12
Total Derivatives
Now that we know how to find total differentials, we are closer to being able to figure out
how to differentiate a function when the arguments of the function are not independent.
Returning to our earlier example, we are a step closer
8
General-Function Models
In all the models weve dealt with so far, weve been able to solve for the reduced form
equations. This has allowed us to use partial differentiation to figure out the comparative
statics of our model. But to be able to use partia
7.1
Applications to Comparative Static Analysis
We analyse the comparative statics of the equilibrium of economic models that weve
already solved.
Example 44 Market Model
This model is the familiar supply and demand framework in a market producing 1 good.
Lecture 7
Sections 15.1, 15.3, 15.5 from
Fundamental methods of Mathematical Economics, McGraw Hill 2005, 4th Edition.
By A. C. Chiang & Kevin Wainwright are covered.
Separable variables
When the ordinary differential equation (linear or nonlinear) reduce
Lecture 19
Sections 17.1, 17.2 from
Fundamental methods of Mathematical Economics, McGraw Hill 2005, 4th Edition.
By A. C. Chiang & Kevin Wainwright is covered.
Discrete time, differences, and difference equations
Read Section 17.1 page numbers 544-546 fr
Lecture 23
Section 17.3 from
Fundamental methods of Mathematical Economics, McGraw Hill 2005, 4th Edition.
By A. C. Chiang & Kevin Wainwright is covered.
The dynamic stability of equilibrium
The significance of b
Read details from book page 551-554.
Wheth
Lecture 2
Sections 13.1 and 13.2 from
Fundamental methods of Mathematical Economics, McGraw Hill 2005, 4th Edition.
By A. C. Chiang & Kevin Wainwright is covered.
Problem:
Maximize = (1 , 2 ) subject to 1 1 , 2 0, 2 1 , 2 0, 1 , 2 0 . The
Lagrangian funct
Lecture 20
Section 17.3 from
Fundamental methods of Mathematical Economics, McGraw Hill 2005, 4th Edition.
By A. C. Chiang & Kevin Wainwright is covered.
The dynamic stability of equilibrium
The significance of b
Read details from book page 551-554.
Wheth
Lecture 1
Section 13.1 from
Fundamental methods of Mathematical Economics, McGraw Hill 2005, 4th Edition.
By A. C. Chiang & Kevin Wainwright is covered.
Problem:
Maximize = (1 , 2 ) subject to 1 , 2 0, 1 , 2 0 . The Lagrangian function
is = 1 , 2 + (1 , 2
Lecture 24
Section 17.4 from
Fundamental methods of Mathematical Economics, McGraw Hill 2005, 4th Edition.
By A. C. Chiang & Kevin Wainwright is covered.
The Cobweb model
Read details from book.
Question: The cobweb model is essentially based on the stati
Lectures 25
Section 17.5 from
Fundamental methods of Mathematical Economics, McGraw Hill 2005, 4th Edition.
A market model with inventory
Read details of general case from book including table 17.2.
A market model with inventory some numerical examples
No
Lecture 21
Section 17.5 from
Fundamental methods of Mathematical Economics, McGraw Hill 2005, 4th Edition.
A market model with inventory
Read details of general case from book including table 17.2.
A market model with inventory some numerical examples
Not
So, since an implicit function is defined (at least for some neighbourhood of points), we
can use the implicit function rule:
y
x
y
w
2y 3 x + yw
Fx
= 2 2
Fy
3y x + xw
Fw
3w2 + yx
=
= 2 2
Fy
3y x + xw
=
y
y
and
for any implicit function(s) that may be d
Lectures 13& 14
Sections 14.2, 15.1 from
Fundamental methods of Mathematical Economics, McGraw Hill 2005, 4th Edition.
By A. C. Chiang & Kevin Wainwright are covered.
14.2 Overview basic rules of integration
Differential equations: An equation containing
Lecture 24
Section 20.3
Fundamental methods of Mathematical Economics, McGraw Hill 2005, 4th Edition.
