## (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

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

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

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

Excel and model creation Slide 8 Multiple Linear regression

analysis using Microsoft

Excel?s Data Analysis

tch?v=ZwtxHXh-ZXU

Multiple Regression

Interpretation in Excel

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

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

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...

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