Lecture 2

Topics for today

• Possible problems in Quantitative Analysis Approach

• Variables and their types

• Some basic concepts relating probability

• Derivatives

Possible Problems in the Quantitative Analysis Approach

Problems are not easily identified

Conflicting viewpoints-linear or non linear relationship

Beginning assumptions

Fitting the textbook models

Validity of data

Hard-to-understand mathematics and statistics

Variables and their Types

Ratio scale Two values of a variable say X1 and X2,

(i)X1/X2 (ii)(X1-X2) (iii) X1≤ X2 and vice versa are meaningful quantities. Most economic

variable are ratio scale.

Interval Scale

Satisfies last two properties. Distance b/w two time periods (2012-1990) is meaningful.

But 1990/2012 is senseless.

Ordinal Scale

Only it satisfies the third property of ratio scale. Grades, A,B,C,D. Upper, Middle, Lower.

Example: Indifference curve in Economics

Nominal Scale:

None of the feature of ratio scale. Gender, male, female, marital status, single, married,

divorced, unmarried simply denote categories

Probability

• A probability is a numerical statement about the chance that an event will occur.

• Two basic rules regarding the probability

• 1- The probability, p, of any event is greater than or equal to 0 and less than or

equal to 1. 0≤p≤1

A- 0 means that an event is never expected to occur

b- 1 means that an event is always to occur.

2- The sum of the simple probabilities for all possible outcomes of an activity must be

equal to 1.

Examples:

Quantity Demanded Number of days

0 40 p=40/200 (.20)

1 80 p=80/200 (.40)

2 50 p=(50/200) (.25)

3 20

4 10

Types of probability

Two different ways to determine the probability

• Objective p(event)= number of occurrence of the event /total number of events

• Examples: tossing of a fair coin- it is based on the previous logic.

• Subjective: logic and history are not appropriate. So subjectivity arises.

Examples

• What is the probability that floods will come?

• What is the probability that depression will come in an economy?

• Which party will win the coming election in Pakistan?

• For this opinion polls are conducted and then probabilities are found.

Mutually exclusive and collectively exhaustive events

Mutually exclusive events : If only one of the event can occur on any one trial.

Collectively exhaustive events: They are said to be mutually exhaustive if the list include all the possible outcomes i.e. A U B= S.

Not mutually exclusive

The occurrence of one event does not restrict the occurrence of the other event.

• Examples: Drawing a 5 and drawing a diamond from a deck of cards- it can be both

5 and diamond

Adding mutually exclusive events• We are interested in whether one event or second event will occur.

• When events are mutually exclusive the law of addition is simply as follows.

• P(event A or event B)= p(event A)+ p(event B)

• Drawing spade or drawing a club out of a deck card are mutually exclusive.

13/52+13/52=1/2

• Venn diagram

• Addition of not mutually exclusive events.

• P(A or B)= P(A)+P(B)-P(A and B)

• Venn diagram

• Examples:

• In a math class of 30 students, 17 are boys and 13 are girls. On a unit test, 4 boys and 5

girls made an A grade. If a student is chosen at random from the class, what is the

probability of choosing a girl or a student with A Grade?

• P(girl or A)= P(girl)+ P(A)- P(girl and A)= 13/30+9/30-5/30=17/30

Some Basic Concepts in Mathematics

Derivatives • Definition

• Maxima

• Minima

Rules of Derivatives

1- Constant function rule

2- Power function rule

3- Sum difference rule

4- Product rule

5- Quotient rule

6- Chain rule

7- Inverse function rule

8- Partial Derivatives

Notation

Dependent variable Independent variable

Explained variable Explanatory variable

Predictand Predictor

Regressand Regressor

Response Stimulus

Endogenous Exogenous

Outcome Covariate

Controlled variable Control variable

LHS RHS

Summary

• Quantitative techniques not free from problems

• Probability

• Variables and their types

• Derivative