(solution) Discussion Board Week 2 1. "Estimating Demand and Its

(solution) Discussion Board Week 2 1. "Estimating Demand and Its

Discussion Board Week 2

1.   “Estimating Demand and Its Elasticities” and Statistical Estimation of the Demand Curve
ECO550 Week 2 Scenario Script: Models of Supply and Demand, and Non-Price
Determinants of Each
Slide # Topics Slide 1 Scene 1 Narration An older cottage style family run
business (Katrina?s Candies)
Slide 2 Scene 2
Herb and Maria are in Herb?s office
reviewing the demand model Herb and
Renee formulated and discussing the
data Maria compiled for estimating the
model. ECO550_2_2_Herb-1:Good day,
Maria. Thanks for responding so
quickly to my request for data.
ECO550_2_2_Maria-1:Hello, Herb.
No problem, I am assigned to the team
to help with the data so when I received
your email, I started looking for the data
immediately.
ECO550_2_2_Herb-2:Fantastic. Let?s
get started by reviewing the data you
compiled. Then you can explain how I
can use Excel to estimate the model.
ECO550_2_2_Maria-2:First, would
you review the model with me? I need
to understand how the model is setup.
ECO550_2_2_Herb-3:Oh, okay.
Recall from our team meeting that the
team?s task is to provide Ken with
information he can use to respond to the
Board of Directors? request to expand
Katrina?s into international markets.
ECO550_2_2_Maria-3:Yes, I do recall
that.
ECO550_2_2_Herb-4: Renee and I
met after the team meeting and decided
the best way to proceed is to build a
model of the demand for Katrina?s new
sugar-free-chocolate candy then use the
model to predict the demand. In the
model, the quantity of Katrina?s sugarfree-chocolate candy is the dependent variable and there are five
independent variables. Show the 5 variables on projector:
Price of Katrina?s Sugar Free
Chocolate;
Price of the substitute good;
Complementary good;
Income;
Number of buyers in the market. ECO550_2_2_Maria-4: Very
interesting! Could you please go over
these five independent variables with
me?
ECO550_2_2_Herb-5: Sure! The first
independent variable is theprice of
Katrina?s sugar-free chocolate. The
model must include the price of sugarfree-chocolate; otherwise, there is no
demand curve.
Next is the price of the substitute good.
In the case of chocolate, caffeinated
coffee is the substitute good. Then there
is the complementary good; for
Katrina?s model, we selected bottled
water; therefore the price of bottled
water is the next independent variable.
Income is another variable typically
included in a demand curve. For our
model, we selected median household
income.
Last, since we are interested in the
market for Katrina?s sugar-freechocolate, the number of buyers in the
market is included as an independent
variable.
ECO550_2_2_Maria-5: Thanks for
going over that. You and Renee were
certainly busy!
ECO550_2_2_Herb-6: Yes, we were! I
am going to use the data you provided
to estimate the model to see if we
selected the right set of determinants.
Then, Renee and I can use the model to
develop other measures that tell us more
about the market for Katrina?s sugarfree-chocolate. Slide 3 Scene 3
In Herb?s office to explain concept of
estimation
Shows the model on the projector ECO550_2_3_Maria-1:You mentioned
a lot of terms that are sort of new to me.
In this case what does ?estimate? mean?
ECO550_2_3_Herb-1:Here this may
help with the concept of estimation,
here?s what the finalized model should
look like. We will talk about the actual
estimation process in a few moments.
ECO550_2_3_Maria-2: I?m not too
sure of what this model contains, could
you explain further? Show on the projector: The notation on
the left side of the equal sign,
Qsubscript-d-k-s-f-c represents the
dependent variable ECO550_2_3_Herb-2: Gladly! The
notation on the left side of the equal
sign, Q subscript-d-k-s-f-c represents
the dependent variable which is the
quantity of Katrina?s sugar-freechocolate candy. The terms on the
right-side of the equal sign are the
independent variables I just explained.
ECO550_2_3_Maria-3: That makes a
lot more sense now! Where does the
estimation process come into play?
