Tutorial 6: Introduction to Differentiation
Question One: Power Rule
Differentiate the following functions:
f ( x )=6 x 55 x 2+ 2
g ( x ) =xe x
f ( x )=
1
x
f ( x )2 lnx+ x 2
Question Two: Using differentiation
Find the slope of the tangent line to each f
Tutorial 11: Integration
Question One: Standard Integration
Integrate the following functions:
( 4 x 32 ) dx
x dx
1
x2 dx
3 e 2 x dx
Question Two: Integration by Substitution
3
Use the substitution
u=x + 4 x+ 2
Use the substitution
u=x 3 +5
Use the su
Tutorial 2: End of Algebra/Beginning of Matrices
Question One: Simultaneous Equations Revision
5 y3 x=16
2 x +3 y=12
xy=8
x+ 2 y =8
2 x + y =3
2
x +2 y =6
2
Question Two: Net Present Value
What is the NPV (at time 0) of the following cash flow? Discount r
Tutorial 7: Differentiation
Question One: Implicit Differentiation
Use implicit differentiation to find
dy
:
dx
y
xy +e =2
lny=2.lnx
xy +lny=9
x y +3 xe =0
2
y
Question Two: Increasing and Decreasing Intervals
Over what intervals are the functions (i) inc
Tutorial 3: Matrices
Question One: Simultaneous Equations with Matrices
Solve these simultaneous equations using the formula
2 x y=8
5 y2 x=11
x2 y=1
3 x+2 y=20
X =A1 B
7 x+ 2 y=15
3 x5 y=9
Question Two: Determinants, Cofactors and Inverses
Calculate the
Tutorial 1: Algebra and Financial Equations
Question One
Solve the following for x:
e
2 x+1
=e
x+2
ln ( 2 x +1 )=2
(x+ 1)(x2) 0
ln ( x 2 y ) =ln 2
Question Two
What is the slope and elasticity at x=2 of the following lines:
2 yx=6
5 y+ 10 x=12
Question Fo
Tutorial 4: End of Matrices and beginning of Calculus
Question One: Eigenvalues and Eigenvectors
For the following matrix:
a) Calculate its eigenvalues.
b) Calculate the corresponding eigenvector for each eigenvalue.
c) State whether it would have an inve
Tutorial 8: End of differentiation/Beginning of functions of several variables
Question One: Taylors Series
Use the first five terms of the given series to estimate the following values:
e 0.1 (exp series)
1
(exp series)
e
series)
ln (1.1) (log series)
1
Tutorial 9: Differentiation of Several Variables cont.
Question One: Total Differentials
Find the total differential of the following functions:
given x = 2, y = 4, dx = 0.1, dy = 0.2
z=2 x2 +3 y 2
2
z=x y y x
2
given x = 4, y = 6, dx = 0.2, dy = 0.3
Ques
Tutorial 10: Langrangian Multipliers
Use the method of Langrangian multipliers to find the quantities x and y which minimise the
function:
u ( x , y )=x 2 +5 y3 xy
subject to the budget constraint: 2 x +3 y=250
Check the second order condition for a minim
BSNS104
Lecture 12, August 5
Today
Price Controls
Why would the govt introduce price controls (maximum or minimum prices)?
What effect does this have on the workings of the market?
Reading
Chapter 6 (first part)
Learning Objectives
To understand the im
Lecture 2 (July 9)
Today: Some key lessons from economics & thinking like an
economist
Reading: Chapters 1 & 2
Learning objectives:
To understand some key economic lessons/principles and be
able to apply these
1
SEMESTER TWO 2016
Are you
proactive, frie
BSNS104
Today
Lecture #4
19 July
Some brief New Zealand economic history
Alternative economic systems (e.g. markets v planning)
Note: We wont start covering trade till next time
Reading
Fortress NZ TV series (on blackboard)
Learning objectives
Begin to un
BSNS104
Lecture 8, July 28
Today
Finish off supply & demand
Elasticity: how responsive are supply and demand to changes in price,
and why is this important
Reading
Chapter 4 (on supply and demand)
Chapter 5 (elasticity)
Learning Objectives
To underst
BSNS104
Lecture #5
21 July
Today: Gains from trade
Reading:
Chapter 3, Interdependence and the gains from trade
Recommended: three short supplementary readings (in Interesting Econ on
blackboard)
Why trade is good for you, Economist article
Lessons for tr
BSNS104
Lecture #6
22 July
Today
Finish off Gains from Trade
Trade in competitive markets (supply and demand)
Reading
Chapter 4, Supply and Demand 1: How markets work
Learning objectives (for today)
Understand the characteristics of a competitive marke
BSNS104
Lecture #7, 26 July
Today
The difference between a movement along the demand curve and a
shift of the curve
Supply
Determination of equilibrium quantity and price
Reading
Chapter Four
Learning Objectives
Understand the difference between a mo
BSNS104
Lecture 10, August 2
Today
Finish elasticity of demand
Elasticity of supply
Applications of elasticity
Can higher agricultural prices be bad news for farmers?
Why would the govt pay farmers to grow fewer crops?
Reading
Chapter 5 (elasticity)
Training
1
Monday
Run 25min
2
Run 30min
3
Run 35 min
Arms and
core 25 min
4
Run 40 min
Ill 5
Run 45min
Arms and
core 30 min
6
Run 60min
7
Run 30 min
Recovery
8
Run 65 min
9
10
11
Recovery
12
13
14
15
Recovery
16
17
18
19
20
Run 50min
Tuesday
Spin
45min
Sw
ECON 202
Macroeconomics
2015 Semester 2
Topic 2: The Short-run Economy A Simple Keynesian Framework
0. Introduction
This topic builds a simple Keynesian model of short-run economic
performance. The model uses ad hoc assumptions about behaviour,
but can pr
ECON202
Lecture 9- Thursday 4th August
Minimum wage causes a price floor and therefor eyou get less employed
people- involuntary unemployment
Labour contracts- if there is a change then there isnt a change of real
wages now itll be over a period of time
BSNS103 tut
Tutor: Shabnam
[email protected]
Thursday 11-12
CO6.15
mid term 1- 10 aug during lecture
mid term 2- 28 september during lecture
actual tut
whoa re WEIRDos? Western, educated ppl (undergrad students)
what was intetersting for yo
Essay Plans
1. How has the definition of consumption changed over time?
Intro- was an econmics/production perspective and now consumers have
possesion motives.
Para 1- what is consumption? More than just a monetary value and
material/physical good, how
ECO202 Notes Lecture 5 Wednesday 20th July
AD- output to inflation relationship
Look up William Phillips economics
CPI inflation and inflation tend to move together
Inverse relationship between infaltiona and unemployment rate-philips
curve
Put up with in
Econ202 lecture 3 Thursday 14th July
Do hand in assignment after the tut as the answers for tut will help for
the assignment
Lending money you lose the real purchasing power with that money
Real is nominal adjusted with inflation
If actual real is bigger
Interco
1. Assess Intercos financial performance. Why is the company a target of a
hostile takeover attempt?
2. What do you think of Intercos stated goals and strategic repositioning
program?
3. As a member of Intercos board are you persuaded by the premi