
1
1) We are given a following production function, Q =80 K  0.25 +(1  0.4) L 0.25 0.25 .
0.4
a) Find out the MRTS.
b) Find out an expression for the expansion path.
c) What is the elasticity of substitution?
(6)
(2)
(2)
2) Given a production function
DepartmentofEconomicsSummer2014
Assignment1(Marks:15)ECO244Section:1
Faculty:HumairaHusain
Question:1(5+5=10)
a)If y f ( x) x 3 6 x 2 7 ,findthelocalminimumormaximumbyapplyingthe
1stand2ndderivativetest.
b)If y f ( x) x 2 3 ,findthelocalminimumormaximumby
ECO244:AppliedMathematics2Fall2010
MOREPRACTICEPROBLEMS
Topic:Integrationbyparts&Integrationbysubstitution
CourseInstructor:(HHn)
Question1:Find:
3dx
2x
dx
dx c)
a) ( x 0) b) 2
( x 2)
x
x 2
x 3
x
dx
d) 2
3x 5
Question:2Find:
(
a) 5e x
3
4x
3
)dx ( x 0
ECO244: Applied Mathematics 2 Fall 2010
PRACTICE PROBLEMS
Topic: Optimization
Course Instructor: (HHn)
Topic: Constrained optimization (Lagrange multipliers)
Q1. Use lagrange multipliers to maximize z = x + 2 xy , subject to the constraint
x + 2y = 5 .
Q2
ECO244:AppliedMathematics2Fall2010
PRACTICEPROBLEMS
Topic:Optimization
CourseInstructor:(HHn)
Topic:Constrainedoptimization(Lagrangemultipliers)
Q1.Uselagrangemultiplierstomaximize z x 2 xy ,subjecttotheconstraint
x 2 y 5 .
Q2.Findthemaximumvalueof Q 10 K
MFE_C03b.qxd 16/12/2005 11:02 Page 194
section
3.2
Compound interest
Objectives
At the end of this section you should be able to:
Understand the difference between simple and compound interest.
Calculate the future value of a principal under annual compou
MFE_C04f.qxd 16/12/2005 11:16 Page 298
section
4.6
Optimization of
economic functions
Objectives
At the end of this section you should be able to:
Use the rstorder derivative to nd the stationary points of a function.
Use the secondorder derivative to c
MFE_C02d.qxd 16/12/2005 11:01 Page 162
section
2.4
The exponential and natural
logarithm functions
Objectives
At the end of this section you should be able to:
Sketch graphs of general exponential functions.
Understand how the number e is dened.
Use the e
Paul R. Krugman
https:/en.wikipedia.org/wiki/Paul_Krugman
Chapter 2
National income accounting and the
balance of payments
International Economics
In international economics we study how the
interactions of national economies influence the
worldwide patt
Macroeconomics assignment on
Could great depression happen again in the US?
ECO  104, SEC25
Prepared For
Kanti Ananta Nuzhat (KnZ)
School of Business and Economics
North South University
Prepared By:
NAME
YASIR ARFAT PRIVEL
ID#
142 1075 030
If the Unite
MFE_C03d.qxd 16/12/2005 11:03 Page 225
3.4 Investment appraisal
The results of this example show that the IRR method is an unreliable way of comparing
investment opportunities when there are signicant differences between the amounts involved.
This is beca
Topic:4 Attributes of Production function
Homogeneity of production function:
There are occasions throughout this book when we use the rules of indices and definitions
of bn. For the moment, we concentrate on one specific application where we see these id
MFE_C05e.qxd 16/12/2005 10:43 Page 400
section
5.5
Constrained optimization
Objectives
At the end of this section you should be able to:
Give a graphical interpretation of constrained optimization.
Show that when a rm maximizes output subject to a cost co
MFE_C06b.qxd 16/12/2005 11:21 Page 437
section
6.2
Definite integration
Objectives
At the end of this section you should be able to:
Recognize the notation for denite integration.
Evaluate denite integrals in simple cases.
Calculate the consumers surplus.
MFE_C09a.qxd 16/12/2005 10:49 Page 553
section
9.1
Difference equations
Objectives
At the end of this section you should be able to:
Find the complementary function of a difference equation.
Find the particular solution of a difference equation.
Analyse t
MFE_C09b.qxd 16/12/2005 10:49 Page 569
section
9.2
Differential equations
Objectives
At the end of this section you should be able to:
Find the complementary function of a differential equation.
Find the particular solution of a differential equation.
Ana
Hand out : ECO244
Topic: Basic attributes of production functions:
Summer 2012
HHn
We introduce two types of production functions:
I. Cobb Douglas
II. CES (Constant elasticity of Substitution)
Cobb Douglas Production function:
The General version: Q AK
MFE_C06a.qxd 16/12/2005 11:22 Page 423
section
6.1
Indefinite integration
Objectives
At the end of this section you should be able to:
Recognize the notation for indenite integration.
Write down the integrals of simple power and exponential functions.
Int
MFE_Z01.qxd 16/12/2005 10:50 Page 594
Appendix 3
Hessians
In this appendix we describe what a Hessian is, and how it can be used to classify the stationary points of an unconstrained optimization problem. In Section 5.4 (page 391) the conditions
for a fun
MFE_C05d.qxd 16/12/2005 10:42 Page 386
section
5.4
Unconstrained optimization
Objectives
At the end of this section you should be able to:
Use the rstorder partial derivatives to nd the stationary points of a function
of two variables.
Use the secondord
A Reply Sent to an Erring Customer
Dear Sir,
Your letter of the 23rd, with a cheque for Rs. 25,000/ on account, is to hand.
We note what you say as to the difficulty you experience in collecting your outstanding
accounts, but we are compelled to remark t