ECO550_2_3_Herb-3: Estimating the
model means to find values for the
coefficients, which in our model are the
?b?s?. Coefficients are numeric values
that indicate how much the quantity of
the dependent variable will change as
independent variables change. The data
you compiled will be used to calculate
the coefficient values. This information
is important as it helps determine the
quantity demanded of sugar-freechocolate changes in response to
changes in the independent variables
included in the model.
ECO550_2_3_Maria-4:Okay, got it.
You?ve used the terms ?dependent
variable? and ?independent
variable?while explaining the model.Could you provide me with some
insight on these terms?
ECO550_2_3_Herb-4:Yes, of course.
A dependent variable is a variable that
changes value when changes occur in
some other variable. The term
?variable? is used to capture the fact
that the value can change. On the
flipside, an independent variable is a
variable that impacts or causes a change
in the dependent variable.
ECO550_2_3_Maria-5:Okay, Herb, I
think I understand now. Can you give
me examples of dependent and
independent variables that are different
from Katrina?s sugar-free-chocolate
candy?
ECO550_2_3_Herb-5:Yes I can,
Maria. I believe a good example is
umbrellas. Think about umbrella sales,
when the weather changes from clear to
rainy, people buy more umbrellas. This
is especially prevalent with people who
may have left their umbrellas at home.
In this example, the quantity of
umbrellaspurchased changes when the
weather changes, so it is quite easy to
identify the dependent and independent
variables in this example. The
quantity of umbrellas sold is the
dependent variable while rain is the
independent variable.
ECO550_2_3_Maria-6:That?s
anexcellent example, Herb. I understand
exactly how the model functions now.
The independent variables you and
Renee selected will explain what caused
or is causing the demand for Katrina?s
sugar-free chocolate candy to change.
ECO550_2_3_Herb-6: Yes, Maria,
that?s right. Using the data you
provided, we are going to see how well the model we formulated explains the
demand for sugar-free-chocolate candy. Slide 4 Scene 4
Herb?s office to go over the data Maria
collected. ECO550_2_4_Herb-1: Maria, could
you update me on the data you collected
for this project?
ECO550_2_4_Maria-1:I located most
of the data you requested involving the
number of sugar-free-chocolates
Katrina?s sold since introducing the new
candy and the selling prices. You will
notice that this data is available in our
accounting database. However, I had to
search outside of the database for other
data.
ECO550_2_4_Herb-2: What other data
did you need to acquire and how did
you go about doing this search?
ECO550_2_4_Maria-2:I needed to
find the prices of coffee and I simply
did a Google search and looked for
reliable sources of information
pertaining to concepts such as the price
of coffee. Insert the URL for the Census Bureau Show a pictures of the Strayer Resource
Center ECO550_2_4_Herb-3: Okay, that
leaves data on the price of water,
median income and the number of
buyers. Where did you retrieve data for
these independent variables?
ECO550_2_4_Maria-3: Well, I
retrieved median household income
data from the U.S. Census Bureau
website. Census data is easy to find,
reliable and easy to use. I just went to
the Census Bureau website, typed in the
key term, ?household income,? then
selected the median household income
for the appropriate years. ECO550_2_4_Herb-4:Did you know
you could have retrieved data on
income and other variables by going
through Strayer?s Global campus?
Resources Center?
ECO550_2_4_Maria-4: No, I didn?t
know that, Herb. Isn?t access to
Strayer?s Resources Center restricted?
ECO550_2_4_Herb-5:Yes, only
enrolled students, faculty and staff and
subscribers can use the Resource
Center. However, since there are so
many Strayer educated employees here
at Katrina?s, we have free access to the
Resource Center.
ECO550_2_4_Maria-5:That?s great
news, Herb!
ECO550_2_4_Herb-6: I agree! So in
the future when you need to search for
data, check out the Resource Center
first.
