Assignment
SECTION OVERVIEW: Chapter 6 concerns the issue of customer responsiveness to price changes, which economists call demand elasticity. The law of demand suggests an inverse relationship between price and quantity demanded, but it doesn't tell us how strongly demand responds to price changes. Consumers may react strongly (elastic) or weakly (inelastic), depending on several factors. Similar concepts apply to changes in income and changes in prices of related products. Chapter 7 also relates to quantifying demand in terms of estimating future demand from past data. OLS is used to estimate demand functions which can be used to extrapolate demand in other periods or areas.
LEARNING GOALS: Upon completing this section, we will understand the qualitative meaning of different values of own-price, income, and cross-price elasticity. We will be able to calculate elasticity values given data on prices and quantities demanded. We will recognize the impact on total revenue of price changes made in elastic vs. inelastic ranges. We will also be equipped to estimate demand functions using Excel's OLS and graphing features.
1. Let's examine the history of LSUS undergraduate enrollment vs. its tuition and fees. Go to this link 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 1984-2015, but credit hour data only goes from 1986-2015. Use 1987 as the beginning year of your data.
|
Year
|
undergrad enrollment
|
total credit hour production
|
undergrad tuition and fees
|
|
1987
|
3923
|
100562
|
600
|
|
1988
|
3995
|
104409
|
660
|
|
1989
|
3594
|
94450
|
730
|
|
1990
|
3540
|
90404
|
740
|
|
1991
|
3756
|
98635
|
740
|
|
1992
|
4017
|
102826
|
740
|
|
1993
|
3890
|
96864
|
965
|
|
1994
|
3656
|
91152
|
965
|
|
1995
|
3631
|
90216
|
965
|
|
1996
|
3354
|
86790
|
965
|
|
1997
|
3516
|
91578
|
1025
|
|
1998
|
3678
|
94979
|
1025
|
|
1999
|
3553
|
94396
|
1025
|
|
2000
|
3422
|
90624
|
1025
|
|
2001
|
3419
|
94446
|
1150
|
|
2002
|
3543
|
96039
|
1184
|
|
2003
|
3655
|
101352
|
1442
|
|
2004
|
3910
|
101868
|
1545
|
|
2005
|
3940
|
100181
|
1621
|
|
2006
|
3594
|
92486
|
1667
|
|
2007
|
3556
|
92123
|
1667
|
|
2008
|
3903
|
94639
|
1751
|
|
2009
|
4220
|
101972
|
1867
|
|
2010
|
4058
|
98137
|
2062
|
|
2011
|
4134
|
98372
|
2247
|
|
2012
|
4124
|
93163
|
2472
|
|
2013
|
3674
|
85292
|
2803
|
|
2014
|
3203
|
87907
|
3084
|
|
2015
|
2775
|
91021
|
3355
|
Next, go here to get tuition data and look at the PDF "LSUS Data Profiles 2011-2012." 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 1988-2015), and the average elasticity for credit hour (from 1988-2015).
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.
2. Copy and paste the following data into Excel:
|
P
|
Q
|
|
$40
|
120
|
|
$38
|
134
|
|
$36
|
142
|
|
$34
|
148
|
|
$32
|
157
|
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 point-price 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 total-revenue maximizing price and quantity, and how much revenue is earned there? Compare that to the TR when P = $34 and P = $31.
3. Illustration 7.3 (p. 262-4) describes time-series forecasting of new home sales, but you can see that the data is old. 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 t2 column too (since, if you look at the data, you can see sales dropping until about mid-2011 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) seasonally unadjusted monthly as the dependent, and t and t2as the independents, 2) seasonally unadjusted monthly as the dependent, and t, t2, and D as the independents, 3) seasonally adjusted monthly as the dependent, and t and t2as the independents, and 4) seasonally adjusted monthly as the dependent, and t, t2, 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 p-values, remember that, say, 1.0E-08 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:
where Q is the quantity demanded of the product Conlan Enterprises sells, P is the price of that product, M is income, and PRis the price of a related product. The regression results are:
|
Adjusted R Square
|
0.7270
|
|
|
|
|
Coefficients
|
Standard Error
|
t Stat
|
P-value
|
|
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 own-price, income, and cross-price elasticities?
d. If P increases by 5%, what would happen (in percentage terms) to quantity demanded?
e. If M increases by 8%, what would happen (in percentage terms) to quantity demanded?
f. If PR decreases by 4%, what would happen (in percentage terms) to quantity demanded?