ECO 134 (4,8) Notes on Economic Modelling Based on Ch 2.1, 2.4, 2.5 & 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: Q d = Q S. 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 model consists of three equations pg. 32 (3.1) The first one is a conditional equation – telling us the equilibrium condition of the market: Q d = Q s 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. The Partial Market Equilibrium Model (PMEM)

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 (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.