By A. C. Chiang & Kevin Wainwright is covered.
1
1. Imagine the following neoclassical growth problem:
Maximize
ln
()
0
Subject to
= , > 0,
(a) Write
Lecture 23
Section 20.1, 20.2 from
Fundamental methods of Mathematical Economics, McGraw Hill 2005, 4th Edition.
By A. C. Chiang & Kevin Wainwright is covered.
Fixed terminal point
The optimal control problem is
0
Maximize
, ,
= (, , )
0 = , = and u(t)
Lecture 15
Sections 15.1, 15.3, 15.5 from
Fundamental methods of Mathematical Economics, McGraw Hill 2005, 4th Edition.
By A. C. Chiang & Kevin Wainwright are covered.
Separable variables
When the ordinary differential equation (linear or nonlinear) reduc
Lecture 16
Section 15.4 from
Fundamental methods of Mathematical Economics, McGraw Hill 2005, 4th Edition.
By A. C. Chiang & Kevin Wainwright is covered.
Solution of first-order linear ordinary differential equations by integrating factor method:
The gene
Review Problem set
Power, Taylor and Maclaurin Series:
1. Determine the radius of convergence and the interval of absolute convergence for the given power
series:
(i)
=0 5
=1
(ii)
=1
(iii)
5
!
2.
Use differentiation to find a power series representa
Is Foreign Investment the most significant influence on Australias external stability?
In Australia, foreign investment has increased, with many more countries investing into the
Australian economy over the past few decades. Australias twenty-four years o
Monetary Economics (Quiz 2A)
Lahore School of Economics
Monetary Economics
Winter Term, 2012
Quiz 2A: B.Sc. III B
Instructions: Answer all questions in the spaces provided below. For full marks, make sure you
write all relevant points and do all necessary
Monetary Economics (Quiz 4A)
Lahore School of Economics
Monetary Economics
Winter Term, 2012
Quiz 4A: B.Sc. III B Suggested Solutions
Instructions:
Answer all questions in the spaces provided below. For full marks, make sure you write all
relevant points
Monetary Economics (Quiz 4B)
Lahore School of Economics
Monetary Economics
Winter Term, 2012
Quiz 4B: B.Sc. III B Suggested Solutions
Instructions:
Answer all questions in the spaces provided below. For full marks, make sure you write all
relevant points
Monetary Economics (Quiz 3B)
Lahore School of Economics
Monetary Economics
Winter Term, 2012
Quiz 3B: B.Sc. III Suggested Solutions
Instructions:
Answer all questions in the spaces provided below. For full marks, make sure you write all
relevant points an
Monetary Economics (Quiz 2B)
Lahore School of Economics
Monetary Economics
Winter Term, 2012
Quiz 2B: B.Sc. III C
Instructions: Answer all questions in the spaces provided below. For full marks, make sure you
write all relevant points and do all necessary
Monetary Economics (Quiz 3A)
Lahore School of Economics
Monetary Economics
Winter Term, 2012
Quiz 3A: B.Sc. III Suggested Solutions
Instructions:
Answer all questions in the spaces provided below. For full marks, make sure you write all
relevant points an
Management, 12e (Robbins/Coulter)
Chapter 1 Management and Organizations
1) A great manager makes a job more enjoyable and productive.
Answer: TRUE
Page Ref: 4
Learning Outcome: Describe the roles of managers and the skills they need to succeed within an
Lahore School of Economics
Macroeconomics I
Problem Set 2 Solutions
Q1. The effect of a government tax increase of $100 billion on (a) public saving, (b) private saving, and (c) national
saving can be analyzed by using the following relationships:
Nationa
Causes and Consequences of Illiteracy in
Pakistan
Researchers:
Muhammad Faizan Altaf
Muhammad Zain Mahmood
Course: Macro Economics
Section A
Session: Winter 2015
Date of Submission: 9 December 2015
Instructor: Dr Waqar Ahmed Wadho,
Lahore School of Econom