NAME:
REG.NO.
OLOO IDI GEORGE
KM15/2469/09
HEZRON NYARINDO ISABOKE
KM17/2399/09
REBECCAH WAIRIMU WANJIRU
KM17/2405/09
Linear Programming
Learning Objectives
To understand the LP assumptions
Appreciate the Application of LP
Apply the methods

The Simplex Method
Maximize
p= 4y1 + 5y2
where y1 and y2 are two commodities.
The 4 and 5 represent the price per unit of y1 and
y2,
respectively.
The constraints are
2y1 + 1y2 <_ 12
1y1 + 2y2 <_ 16
y1, y2 >_ 0
Simplex contd
The first step is to intr

Homogeneous Production Functions
The terms Economy or diseconomy of scale are
defined with reference to a particular class of
production functions, known as homogeneous
production functions.
A production function is said to be homogeneous of
degree n if

Homogeneous Production Functions
The terms Economy or diseconomy of scale are
defined with reference to a particular class of
production functions, known as homogeneous
production functions.
A production function is said to be homogeneous of
degree n if

Graphical Method
Introduction
An optimal as well as feasible solution to an
LP problem is obtained by choosing from
several values of decision variables X1,
X2.Xn, the one set of constraints
simultaneously and also provides the
optimal ( maximum or minim

THE COBB-DOUGLAS PRODUCTION FUNCTION
1.1 Introduction
The paper describing the Cobb Douglas production function was published in the
journal American Economic Review in 1928. The original article dealt with an early
empirical effort to estimate the compar

The CES Production Functions
The constant elasticity of substitution production functions dominates in applied
research. The parametric structure is
(1)
1/
Y = A [ (aKK) + (1-) (aNN) ]
.
Here 0 < < 1 is the share parameter and determines the degree of su

Grace ,Joseph and Bernard
1
Agenda
Defining Risk and Its Different Types
Explain expected utility
Understanding risk aversion
Management Tools for Risk
Insurance decisions
2
Definition of Uncertainty
In an uncertain
environment, possible
outcomes and thei

Grace ,Joseph and Bernard
1
Agenda
Defining Risk and Its Different Types
Explain expected utility
Understand risk aversion
Management Tools for Risk
Deciding whether to insure
2
Very few business decisions involve certainty in
which an action invariably l

Unconstrained profit Maximization with Two Inputs
The criteria for maximizing a function can be
further illustrated with an agricultural example
using a profit function for corn.
y = f(x1, x2)
where y = corn yield in bushels per acre
x1 = pounds of po

THE COBB-DOUGLAS PRODUCTION FUNCTION
1.1 Introduction
The paper describing the Cobb Douglas production function was published in the
journal American Economic Review in 1928. The original article dealt with an early
empirical effort to estimate the compar

group V
Topic: Risk and Uncertainty
Grace ,Joseph and Bernard
1
Agenda
Defining Risk and Its Different Types
Explain expected utility
Understand risk aversion
Management Tools for Risk
Deciding whether to insure
2
Very few business decisions involve certa

22.1 Introduction
22.2 Classical Optimization and Linear Programming
Linear programming involves the maximization or minimization of a linear function
subject to linear constraints. Unlike classical optimization problems, in which at least one of the
func

1
The CES production function
The homogenous Constant Elasticity of Substitution (CES) production function takes the form
n
o 1/
Q = K +(1 )L
exp(U ), 1, 0 1, > 0, (1)
where K is capital, L is labor, Q is output, and U is an error term satisfying
E[U |K,

Introduction
A macroeconomic production function is mathematical
expression that describes a systematic relationship between
inputs and output in an economy, and the Cobb-Douglas and
constant elasticity of substitution (CES) are two functions that
have b

Euler's theorem is a mathematical relationship that applies to any homogeneous
function. It has implications for agricultural economists who make use of
homogeneous
production functions. Euler's theorem states that if a function is homogeneous of
degree n

A Review of the production
function
The production function is a technical
relationship depicting the transformation of
inputs(resources) into outputs(commodities).
The production function is devoid of
economic content.
A general way of writing a produ

GROUP 6
PRESENTED BY:
NAME:
REG.NO.
OLOO IDI GEORGE
KM15/2469/09
HEZRON NYARINDO ISABOKE
KM17/2399/09
REBECCAH WAIRIMU WANJIRU
KM17/2405/09
Linear Programming
Learning Objectives
To understand the LP assumptions
Appreciate the Application of LP
Apply the

Utility Theory
1
Here the focus is on the Utility Theory. Before we do so lets
consider an example.
Say one option for you is to take a bet that pays $5,000,000 if a
coin flipped comes up tails and you get $0 if the coin comes up
heads.
The other option i

TOPIC
Cost, Profit and Supply Functions
of the Firm
Cost of production
Production Costs: are expenses incurred in
organizing and carrying out production and
are in 2 main categories.
Variable costs (VC) are the costs of production
that vary with the level

COBB-DOUGLAS
PRODUCTION
FUNCTION
INTRODUCTION
Cobb-Douglas is the most
famous of all production
functions used to represent
production processes both
in and out of agriculture.
It was published in 1928 in an empirical
study dealing with the productivity

Maximizing a Profit Function with Two Inputs
The criteria for maximizing a function can be further illustrated with
an agricultural example using a profit function for corn. Suppose that the
production function
for corn is given by
y = f(x1, x2)
where y =

Risk and Uncertainty
Vani K Borooah
University of Ulster
Basic Concepts
Gamble: An action with more than one possible
outcome, such that with each outcome there is an
associated probability of that outcome occurring. If
the outcomes are good (G) and bad (

Homogeneous Production Functions
The terms Economy or diseconomy of scale are
defined with reference to a particular class of
production functions, known as homogeneous
production functions.
A production function is said to be homogeneous of
degree n if

Chapter 6
5/1/16 05:28:37 AM
Uncertainty, Default, and Risk
We maintain the assumptions of the previous chapter:
We assume perfect markets, so we assume four market features:
1. No differences in opinion.
2. No taxes.
3. No transaction costs.
4. No big s

OBJECTIVES
To distinguish between the concept of size and scale
To demonstrate graphically a case where we have
economies of scale, constant returns to scale and
diseconomies of scale
ECONOMIES OF SIZE
It can be looked at in 3 dimensions
1)Seeks to answer

Representing technology in a one
output and two Input case
So far problems faced by a farmer
wishing to determine how much of a single
input to use or how much of a single
output to produce to maximize profits were
addressed.
Suppose instead that two in