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Welcome toPMBA0608: Economics/Statistics Foundation
Fall 2006Session 4: September 6
Study
Chapters 1 through 4 of Mankiw Chapters 1 through 3 of Mendenhall,
Beaver and Beaver Send me your questions I will do one or all of the following
Answer you privately Publish the answer to your question on line Answer your question in our next class
Discuss Assignment 1
1) Problem 5, Page 16 of Mankiw $5 million is sunk cost MC = $1 million MB = $3 million MB>MC should complete the
project As long as MB >MC, the answer is
the same
Discuss Assignment 1
2) Problem 8, Page 17 of Mankiw The new bill will increase the incentive for
economic activity. Efficiency may increase for two reasons
Resources are not wasted as much as before If tax rates go down current work force will
have an incentive to work harder Equity may decline as
Current workers’ tax rate may go down Some current welfare recipients may not be
able to find jobs the pay a much as welfare.
Discuss Assignment 1
3) The discussion on the connection between the article and the economic principle should be well developed.
Discuss Assignment 1
4) Question 1.2, Page 10 of Mendenhall, Beaver and Beaver Population of interest is the population of the
measurements of the appraisals of the land by all experienced appraisers.
Population is large but it does exist, so it is not conceptual.
Populations are different Buyers may underestimate. Sellers may over
estimate…. More than one appraisal should be used.
Discuss Assignment 1
5) Question 1.7, Page 10 of Mendenhall, Beaver and Beaver Population of shopper opinions (in favor or
opposed background music) Not possible to examine the entire population as
future shoppers are not known. No, sample percentages will not be the same as
population percentage but it will serve as an estimate as population percentage.
Back to Chapter 2 of Mankiw: Macro/micro economics
Macro = big Picture = Forest Focuses on the aggregate
markets Micro = small picture = tree
Focuses on individual markets
Which of the following is a macro/micro topic?
The effect of tax policy on the price of gas in Ohio.
The effect of tax policy on the general price level in Ohio.
The effect of agricultural subsides on the income of farmers.
The effect of agricultural subsidies on income tax rates in the U.S.
Which of these topics will be covered in a macro/micro economics course?
The impact of the 1987 market crash on consumers’ spending.
How a higher rate of inflation alters the distribution of wealth and income.
The effect of war in Iraq on the price of oil. The effect of the increase in the price of
oil on the overall unemployment rate.
Normative/Positive Statements
Positive Statement is descriptive But not necessarily true can be tested for validity Example
Normative statement is an opinion can not be tested for validity Example
Note
A normative economic statement that is not backed up by positive statement is worthless.
Chapter 2 of Mendenhall, Beaver & Beaver (Stat)
Which of the following is (are) a Variable?1. Interest rates 2. My name 3. My weight 4. Price of gasoline
1, 3 and 4. Variable = characteristics that change over
time or across different objects.
Which of the following is (are) experimental unit (s)?
1. Jackie2. United States3. Unemployment rate4. A PMBA student 1, 2 and 4 Experimental unit = an individual or
object on which a variable is measured.
Which of the following variables is (are) qualitative?
1. Gender of students in this class2. Height of students in this class3. Seasons4. Cost of production 1 and 3 Qualitative variables can be
categorized but not measured.
Which of the following variables is continuous?
1. The number of your children over time.
2. Your weight over time.3. The year 2 Continuous variable can assume all
of the infinitely many values corresponding to a line interval.
Can a qualitative variable be continuous?
No. Gender
Male = 1 Female = 2
Budget deficit in billions of dollars. (What kind of graph is this?)
-600
-500
-400
-300
-200
-100
0
100
2000 2001 2002 2003 2004 2005
Prime rate in the US(What type of graph is this?)
Make sure
You know how to create a graph using Excel or any other program. Highlight your columns that contain data
and click on Chart Wizard.
You know what type of graph is more appropriate in different scenarios and why?
Histograms are used to show relative frequencies: Example
Individual Number of children
Mark 1
Jan 0
Mary 0
Jackie 3
Total 4
Histograms are used to show relative frequencies: Example
Number of children Relative frequency
0-1 ¾ = 75%
2-3 ¼ = 25%
Histograms are used to show relative frequencies: Example
Relative frequency
Number of kids01 2 3
75%
25%
Do you use a bar graph or a histogram in each of the following situations?
1. You want to compare heights of 10 individuals in this class.
Bar
2. You want to compare total revenues of five different companies.
Bar
3. You want to compare numbers of companies that make from 0 to $10,000; from $10,000 to $20,000; from $20,000 to $30,000 and so on.
