Transcript Aug. 29

Economics 214
Lecture 2
Mathematical Framework of
Economic Analysis Continued
Linear Models
The equations of our model are in the linear
equation form.
y  a  bx  cz where
y  dependent var iable
x, z  independen t var iables , and
a, b, c  parameters
Linear Equations
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Systems of linear equations can be solved
by linear algebra or matrix algebra.
Matrix algebra can tells us if our system has
an unique solution.
Matrix algebra can be used to do
comparative statics.
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How does an equilibrium value change when
one of the exogenous variables change. i.e. how
does equilibrium national income change when
investment changes.
Differential Calculus
Suppose the events of the past several months
cause consumers in our economy to decide to
increase their rate of saving. i.e. reduce β in
our consumption function. We may ask
ourselves how this change in behavior affects
the equilibrium national income in our
economy. To analyze this problem we will have
to make use of differential calculus. In
Economics 111, we called this event the
Paradox of Thrift.
Extreme Values
Total Output
120
100
Output
80
60
Output
40
20
0
0
5
10
15
Labor
20
25
Extreme Value
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From the previous graph, we might ask
ourselves at what level of employment
is output maximum?
This is an example of an extreme
value problem.
We need differential calculus to
solve this problem.
Production Example
Isoquant and Isocost
50
Input B
40
isocost3
isocost2
30
isocost1
Isoquant
20
10
0
1
2
3
4
5
6
Input A
7
8
9 10
Constrained Optimization
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In microeconomics, we learned we could
produce given level of output with various
mixtures of the inputs.
We asked what combination minimized the
cost of producing a given level of output.
This is a constrained optimization
problem.
We need differential calculus to get a
solution.
Dynamic Analysis
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Dynamic Analysis focuses on models
in which time and the time path of
variables are explicitly included.
Difference equations focuses on
models in which time is treated as a
series of distinct periods.