Department of Economics, North South University
Fall 2013.
ECO244: Applied Mathematics Section. 8, 11 & 14
Instructor: Humaira Husain (HHn) Lecturer, Dept. of Economics
Office: NAC 819
Consultation hours: ST: 12.00pm to 1.00pm and 3.15 pm to 4.15pm
MW : 1
Lecture Notes for Chapter 9
Kevin Wainwright
April 26, 2014
1
Optimization of One Variable
1.1
Critical Points
A critical point occurs whenever the rest derivative of a function is
equal to zero.
ie.
If y = f (x)
dy
Then
= f 0 (x) = 0 is a critical point
North South University
School Business and Economics
Assignment- I ECO244.2: Applied Mathematics II Spring 2016
Topic: Basic attributes of production functions and One variable
unconstrained optimization ,Total Marks:10
Answer all following questions:
Que
Faculty of Business and Economics , Spring
ECO244.2 Applied Mathematics II
Assignment -I Marks: 10
Q1. Suppose the Cobb- Douglas is Q AK L1 .
2016
(5)
Show that is elasticity of output with respect to capital and 1 is
the elasticity of output with respect
North South University, Summer 2016
Eco 244, Section 17
Answer: Quiz 2
1. A firm has 2 products, 1 and 2 which are sold in separate markets with the demand
schedules:
1 = 20 41
Firms total cost schedule is:
2 = 10 42
= 8 + 12 + 22 + 51 2
a. How much shou
North South University, Summer 2016
Eco 244, Sec 17 & 18
Answer: Assignment 1
1.If the firm faces the demand schedule: = 225 0.122 and the cost to produce a good is zero:
a. Find out the MR (Marginal Revenue), MC (Marginal Cost), AR (Average Revenue) and
North South University, Summer 2016
ECO 244, Section 17 and 18
Assignment 2
Due Date: 21 June, 2016
1. Find extremum values of the following functions. Check whether they are maxima or
minima.
a. = 32 + 3 + 62 + 9
b. = 22 + 6 2 6 + 8 + 12 2
2. Use the Lag
North South University, Summer 2016
Eco 244, Section 18
Answer: Quiz 2
1. Use the Lagrange multiplier to find the stationary values of z and determine whether the
stationary value of z is minimum or maximum.
= 2 + subject to 10 + + = 11
Answer:
= 2 + +
Eco 244, Sect 18
Answer: Quiz 1
1. Find the optimum value(s) of y:
1
= 3 5 2 + 9 + 9
3
Mark the maximum and minimum values of y in your answer. For that you need to do
second derivative test
Answer:
F.O.C.
1
= 3 3 31 5 2 21 + 9 = 0
=> 2 10 + 9 = 0
=> 2 9
North South University, Summer 2016
Eco 244, Section 18
Name:
NSU ID:
Quiz 3 (20 minutes)
Date: July 17, 2016
Total Marks: 10
1. Verify that the following differential equation is exact and, solve by the four step procedure:
3 2 + ( 3 + 2) = 0
2. A televi
North South University, Summer 2016
ECO 244, Section 17 and 18
Assignment I
Due Date: June 03, 2016 (Friday) before the midterm starts
1. If the firm faces the demand schedule: = 225 0.122 and the cost to produce a good is zero:
a. Find out the MR (Margin
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
Handout:ECO244
Topic:Basicattributesofproductionfunctions:
Summer2012
HHn
Weintroducetwotypesofproductionfunctions:
I. CobbDouglas
II. CES(ConstantelasticityofSubstitution)
CobbDouglasProductionfunction:
TheGeneralversion: Q AK L ,thisfunctionshowsconstan
Lecture Notes for Chapter 13
Kevin Wainwright
April 26, 2014
1
Introduction
This chapter covers two major topics. The rst is nonlinear programming, or Kuhn-Tucker conditions. Here we extend the the techiques
constrained optimization covered in chapter 12