1. Let’s examine the history of LSUS
undergraduate enrollment vs. its tuition and fees. Go to this link (.lsus.edu/officesandservices/institutionaleffectivenessandplanning/factbook">http://www.lsus.edu/officesandservices/institutionaleffectivenessandplanning/factbook)
and look at the PDF “FACT BOOK 2015.” Collect two types of quantity data: the
Fall Headcount for undergrads on pg. 6 (9 of the PDF), and the Total (summer,
spring, and fall) student credit hour production on pg. 11 (8 of the PDF). Headcount
data goes from 19842015, but credit hour data only goes from 19862015. Use
1987 as the beginning year of your data.
Next, go here to get tuition data:.lsus.edu/officesandservices/institutionaleffectivenessandplanning/lsusdataprofile">http://www.lsus.edu/officesandservices/institutionaleffectivenessandplanning/lsusdataprofile,
and look at the PDF “LSUS Data Profiles 20112012.” The price (undergraduate fall
tuition and fees) data is on pg. 106. You will only need from 1984 through
2011; for the remaining years, use 2012 = $2,472, 2013 = $2,803, 2014 = $3,084,
and 2015 = $3,355.
Calculate annual elasticities for both types of quantity variables
(i.e., you will have an elasticity of price vs. headcount, and one of price vs.
credit hour). You will get an error message in your calculations a few times
when the tuition doesn't change, since the elasticity calculation will be
trying to divide by zero; just delete those in your Excel table. The first headcount
elasticity will be calculated based on the 1987 and 1988 values of tuition and
headcount and should be about 0.191; the first credit hour elasticity will be
based on the 1987 and 1988 values and should be about 0.394). Calculate the
average elasticity for headcount (from 19882015), and the average elasticity
for credit hour (from 19882015).
Many administrators argue that, to increase revenue to LSUS to cover
budget shortfalls, tuition should be raised. Comment on this suggestion, using
the evidence you’ve uncovered.
a. Run OLS to determine the inverse demand
function (P = f(Q)); how much confidence do you have in this estimated
equation? Use algebra to then find the direct demand function (Q = f(P)).
b. Using calculus to determine dQ/dP, construct
a column which calculates the pointprice elasticity for each (P,Q)
combination.
c. What is the point price elasticity of
demand when P=$36? What is the point price elasticity of demand when P=$31?
d. To maximize total revenue, what would you
recommend if the company was currently charging P=$34? If it was charging
P=$31?
e. Determine an equation for MR as a
function of Q, and create a graph of P and MR on the vertical and Q on the
horizontal axis.
f. Use your direct demand function to
construct an equation and column for TR. What is the totalrevenue
maximizing price and quantity, and how much revenue is earned there?
Compare that to the TR when P = $34 and P = $31.


2. Copy and paste the
following data into Excel:
P

Q

$40

120

$38

134

$36

142

$34

148

$32

157

3. Illustration 7.3 (p. 2624) describes
timeseries forecasting of new home sales, but you can see that the data is
old. Click here (.census.gov/construction/nrs/historical_data/index.html">https://www.census.gov/construction/nrs/historical_data/index.html)
and download the first table: Houses Sold – Seasonal Factors, Total (Excel file
is sold_cust.xls). Look at the monthly data on the “Reg Sold” tab.
Only keep the dates beginning in January 2008, so delete the earlier
observations, and use the data through May 2017. Keep only the US data, both
the seasonally unadjusted monthly (column B) and the seasonally adjusted annual
(column G). Make a new column of seasonally adjusted monthly by dividing the
annual data by 12. Make a column called “t” similar to the book’s column 4 on page
262 (t will go from 1 to 113 through May 2017); make a t^{2} column too
(since, if you look at the data, you can see sales dropping until about
mid2011 then rising again; hence the quadratic). Also make a column “D” that
is a dummy variable equal to one during the spring and summer months, similar
to the book’s column 5.
Determine the correlation between the unadjusted and the adjusted monthly
data (=CORREL(unadjust., adjust.) in Excel), and produce scatterplots (with
connectors) of both. Do you think making a seasonal adjustment will be useful,
given what you observe at this point?
Run four regressions: 1) seasonallyunadjusted monthly as the dependent,
and t and t^{2} as the independents, 2) seasonallyunadjusted monthly as the
dependent, and t, t^{2}, and D as the independents, 3) seasonally
adjusted monthly as the dependent, and t and t^{2} as the independents,
and 4) seasonally adjusted monthly as the dependent, and t, t^{2}, and
D as the independents. Discuss your findings, and determine which of the four
models is the best for forecasting new home sales. In interpreting your pvalues,
remember that, say, 1.0E08 is 1.0 * 10^8, which is 0.00000001. State the
equation that would be used to forecast sales.
4. Conlan
Enterprises has the following demand function:
.gif">
whereQ is the quantity demanded of the
product Conlan Enterprises sells,P
is the price of that product,M is
income, andP_{R} is the
price of a related product. The regression
results are:
Adjusted R Square

0.7270





Coefficients

Standard
Error

t Stat

Pvalue

Intercept

97.507

107.527

0.907

0.371

P

4.489

1.145

3.921

0.0004

M

0.0034

0.0015

2.190

0.036

PR

4.034

1.315

3.068

0.004

a. Discuss whether you think
these regression results will generate good sales estimates for Conlan.
Now assume that
the income is $33,000, the price of the related good is $55, and Conlan chooses
to set the price of its product at $32.
b. What is the estimated number of units sold given the data above?
c. What are the values for the ownprice,
income, and crossprice elasticities?
d. IfP
increases by 5%, what would happen (in percentage terms) to quantity demanded?
e. IfM
increases by 8%, what would happen (in percentage terms) to quantity demanded?
f. IfP_{R}
decreases by 4%, what would happen (in percentage terms) to quantity demanded?