Determine the correlation between the unadjusted and the adjusted monthly data

Let’s examine the history of LSUS undergraduate enrollment vs. its tuition and fees. Go to this link (http://www.lsus.edu/offices-and-services/institutional-effectiveness-and-planning/fact-book) 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.

Next, go here to get tuition data: http://www.lsus.edu/offices-and-services/institutional-effectiveness-and-planning/lsus-data-profile, 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 1984 and 1985 values of tuition and headcount and should be about -0.043; 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 1985-2015), and the average elasticity for credit hour (from 1988-2015).

Question 1

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The headcount elasticity between the years 2010-2011 is approximately equal to

Select one:

a. 0.216

b. -0.394

c. -0.357

d. 4,134

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Question 2

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The average (over all years) headcount elasticity is approximately _______. Demand in terms of headcount would be considered ________.

Select one:

a. 2,775; elastic.

b. -0.176; inelastic.

c. -5.68; elastic.

d. -1.70; elastic.

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Question 3

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The average (over all years) credit hour elasticity is approximately _______.

Select one:

a. -0.2245; this better demonstrates the law of demand since tuition is on a per-12-credit-hour basis, so credit hour is a more appropriate quantity variable to use than headcount.

b. -4.45; this is unexpected since credit hour demand should be inelastic.

c. 0.414; this is unexpected since the relationship between tuition and credit hours should be negative according to the law of demand.

d. 0.394; this is unexpected since the value is too small. Demand should be considered elastic and thus the value should be greater than 1.0.

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Question 4

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Many administrators argue that, to increase revenue to LSUS to cover budget shortfalls, tuition should be raised. The credit hour elasticity estimate suggests that

Select one:

a. tuition should only be decreased, since the elasticity value is negative. Raising tuition will only decrease the amount of revenue LSUS enjoys.

b. increasing fees may reduce credit hours, but not by much since credit hour demand is inelastic (in the data analyzed above). Raising fees hypothetically would increase LSUS revenue.

c. raising tuition will increase credit hours, since the elasticity is unexpectedly negative.

d. raising fees would be detrimental to LSUS’ budget, since the law of demand says that fewer credit hours will be pursued as a result. Fewer credit hours would mean less revenue for LSUS.

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Use the following data to answer the questions below.

P	Q
$130	78
$110	155
$90	246
$70	318
$50	397

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Using OLS, the estimated inverse demand function (P = f(Q)) is

Select one:

a. Q = 149.56 – 0.25P

b. P = 599.65 – 4.01Q

c. Q = 599.65 – 4.01P

d. P = 149.56 – 0.25Q

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Question 6

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Using algebra to transform the indirect demand function, the direct demand function (Q = f(P)) is

Select one:

a. Q = 118.67 – 52.18P

b. Q = 1.26 + 0.0048P

c. P = 599.65 – 4.01Q

d. Q = 599.65 – 4.01P

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Question 7

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Using calculus to determine dQ/dP, construct a column which calculates the point-price elasticity for each (P,Q) combination. What is the point price elasticity of demand when P=$90?

Select one:

a. -6.682

b. -0.883

c. -1.467

d. -0.505

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Question 8

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What is the point price elasticity of demand when P=$83?

Select one:

a. 0.018

b. -1.247

c. -1.351

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Question 9

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To maximize total revenue, what would you recommend if the company was currently charging P=$83? If it was charging P=$70?

Select one:

a. Price should be raised above both $70 and $83.

b. Raise the price if it is currently $83; lower the price if it is currently $70.

c. Lower the price if it is currently $83; raise the price if it is currently $70.

d. Price should be lower than both $83 and $70.

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.

Question 10

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Use your algebraically-derived direct demand function to determine an equation for TR and MR as functions of Q. What is total revenue when P=$83 and when P = $70?

Select one:

a. At P = $83, TR = $22,150; at P = $70, TR = $22,338.

b. At P = $83, TR = $45,676; at P = $70, TR = $50,122.

c. At P = $83, TR = $8,459; at P = $70, TR = -$3,442.

d. At P = $83, TR = $12,458; at P = $70, TR = $35,790.

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Question 11

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What is the total-revenue maximizing price and quantity, and how much revenue is earned there?

Select one:

a. P* = $90, Q* = 246, TR* = $21,698

b. P* = $74.78, Q* = 299.82, TR* = $22,421

c. P* = $70, Q* = 318, TR* = $22,338

d. P* = $83, Q* = 266.87, TR* = $22,150

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Illustration 7.3 (p. 262-3) describes time-series forecasting of new home sales, but you can see that the data is old. Visit the website indicated, click on the Historical Data tab, and download the first table “Houses Sold” (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. 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 263 (t will go from 1 to 105 through Sept. 2016); 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.

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Do you think making a seasonal adjustment will be useful, given what you observe at this point?

Select one:

a. No since, even though the unadjusted is more volatile than the adjusted, it is expected to be and thus making the adjustment will not improve the analysis.

b. Yes, since the seasonally unadjusted data traces a smoother path (graphically speaking) than the seasonally adjusted data.

c. No, since there is no discernible difference between the two data series, as far as is evident in the graph.

d. Yes since, even though they follow the same general trend, the seasonally unadjusted data is predictably more volatile than the seasonally adjusted data.

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Run four regressions:

1. seasonally unadjusted monthly as the dependent, and t and t² as 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 t² as the independents, and
4. seasonally adjusted monthly as the dependent, and t, t², and D as the independents.

In interpreting your p-values, remember that, say, 1.0E-08 is 1.0 * 10^-8, which is 0.00000001

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In comparing the regression results between model 1 and 2 (the unadjusted sales), it is notable that including the extra variable D in model 2

Select one:

a. increases the R² as expected but reduces the adjusted R², suggesting that D does not contribute to the explanatory power of the model.

b. makes the t and t² variables statistically insignificant in model 2, whereas they were significant in model 1.

c. dramatically improves the explanatory power of the model.

d. increases the R², but it is insignificant and has an unexpected sign.