Histogram
Check out the following interactive site for creating histograms
http://www.shodor.org/interactivate/activities/histogram/?jv=1.4.1_02&jb=MSIE
The arithmetic mean Helps us describe the sample (xbar)or the
population (μ) The sample mean, xbar is
xbar = (x1 + x2 + . . . + xn) / n . Mean member of US households
= total population /number of households In 2003 =2.57
Mean household income in the US = total income/households In 2003 =$59,067
What is median?
50% of observations fall below median and 50% of observations fall above median
In 2003 median income of a household in the US was $43,318 50% of households received less than
$43,318. 50% of households made over $43,318.
Mean /medianNote: Area under the curve is 100%
What does this tell you about income equality in the US?
$43,318 = median
$59,067 = mean
Relative frequency
Income household
50% of households
50% of households
Which nation has more poor households?
Mean income is the same
Relative frequency
income$60,000
Relative frequency
income60,000Nation A Nation B
Need a measure of dispersion in order to describe our data better
1. Range Maximum value – minimum
value Makes more sense for small
samples
Are these two samples the same? Weight sample 1
Four observations: 100, 110, 170, 200 Mean = 145 Median = 140 Range = 100
Weight sample 2 Eight observations: 100, 115, 125, 130, 150,
160, 180,200 Mean = 145 Median = 140 Range= 100
According to mean, median and range, yes.
Measures of dispersion: (2) Mean Absolute Deviation (MAD)
= mean of absolute values of deviation of each observation from mean
Weight of individual (wi) in Sample 1 |wi- wbar|
100 45
110 35
170 25
200 55
•MAD = (Σ |wi- wbar|)/n) =(45+35+25+55)/4= 40
What is MAD for Sample 2?
Weight sample 2 100, 115, 125, 130, 150, 160, 180,200 Mean = 145
MAD = 27.5 MAD in sample 2 < MAD in sample 1 What does this mean? The distribution of Sample 2 is tighter
Measures of dispersion:(3) Variance
In population = Σ(wi- wbar)2/n In sample = Σ(wi- wbar)2/n-1 Calculate the variance in Sample 1
and Sample 2 Variance in Sample 1 = 2300 Variance in Sample 2 =1150
Standard deviation is the square root of variance.
Empirical Rule If the sample is very large
population If the relative frequency distribution is
bell shaped Then
68% of observations fall within one standard deviation from the mean
95% of observations fall within two standard deviation from the mean
Empirical Rule
Suppose standard deviation is 30
weight145
68%
Rela. frequency
95%
175
115
205
85
In our example, both samples had the same mean and Sample 1 had a higher standard deviation
So, Sample 1 was more variable. But what if two samples have different
means? How do we measure which one is more
variable? Coefficient of variation = (standard
deviating/mean) * 100 The higher the mean, the ______ the CV. The higher the standard deviation, the _____ the
CV.
Bivariate data
Sometimes we want to focus on two variables at the same time
Example 1 Are women earning less than men for
doing the same job? One of my students wanted to answer
this question Collected a sample of area attorneys at
different stages of their careers
Bivariate data
The study of earning gap
Years after graduation
EarningsMale
Female
Bivariate data: relationship
There is economic theory suggesting that there is a negative relationship (trade off) between inflation and unemployment
Collect data on both variables
Bivariate data: relationship Plot your points
Unemployment rate
Inflation
1990
1991
1992
1993
1994
•What type of relationship is there between inflation and unemployment?
Is there a measure of correlation between two variables (x and y)?
Yes? Correlation coefficient (r)
Takes a value between -1 to +1 If r =0 x and y are not correlated If r = -1 x and y are perfectly and
indirectly correlated If r = +1 x and y are perfectly and
directly correlated
How do we calculate r?
Formula on Page 66 of stat book Excel calculates it automatically Under fx type
=CORREL (A2:A10;B2:B10)
Suppose you are told that your salary is at 70th percentile in the distribution of salaries in your organization. What does this mean?
70% of other salaries in your organization are lower than your salary and 30% are higher than your salary.
Another measure of relative standing is z-score
Measures the number of standard deviations between an observation an the mean of the set.
Example If z = 2 Then your salary is lies 2 standard
deviations above the mean Formula on page 71 of Stat Book
Note:
Sections 2.5 and 2.13 of this Chapter are dropped.
Assignment 2 Due: On or before September 161. Problem 3, Page 59 of Mankiw2. Problem 6. Page 60 of Mankiw3. Application 2.6, Page 24 of Mendenhall, Beaver and
Beaver (Use Excel or similar program. Explain why one presentation is more effective.)
4. Application 2.12, Page 33 of Mendenhall, Beaver and Beaver (Use Excel or similar program.)
5. Exercise 2.47, Page 67 of Mendenhall, Beaver and Beaver (Use Excel or similar program.)
Notes:1) Each question has 4 points.2) Don’t hesitate to contact me.
