1
Economic applications of dierentials and total dierentials
April 9, 2012 dier.pdf
1.1
The basic theory
The dierential dy is a measure of how much y changes
Dierentials are very useful for deriving isoquants, indierence curves, and
other boundaries of le
1
Derivation of the cost function: The production managers problem
revised April 12, 2012
Lets consider the cost function in a bit more detail. Where does it come
from?
Imagine that you have graduated from C.U. (maybe hard to imagine given
that you are ta
1
Economic Examples of Partial Derivatives
partialeg.tex April 3, 2012
Let start with production functions. A production function is one of the
many ways to describe the state of technology for producing some good/product.
Assume the rm produces a single
1
Economic applications of total dierentials
April 26, 2012
Total dierentials are very useful for getting a better understanding of a lot
of the common economic graphs. Graphs such as isoquants, indierence curves,
and isocost lines.
Lets start with produc
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1
Partial Derivatives
April 2, 2012
While derivatives are of interest to economists, as our previous examples
show, they are often not applicable because most of the mathematical functions
used to describe economic concepts are multivariate functions.
E.g
TEACHING OF APPLICATION OF MATHEMATICAL METHODS IN ECONOMICS
ORGANIZATION IN BANKING INSTITUTION OF HIGHER EDUCATION IN LATVIA
Asoc. prof. Gaida Pettere, asoc. prof. Ivars Brivers,
M. oec. Inese Vingre-Ruskule
The Latvian Banking Institution of Higher Edu
1
Optimization
optim-start.tex April 26, 2012
1.1
A start
I am going to start by solving some problems that we are familiar with. I
will add theory after we get a sense of the issues involved in optimization. We
currently have enough tools to solve a lot
1
Economic Models and Static Analysis
equilibrium revised February 28, 2012, equilibrium.tex
Equilibrium dened
denition
static equilibrium and comparative statics
dynamic equilibrium
some background
the continuum from partial to general equilibrium models
derivative.tex March 8, 2012
1
1.1
Economic Applications of Dierential Calculus
The concept of a derivative
slopes, continuity, limits and derivatives
1.2
Rules of dierentiation
functions of single variables
economic applications
marginal revenue, margina
Tour-syl.nb
1
A Brief Tour of Mathematica
First, consider the Cobb-Douglass production function
x = f(k,l) = k^a l^b
where x is units of output, k is units of
capital services and l is units of labor
Null
Now let's use Mathematica to graph this function f
1
Economic Application of Derivatives
deriv-applic.tex and .pdf April 5, 2007
In earlier notes, we have already considered marginal cost as the derivative
of the cost function. That is
mc(x) = c0 (x)
How would you dene, in words, the cost function and the
1
Elasticities
elasticity.tex April 5, 2012
One of the problems with marginal product functions is that the marginal
product is sensitive to the units in which x, l, and k are measured. For example,
changing the ouput from pounds of stu to tons of stu wil
1
Consider higher-order derivatives
April 12, 2007
higher.tex
We have dened the cost function, c = c(x), and the marginal cost function
as mc(x) = c0 (x).
Since mc(x) is itself a function, one could take its derivative. E.g.
dmc(x)
dx
mc0 (x) = c00 (x)
d
1
Rules for Dierentiation
rules.tex and .pdf April 3, 2007
Deriving the derivative of a function using the basic denition of a derivative
is revealing but is typically quite tedious when one wants to dierentiate a
complicated function. So typically when w
1
Theory of the rm in a nutshell
Oct 24, 2008
You need to read all of the chapters on the theory of the rm in your microeconomics book (introductory book such as KW, or your intermediate micro
book)
Like the consumer, the rm wants to do the best it can su
World Bank
Skopje, October 26-28, 2011
Input-Output Analysis
1
Outline
Input-Output Definitions
Simplest form of Input-Output Analysis (a quick
review)
Input-Output Analysis with Examples
Input-Output Multipliers
Power and Problems of Input-Output Analysi
UNIVERSITY OF COLORADO, BOULDER
DEPARTMENT OF ECONOIVIICS
QUANTITATIVE
ANALYSIS 68.08
A QUICK INTRODUCTION TO TI
MA THEMA TICA FOR WINDOWS ;
Notes from the user’s guide
for Microsoft Windows
TA: JUAN 5'. BL YDE
Fail 1995
IV Initial tips:
oMathemat
Math 129 An Input-Output Analysis Example
Suppose that the table below gives the interaction between two sectors in a hypothetical
economy, and that we are asked to determine what the total outputs of the two sectors
should be in order to meet predicted f