Slide 5 Scene 5
Herb?s office to go over the data Maria
collected and investigate briefly the
Resource Center ECO550_2_5_Maria-1:The Resource
Center seems very easy to use. I?ll
definitely use it next time I need to find
data. Let?s see where we are with the
data I compiled. I told you about data
for the quantity and price of Katrina?s
sugar-free-chocolate candy, data on the
price of caffeinated coffee and median
household income. Now, I have to tell
you, I had a problem finding price data
for bottled water and finding the
number of consumers who purchase
chocolate candy.
ECO550_2_5_Herb-1:Oh, no. Does
this mean we have to change our
model?
ECO550_2_5_Maria-2:That depends
upon whether you accept the proxy
variables I found and recommend using them to ?estimate? the model.
ECO550_2_5_Herb-2: I?m not quite
sure about these ?proxy variables.?
Could you elaborate on this concept?
ECO550_2_5_Maria-3: Sure thing!
When data is not available for a
variable, analysts often use data from
another variable to capture the same
relationship as the original variable. It is
this substitute variable that is referred to
as ?proxy variable.?
ECO550_2_5_Herb-3: Does data for
proxy variables work as well when the
model is estimated?
ECO550_2_5_Maria-4:That depends,
in some cases the answer is yes and in
others it is no. In order to determine the
answer, you are required to estimate the
model to find out. Keep in mind that if
the proxy data does not work, then the
variable is dropped from the model. Slide 6 Scene 6
Herb?s office to go over the data Maria
collected. Show data table of per capita
consumption of bottled water. ECO550_2_5_Herb-4: Thanks for the
clarification on this subject. We can
continue with our updates on the data
you collected.
ECO550_2_6_Maria-1:Again, since I
was unable to locate the price of bottled
water, I had to add a proxy variable.
The data I used dealt with the per capita
consumption of bottled water.
ECO550_2_6_Herb-1:The data I?m
looking at shows the per capita
consumption of bottled water, by gallon
over twelve years. I think this data
works well as a proxy. What data did
you find to proxy the number of
buyers?
ECO550_2_6_Maria-2: I had to think
hard about a number of buyers proxy. In the end, I found a good proxy in a
Department of Commerce report, it is
called ?Current Industrial Reports.? The
proxy I used dealt with the
confectionery exports of domestic
merchandise measured in pounds per
year.
ECO550_2_6_Herb-2:This data also
serves as a great proxy. Of course, I?ll
have to consult with Renee to get her
opinion because she?s the one
mentoring me on this project. But I?m
fairly certain Renee will agree with me.
ECO550_2_6_Maria-3:Okay! Here?s
the data I compiled from our accounting
records.
ECO550_2_6_Herb-3: Great! Now,
can we create the data set in Excel and
then estimate the model?
ECO550_2_6_Maria-4:That?s correct!
I have some great resources that will
help you review how to create datasets
in Excel and how to use Excel functions
to estimate the model. Please look over
these resources and I will get back to
you once you are finished.
ECO550_2_6_Herb-4:Okay that
sounds great! Slide 7 Scene 7
Interaction Slide
Incorporate iPad to show Videos about
Excel and model creation Slide 8 Multiple Linear regression
analysis using Microsoft
Excel?s Data Analysis
toolhttp://www.youtube.com/wa
tch?v=ZwtxHXh-ZXU
Multiple Regression
Interpretation in Excel
http://www.youtube.com/watch?
v=tlbdkgYz7FM Scene 8
Herb?s office to go over the data Maria
collected Show regression output table ECO550_2_8_Maria-1: I hope those
videos helped you gain a better
understanding of using Excel to create
data sets. I want you to keep in mind
that the procedure we will be using to
estimate the model is regression. The
model Renee and you formulated is a
multiple regression model because there
is more than the price of chocolate
included as an independent variable.
Take a look at the regression output for
our estimated model.
ECO550_2_8_Herb-1: Wow! That was
fast!
ECO550_2_8_Maria-2:Yes, Herb,
Excel generates results almost
instantaneously. Herb shows formula ECO550_2_8_Herb-2: Okay, let?s see
what we have. I see the coefficients are
presented in a single column. Let me
rewrite the model to include the
coefficient values.
