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Mathematics Summary IBA Erasmus Year 1 - Block 1
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Charlotte Soer IBA 2021-2022 MathematicsUnit 1 - Application of Preknowledge
2.2 Mathematical Modelling
Models
Physical Abstract
Static Dynamic Deterministic Stochastic
Static Dynamic
Physical models (static) : fashion models, miniature replicates of buildings, cars.
Physical models (dynamic) : the aerodynamics of a car in a wind tunnel.
Abstract models (static) : the design of a car engine, the age/sex structure of a population.
Abstract models (dynamic) : flow of information in an organisation, how the population
changes overtime.
Deterministic model = the outcome can be determined exactly when all the inputs are
given
Example: P and Q functions in Economics.
Stochastic model = the outcome is calculated with a certain probability, contains random
variables instead of variables
Example: The probability of getting a certain number by throwing a dice.
Economics = a social science which studies how individuals within an economy make
economic decisions on the allocation, distribution and utilisation of
resources in order to satisfy their needs and wants
Economic models
Microeconomics Macroeconomics
Microeconomics = this studies the economic decisions of individual households and firms,
analyses how governments can affect these decisions through the use
of taxes and how individual markets operate
Example: Individual household demand and individual firm supply of good X.
Macroeconomics = this studies the economy as a whole, as well as it studies the
aggregate of all economic decisions
Example: Total planned investment in the economy.
1
,Charlotte Soer IBA 2021-2022 Mathematics
See page 58 for the the circular flow model.
The circular flow model assumes that the economy is composed of the following:
O Three economic agents:
1. Households (consumers)
2. Firms (producers)
3. The government
O Three markets:
1. The goods market
2. The labour market
3. The money market
O Both households and firms operate simultaneously (at the same time)
O Both households and firms have a dual role in the economy due to:
1. Firms are suppliers of goods, but demanders of labour
2. Households are demanders of goods, but suppliers of labour
O Flows 1-4 and 5-6 are a circulation of itself
O Households do not spend all their income -> save -> those savings may be used by
financial organisations to invest
Withdrawals = when money is being taken from the circulation
Example: Taxes.
Injections = when money is being given to the circulation
Example: Subsidies.
2.3 Applications: Demand, Supply, Cost, Revenue
General demand function :
Q = f ( P, Y, Ps, Pc, Ta, A, … )
where;
Q is the quantity demanded of good X
P is the price of good X
Y is the income of the consumer
Ps is the price of substitute goods
Pc is the price of complementary goods
Ta is the taste or fashion of the consumer
A is the level of advertising
Substitute good = a good that can replace another good
Example: Trains and buses.
Complementary good = a good that is consumed with another good
Example: Petrol and cars.
2
, Charlotte Soer IBA 2021-2022 Mathematics
Simplest model for the demand function :
Q = f (P)
In this model, all the other conditions, that are stated before, are constant (also called
ceteris paribus).
Law of demand = a basic economic hypothesis which states that there is a negative
relationship between quantity demanded and price
This means that if the price of a certain good increases, the quantity demanded will
decrease, while all the other conditions remain constant.
Q is plotted horizontally, P vertically.
P = f^-1 (Q) = g(Q)
Use the inverse to go from a Q-function to a P-function.
P = g(Q) can be modelled by a simple lineair equation:
P = a - bQ
where;
a and b are constants
a > 0: when Q = 0, the price per unit is P = a (so the vertical intercept is positive)
(-b) < 0: the price drops by b units for each unit increase in quantity (so the slope is
negative)
P = a + (-b)Q
. . . .
. . . .
Y = c + (m)x
These two mean the same.
Q = a : b because;
P = a - bQ intersects the horizontal axis at the point where P = 0
Substituting the P = 0 into the demand function gives:
0 = a - bQ -> bQ = a -> Q = a : b
3
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