Introduction
The globalization of organisations in conjunction to the increasing sophistication of
information processing technology leaves managers faced with more new ideas, products and
challenges than ever before (Fritzenschaft, 2013). Thus, managers

Chapter 5: Markets in Action
Demand and Marginal Benefit
Resources are allocated efficiently when they are allocated in the
ways that people value most highly. This occurs when marginal
benefit equals marginal cost. A demand curve is a marginal benefit
cu

Chapter 17 Macroeconomics Overview
Gross Domestic Product
Economic growth is the expansion of the economys production possibilities. It can be pictured as an
outward shift of the production possibilities frontier. Economic growth is measured by the increa

Chapter 12: Monopolistic Competition and Oligopolies
Monopolistic competition is market structure in which there are many buyers and sellers and firms are free
to enter and exit the industry. However, unlike perfect competition, firms produce products tha

Chapter 10: Perfect Competition
Perfect Competition is when there are many buyers and many
sellers so no one person can affect the price of products and
services in the market. Agricultural products can be used in an
example of perfect competition. Perfec

Chapter 9: Output and Costs
Production is the process of transforming inputs (or factors) into outputs (goods and services.) Decisions in
the production process are dependent of the size of the decision and the time frame in which it must be
made. Size is

Chapter 18 Measuring GDP and Economic Growth
GDP Definition
A countrys gross domestic profit is the market value of all the final goods and services produced within a
country in a given time period. Market value must be measured with a standard unit of va

Chapter 11: Monopoly
Market power is the ability to influence the market, specifically the market price, by influencing the total
quantity offered for sale. A monopoly is a firm that produces goods or services for which there are no close
substitutes and

Chapter 19 Jobs and the Price Level
The Labour Force
The working age population is the total number of people aged 16 years and over who are not in jail,
hospital of some other form of institutional care. The labour force can be divided into employed and

Chapter 22 Exchange Rates and the Balance of Payments
Foreign currency is the money of other countries regardless of whether that money is in the form of bank
notes, coins or deposits. The foreign exchange market is the market in which the currency of one

Chapter 20 Classical Model
The Classical Model
The separation of macroeconomic performance into real and nominal parts is the basis of a huge discovery
called the classical dichotomy. The classical dichotomy states that At full employment, the forces that

Chapter 21 Money, the Price Level and Inflation
Money
Money is any commodity or token that is generally accepted as a means of payment. A means of payment is
a method of settling a debt. Money can be used as a means of payment, unit of account or store of

Chapter 25 Fiscal Policy
The National Budget
The annual statement of the outlays and tax revenues of the government of South Africa together with the
laws and regulations that approve and support those outlays and tax revenues make up the national budget.

Chapter 24 The Keynesian Model
Fixed Price and Planned Expenditure
The Keynesian model is used to describe the economy in the very short run. It focuses on the point in time
where the business cycle is at a peak or a trough. This model assumes that firms

Chapter 26 Monetary Policy
The primary objective of South Africas monetary policy is to protect the value of our currency so that the
economy can obtain balanced and sustainable economic growth. Financial stability is achieved through price
stability and

Chapter 8: Organising Production
Firms are institutions that hire factors of production and organise those factors to produce and sell goods
and services. The main goal of any firm is to maximise profit. An indirect result of this goal is that firms aim
t

Chapter 6: Utility and Demand
A households budget places limits on its consumption choices and their
preferences determine which of all its possible choices it makes. A households
budget line describes the limits to its consumption choices. A budget line

Tutorial 8
Solve the following Constrained Optimization Problems
1
1. Given a utility function U=2 x 12 + x 2
subject to usual budget constraint
of p1 x 1 + p 2 x 2=m .
Find the optimal values of the choice variables as well as the shadow
price.
Is the co

Tutorial 6
1. You are given the following utility function:
U ( x ) =x3 + x 210 x +8
x is the consumption of a beverage.
a. Calculate the values of x where the utility derived from its consumption is 0.
Where
b. What is the value of utility when no bevera

Tutorial 5
1. Find the first-order and second-order partial derivatives of the following equations:
a.
y=3 x 31 +8 x21 x 25 x1 x 22+ 4 x 32
b.
z=5 x +3 x y10 x y 3 y
4
2
2
4
2. Calculate the determinant of the following matrices without using Laplace Expa

Tutorial 7
You are presented with 7 firms (A, B, C, D, E, F and G) who compete in the same
market. Each firm sells two goods (goods x 1 and x 2 ). Below, the profit
functions of these firms are displayed.
2
2
2
2
A.
=16 x 1+ 12 x 2x 1x 2
B.
=25 x 1+18 x

Tutorial 2: Cramers Rule,
Jacobian and Hessian
1. Solve the following using Cramers Rule
a.
2 x 5 y =22;
3 x+7 y =2 5
b.
x3 y +5 z=14
2 x + y 6 z=20
3 x2 y+ z =0
c.
10 x2 y=20
8 x+ 3 y + 9=0
d.
x5 y +5 z=5
2 x4 z= y +12
4 x +2 y +5 z=12
2. Determine the f

Tutorial 10 Integration
Calculate the integrals of the following functions to obtain the
objective function
1.
12 x dx
2.
dx2 x
3.
e x 3 dx
4.
3 x 2 ( 2 x 31 ) dx
5.
3 x +2 x
dx
x
6.
x 3 dx
7.
x dx
8.
9.
e x dx
3
(
)
3
( lnx x ) dx
2
x
x
10. ( x +2

Tutorial 9 Inequality Optimization
1. Maximise the following utility function given as U ( x , y )=xy subject to
g ( x , y )=x 2+ y 2 1
2
2
2
2. Maximise U ( x , y )=x y subject to x + y =4, x 0, y 0
2
2
3. Minimise a cost function C ( x , y ) =5 x + 80 x

Change Management
Introduction
The globalization of organisations in conjunction to the increasing sophistication of
information processing technology leaves managers faced with more new ideas, products and
challenges than ever before. This is acknowledge

University Library
Guide to Harvard style of
Referencing
6th Edition
September 2016
Contents
1.
GENERAL INTRODUCTION . 6
1.1 What is referencing . 6
1.2 The Harvard System at Anglia Ruskin University . 7
1.3 Reference list or Bibliography . 8
1.4 Word Cou

Chapter 1: What is Economics?
Microeconomics is the study of choices that individuals and businesses make, the way these choices
interact with markets and the influence of governments.
Macroeconomics is the study of the performance of the national economy

Chapter 3: Demand and Supply
A competitive market is a market in which many buyers and sellers participate so no one buyer or seller can
influence prices. The everyday price of an item is called its money price. The price of one good compared to
another i

Chapter 2: The Economic Problem
The Production Possibilities Frontier is the boundary between the goods and services that can be produced
and the goods and services that cannot be produced. When confronted with limited resources (scarcity)
businesses must