ECO550_2_8_Maria-3: What does all of this mean?
ECO550_2_8_Herb-3: Well, the first
number, three hundred and forty four
thousand and four hundred point five
refers to the number of boxes of sugarfree-chocolate demanded if none of the
independent variables changed their
value. If we assume one of the other
variables changes while all of the others
remain constant, then we calculate a
new number of boxes of chocolate.
ECO550_2_8_Maria-4: Could you
give me an example for this change? Herb shows Maria the updated formula One more formula for Herb to go over Display on projector: The new quantity
demanded is, three hundred seventyfour thousand, three hundred sixty-six
point two boxes of sugar-freechocolates. ECO550_2_8_Herb-4: Sure! For my
example, let?s assume that the price of
Katrina?s sugar-free-chocolates declines
by one dollar while none of the other
independent variables changes.
According to our model, the decrease in
price would cause quantity demanded to
increase by twenty nine thousand and
nine hundred and sixty five point seven
boxes. Each of the other coefficients is
then interpreted similarly. Here?s the
way we calculate the change in quantity
demanded, if price was to change.For
all of the variables that are constant,
that is, those unchanging variables, we
substitute a ?zero.?
ECO550_2_8_Maria-5: That is very
interesting! Is there anything else I
should know?
ECO550_2_8_Herb-5: There is one
more thing I?d like to add. For the price
of Katrina?s sugar-free-chocolate,
substitute one dollar, with a negative
sign in front of it to indicate price
declined. Here, I?ll show you how the
model determines quantity demanded.
After making the changes the new
quantity demanded is, three hundred seventy-four thousand, three hundred
sixty-six point two boxes of sugar-freechocolates.
ECO550_2_8_Maria-6:Thank you for
sharing that with me! Now that you
explained this all to me, things are
much clearer.
ECO550_2_8_Herb-6: Not a problem
at all. As you can see, regression
models are useful but only if the results
from the model are valid.
Slide 9 Scene 9
Herb?s office to conduct significance
test on the model and coefficients with
Maria Display on projector: The coefficient of
determination ranges from 0 to 1.
Display on projector: A higher adjusted Rsquare indicates a better model. http://wn.com/rsquared_or_coefficient_of_determinatio
n ECO550_2_9_Herb-1: Now we need
to check the model and coefficients for
significance.
ECO550_2_9_Maria-1:How do we
that?
ECO550_2_9_Herb-2: First, we
evaluate the adjusted R-square value to
see how much of the variation in the
quantity demanded of sugar-freechocolates is explained by the
independent variables we included in
the model. The closer R-square is to
one, the better is the explanatory power
of the independent variables.The
adjusted R-square for our model?s
results is point seven, nine, nine which
means the model explains seventy-nine
point nine percent of the variation in the
quantity of sugar-free-chocolates.
Maria, I found this video that helps to
explain the coefficient of determination
from another standpoint.
ECO550_2_9_Maria-2:Based upon the
explanation you gave about R-square
being close to one, seventy-nine-pointnine percent is very good.
ECO550_2_9_Herb-3:Yes, it looks as
if we included the right set of independent variables.
ECO550_2_9_Maria-3:What?s next,
Herb?
ECO550_2_9_Herb-4:Now we
evaluate the overall significance of the
independent variable. We are looking
for the answer to the question: Can the
behavior of the dependent variable, our
quantity of sugar-free-chocolates, be
explained without relying on the
independent variables included in the
model? For this test we will evaluate
the F-statistic. We first need to state the
level of significance, called the
?critical-value,? which we will use to
test the F-statistic.
For our model we are going to use the
five-percent level of significance;
therefore,the table gives us a critical Fvalue of four-point-one-two.
ECO550_2_9_Maria-4:I think I
understand how you selected the critical
value. I think now we must compare the
F-statistic generated for the model to
the critical value.
