What is Mathematical Economics? &

How is it different from Econometrics?

Econometrics deals with the study of empirical observations using statistical methods of estimation and hypothesis testing

Mathematical economics refers to the application of mathematics to the purely theoretical aspect of economics analysis with a little or no concern about such statistical problems as the errors of measurement of the variables under study.

What are Variables, Constants & Parameters?

In economic application we may distinguish between three types of equations

1. definitional equation: 𝜋 = 𝑅 − 𝐶

2. behavioral equations: 𝐶 = 75 + 10𝑄

3. equilibrium conditions: 𝑄𝑑 = 𝑄𝑠 or 𝑆 = 𝐼

Types of Functions 1. Linear

2. Quadratic

3. Cubic

4. Rectangular Hyperbolic

5. Exponential Function

Functions with one independent variable: 𝑦 = 𝑓(𝑥)

Functions with two or more independent variables: 𝑦 = 𝑔(𝑥, 𝑦)

Equilibrium Analysis

It is a constellation of selected interrelated variables so adjusted to one another that no inherent tendency to change prevails in a model which they constitute.

The above mentioned equilibrium has relevance only in the context of the particular set of variables chosen, and if the model is enlarged to include additional variables, the equilibrium state pertaining to the smaller model will no longer apply

E.g:

Translating a concept into a Mathematical Statement, where a model can be written as:

𝑄𝑑 = 𝑄𝑠

𝑄𝑑 = 𝑎 − 𝑏𝑃 (𝑎, 𝑏 > 0)

𝑄𝑠 = −𝑐 + 𝑑𝑃 (𝑐, 𝑑 > 0)

The graphical presentation will be

𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 𝑑𝑦

𝑑𝑥 𝑜𝑓 14𝑥3 = 5𝑥3 + 9𝑥3

𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒 𝑑

𝑑𝑥7𝑥4 + 2𝑥3 − 3𝑥 + 37

𝐶 = 𝑄3 − 4𝑄2 + 10𝑄 + 75, 𝐶𝑎𝑙𝑐𝑢𝑙𝑡𝑎 𝑑𝐶

𝑑𝑄

Product Rule:

Find out the derivative of 2𝑥 + 3 3𝑥2

𝐴𝑛𝑠: 18𝑥2 + 18

Divisibility Rule

𝑑

𝑑𝑥

2𝑥−3

𝑥+1=

5

𝑥+1 2