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ECO 134 (4,8)
Notes on Economic Modelling
Based on Ch 2.1, 2.4, 2.5 & 3.1-3.4 of Fundamental Methods of
Mathematical Economics, A.C. Chiang and K. Wainwright. The slides
should be used along with the text book.
Economic Models
Economic models are designed to study a particular economic phenomenon. Some of these models
are mathematical and some are not. But they almost always contain a set of assumptions which
simplifies the ‘real-world’. In this course, we shall focus on mathematical models.
Generally, economic models that are mathematical will contain equations which will be composed
of: variables [whose magnitude can change; e.g. price (P), profit (π), quantity(Q); there are of
variables:endogenous and exogenous], constants (magnitude does not change, represented by real
numbers) and parameters (letters e.g. a,b,c,d that are used to represent constants). The equations
can be classified into three types: conditional, behavioural and definitional equations.
The objective of a model may be to find the solution(s) of endogenous variable(s) in terms of
parameters, constants and/or exogenous variables. So endogenous variables are those variables
whose solutions we are seeking from the model. And exogenous variables are determined outside
the model; we take their values as given (there will not be any explanation in the model for these
variables).
The Partial Market Equilibrium Model
(PMEM)
Let’s look at the concepts mentioned in the previous slide in relation to an
actual economic model. The PMEM – a very simple economics model studies the economic phenomenon of markets (a place where buyers and
sellers meet to trade). The assumption in this model is that: the good we are
considering has no related goods (substitutes or complements). Hence the
market of the good is not affected by the price of other goods (or other
markets). This assumption allows us to focus on one ‘isolated market’.
Generally, the objective of an equilibrium model is to find the solution of
endogenous variables that satisfy the equilibrium condition. In a market the
equilibrium condition is: Qd = QS . And we need to find the unique market
price and quantity (P*,Q*) that satisfy the equilibrium condition i.e. The
equilibrium price and quantity.
The Partial Market Equilibrium Model
(PMEM)
The model consists of three equations pg. 32 (3.1)
The first one is a conditional equation – telling us the equilibrium
condition of the market: Qd = Qs
The next two are behavioural equations – explaining to us the behavior
of the quantity demanded and supplied (how quantity demanded and
supplied behave in response to changes in price). You should
understand why we have the restrictions (a,b > 0) and (c,d > 0). They
have been explained in the paragraph following the equations.
General Market Equilibrium Model (GMEM)
It is not realistic to assume that a good has no other related good(s). So
the general market equilibrium model has been developed which takes
into account all the related good(s) and the market(s) of the related
good(s). There can be many related goods, e.g. the related goods of tea
might be coffee, sugar, milk etc. If a good has only one related good
then we have the simplest kind of a general market equilibrium model:
the two commodity market model (pg.41). Next slide discusses this
model.
We have two goods (1,2) – pg. 41 (3.12)
Market of good (1)
Equilibrium condition: 𝑄𝑑1 = 𝑄𝑠1
Demand and supply of good (1) is
determined by the following
functions:
𝑄𝑑1 = 𝑎0 + 𝑎1 𝑃1 + 𝑎2 𝑃2
𝑄𝑠1 = 𝑏0 + 𝑏1 𝑃1 + 𝑏2 𝑃2
𝑎1 <0 since 𝑃1 and 𝑄𝑑1 is directly
related i.e. If P increases Qdincreases
(law of demand).
𝑎2 >0 if (1) and (2) are substitutes
𝑎2 <0 if (1) and (2) are complements
Market of good (2)
The equations and restrictions of
this market are left to you as an
exercise.
Functions and Graphs
Concepts from 2.4 and 2.5.
In 2.4 we discussed functions which is a special kind of relation between two
variables – denoted by: y = f (x). This is read as ‘y is a function of x’ which
means the value of y depends on x OR y changes if x changes. Hence y is the
dependent variable and x is the independent variable.
In the notation: y can be replaced by any variable we want to study such as
{price (P), cost (C), quantity (Q) profit (π)} and then x should be a replaced by
a variable that the variable of our study depends upon. E.g. C = f (Q) implies
that the total cost of a firm (C) depends upon the quantity of output
produced (Q) i.e. cost is a function of output. The set of values that the
independent variable can take are called the domain of the function and the
set of the corresponding values of y called images is the range of the
function. Example 5 pg. 19 should help you understand these concepts.
y = f (x) is a function of one variable and y = f (x,z) is a function of two
variables where we are saying that the value of y depends upon the
value of x and z. So we have two independent variables. Similarly a
function may contain many more independent variables.
We have already seen examples of functions of two variables in the two
commodity market model in slide (quantity demanded of good 1
depends upon the price of good 1 and 2).
We can sketch the graphs of functions of one variable on the
rectangular Cartesian co-ordinate, but to sketch the graphs of functions
of two variables we need a three dimensional co-ordinate plane (pg.
26, fig 2.9). We won’t have to sketch 3 dimensional graphs in this
course.