ECO550_2_9_Herb-5:Yes, that?s
exactly what we will do. Since the Fcalculated value is eleven-point-ninefive-two and is greater than four-pointone-two, a significant relationship does
exist between the quantity of sugar-freechocolate and the four independent
variables.
ECO550_2_9_Maria-5:Great! So
we?re done then?
ECO550_2_9_Herb-6:No, not quite
yet. We still need to evaluate the
significance of each coefficient. We can
actually use the same method used to
find the critical value of F only this time we will conduct a t-test on each
coefficient value.
Slide 10 Scene 10
Herb?s office to conduct significance
test on the model and coefficients with
Maria ECO550_2_10_Maria-1:So based on
the t-test, tell me which independent
variables are significant.
ECO550_2_10_Herb-1: According to
the t-test, only the price per boxand
bottled water are significant. The
coefficient on median income is
marginally significant; however, we
cannot use the coefficient for anything.
Surprisingly, the caffeinated coffee
coefficient is insignificant.
ECO550_2_10_Maria-2:I see why you
are saying coefficients are insignificant.
ECO550_2_10_Herb-2: Yes, this
revelation about independent variable
significance means we need to drop the
caffeinated coffee variable and reestimate the model.
ECO550_2_10_Maria-3:Is it okay to
drop variables from a model after the
model is estimated?
ECO550_2_10_Herb-3: Yes, if an
independent variable is not significant,
one of the recommended solutions is to
drop the variable from the model. In
our model, this means sugar-freechocolate and caffeinated coffee are not
substitute goods so coffee does not
contribute anything to our
understanding about demand for
Katrina?s sugar-free-coffee.
ECO550_2_10_Maria-4:Does
dropping the insignificant variable
mean we still use the coefficients
generated when caffeinated coffee was
a variable in the model? ECO550_2_10_Herb-4: That is a good
question, Maria! The answer is, no.
When we drop a variable like
caffeinated coffee from the model, we
have to re-estimate the model and then
run the Excel regression procedure
again to generate new coefficient
values.
ECO550_2_10_Maria-5:Let?s run the
regression without data on caffeinated
coffee?I?m anxious to see if there is
any difference in the results.
ECO550_2_10_Herb-5: Okay, but
before we re-estimate the model, I think
we should also drop the bottled water
variable. After some consideration, the
amount of water consumed is not a
good proxy for the price of water. Also,
the correlation coefficient between
bottles of water and income is nearly
one. Therefore, there seems to be a
problem with their correlation. Keep in
mind that we also need to add a Dummy
variable to measure the impact of sugarfree-chocolate which Katrina?s
introduced into the market last year.
Renee and I forgot to include a dummy
variable in the first model.
ECO550_2_10_Maria-6: Whatever
you say, Herb. You know this process
better than I do.
ECO550_2_10_Herb-6:Let me
compute this quick. (pause) Here are the
results now. Scene 11 Scene 11
Herb?s office to conduct significance
test on the model and coefficients with
Maria ECO550_2_11_Maria-1:Are these
results better, Herb?
ECO550_2_11_Herb-1:Yes, everything
is now significant. Now we can use the
regression equation to derive decisionmaking statistics like elasticity
coefficients.
ECO550_2_11_Maria-2:How do we
go about doing that?
ECO550_2_11_Herb-2: Make a note
that the point elasticity of demand is
calculated as the change in quantity
divided by the change in price times
price divided by quantity. Here?s how
the formula looks.
ECO550_2_11_Maria-3:Okay, so
where is the data to calculate elasticity?
ECO550_2_11_Herb-3:The regression
coefficients or the b?s in the model are
the change in quantity divided by a
change in price, so that part is simple.
ECO550_2_11_Maria-4:Do you mean
the negative forty-two thousand, one
hundred eighty-nine that is the
coefficient for the price variable?
ECO550_2_11_Herb-4:Yes, however,
we have to calculate the ?q? that?s in
the elasticity of demand formula.
ECO550_2_11_Maria-5:What does the
?q? stand for?
ECO550_2_11_Herb-5: In the
elasticity formula, q, is the quantity
demanded at a specific price. For this
step, we first find the demand curve.
ECO550_2_11_Maria-6:I thought we
already have the demand curve. ECO550_2_11_Herb-6: Not quite yet,
I was discussing the regression
equation which includes all of the
independent variables we included in
the model. The demand curve is
different, as only the price variable is
included in the demand curve.For our
example we will use some numbers
from 2004. We will then use these
numbers to showcase how to derive the
demand curve. First, go back to the
regression equation. Now substitute the
data as follows. For income, substitute
one-thousand dollars and for exports
substitute two-six-three-three-six-six
point seven.
Slide 12 Scene 12
Herb?s office to conduct significance
test on the model and coefficients with
Maria ECO550_2_12_Maria-1:Okay, I did
that. What about the price variable,
should I substitute for price?
ECO550_2_12_Herb-1:No, not yet.
Just solve what you have as this will
give the demand curve.
ECO550_2_12_Maria-2:Is that all
there is to finding the demand curve
from the regression model?
ECO550_2_12_Herb-2: Yes, that?s it!
We?re nearly finished as we have only
two more steps to calculate elasticity.
Again using the data from 2004
substitute twenty-four dollars for price
variable into thedemand curve and solve
to get a quantity equal to two-million,
ninety-six thousand, seven-hundred
eight-point eight-eight. The elasticity
coefficient is then negative zero point
four-eight-two-nine. We can then round
to negative zero point four-eight-three.
ECO550_2_12_Maria-3:Thank you for
going over this with me. Since you
showed me how to do this, things seem
clearer. Does this mean we are finished with this stage of the process to create
information for Ken to use when he
considers the decision to expand into
international markets?
ECO550_2_12_Herb-3: Yes, we have
completed this stage. We just need to
update Renee on our progress.
ECO550_2_12_Maria-4: I will update
Renee on our findings. While I
complete this task could you complete
this review activity based on what we
just discussed?
Slide 13 Scene 13
Check Your Understanding
Scenario-based and will use folder
structure to present scenario, then have
tabs to represent options for answers
Narrations will be provided for scenario
overview and choices (feedback
included as well) ECO550_2_13_Maria-1: Based upon
the result that the price elasticity of
demand coefficient is -0.483 for
Katrina?s sugar-free-chocolate, Herb
can advise Ken that Katrina?s should
never use price as a tool for increasing
total revenue?
ECO550_2_13_Maria, Agree,
Response 1-2:Agreed, that?s correct
since price elasticity of demand is less
than one it means demand is elastic. As
a result of this, the increasing price
would lower total revenue because
customers would react very strongly to
an increase in price by changing their
purchases by a greater percentage than
the percentage change in price.
Therefore, Herb is giving Ken the
appropriate advice.
ECO550_2_13_Maria Incorrect
response-3:
We should expect the percentage
change in quantity demanded to
change by less than the percentage
change in price.
ECO550_2_13_Maria, Disagree,
Option 2-4: When the absolute value of the price elasticity of demand
coefficient is less than one it means
demand is inelastic, so if price is
increased by a certain percentage, say
ten percent, demand will change by a
lower percentage, such as eight percent.
Therefore, when demand is price
inelastic, increasing the price actually
results in higher total revenue. For
Katrina?s, this means demand for sugarfree-chocolate is price inelastic and the
company could increase total revenue
by increasing price.
Slide 14 Summary
Concluding scene taking place in
conference room ECO550_2_14_Herb-1: Maria, we
have discussed and analyzed a lot today.
ECO550_2_14_Maria-1: We sure
have. Let?s outline the tasks we
completed to make certain we
remember everything. First, you
explained the demand model that you
and Renee formulated. I then described
the data and its sources for the data that
I compiled. We later discussed proxy
data and agreed it was okay to use this
kind of data for two of the variables.
ECO550_2_14_Herb-2: Let?s not
forget about our creation of the data set
in Excel along with the creation of our
estimation model.
ECO550_2_14_Maria-2: I?m glad you
brought that up! Next, we discussed the
results of…