MBA 701 Module 3 Assignment

1. Let's examine the history of LSUS undergraduate enrollment vs. its tuition and fees. Download the "A3Q1 LSUS enrollment data" Excel file; in it you will see historical information on LSUS undergraduate enrollment, total credit hour production, and (12-hour, undergraduate) tuition and fees. (If you wish, you can verify or look up additional information hereandhere.)

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 when the tuition doesn't change (like in 1994-1996), since the elasticity calculation will be trying to divide by zero; delete those error values in your Excel table so that the cells are blank. The first headcount elasticity will be calculated based on the 1992 and 1993 values of tuition and headcount and should be about -0.122; the first credit hour elasticity will also be based on the 1992 and 1993 values and should be about -0.226. Calculate the average annual elasticity for headcount (from 1992-2022), and the average annual elasticity for credit hour (from 1992-2022).

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.

"A3Q1 LSUS enrollment data":

Year	undergrad enrollment	total LSUS credit hour production	undergrad tuition and fees ($)
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	3,422	90,624	1,025
2001	3,419	94,446	1,150
2002	3,543	96,039	1,184
2003	3,655	101,352	1,442
2004	3,910	101,868	1,545
2005	3,940	100,181	1,621
2006	3,594	92,486	1,667
2007	3,556	92,123	1,667
2008	3,903	94,639	1,751
2009	4,220	101,972	1,867
2010	4,058	98,137	2,062
2011	4,134	98,372	2,247
2012	4,124	93,163	2,472
2013	3,674	85,292	2,803
2014	3,202	87,907	3,084
2015	2,775	91,021	3,355
2016	2,587	94,077	3,417
2017	2,638	115,340	3,417
2018	2,511	137,467	3,663
2019	2,577	165,057	3,663
2020	2,553	191,712	3,663
2021	2,477	173,910	3,663
2022	2,465	170,128	3,663

2. Copy and paste the following data into Excel:

P	Q
$107.00	8742
$105.93	8779
$104.86	9421
$100.58	9589
$96.30	9840
$93.09	9909
$89.88	10443
$84.53	10483

a. Run OLS to determine the demand function as P = f(Q); how much confidence do you have in this estimated equation? Use algebra to invert the demand function to 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=$100.58? What is the point price elasticity of demand when P=$91.50?

d. To maximize total revenue, what would you recommend if the company was currently charging P=$105.93? If it was charging P=$91.50?

e. Use your first demand function to determine an equation for TR and MR as a function of Q, and make a graph of P and MR on the vertical and Q on the horizontal axis.

f. What is the total-revenue maximizing price and quantity, and how much revenue is earned there? (Round your price to the nearest cent, your quantity to the nearest whole unit, and your TR to the nearest dollar.) Compare that to the TR when P = $100.58 and P = $91.50.

3. Let's practice time-series forecasting of new home sales. Click here (https://www.census.gov/construction/nrs/historical_data/index.html) to see the newest data in the first table: Houses Sold (Excel file is sold_cust.xls). Look at the monthly data on the "Reg Sold" tab. If you have trouble with the link, I have recreated the data in moodle in the Excel file "A3Q3 Census Housing Data."

Only keep the dates beginning in January 2005, so delete the earlier observations, and use the data through December 2023. 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" where t will go from 1 (Jan. 2005) to 228 (December 2023); make a t² column too (since, if you look at the data, you can see sales are somewhat U-shaped; hence the quadratic). Also make a column "D" that is a dummy variable equal to one during the spring and summer months of March through August.

Determine the correlation between the unadjusted and the adjusted monthly data (=CORREL(unadjust., adjust.) in Excel), and produce scatterplots (with straight lines) 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 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. Discuss your findings, and determine which of the four models is the best for forecasting new home sales. When 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.

"A3Q3 Census Housing Data.":

date	US NSA month	US SA year
Jan-05	92	1203
Feb-05	109	1319
Mar-05	127	1328
Apr-05	116	1260
May-05	120	1286
Jun-05	115	1274
Jul-05	117	1389
Aug-05	110	1255
Sep-05	99	1244
Oct-05	105	1336
Nov-05	86	1214
Dec-05	87	1239
Jan-06	89	1174
Feb-06	88	1061
Mar-06	108	1116
Apr-06	100	1123
May-06	102	1086
Jun-06	98	1074
Jul-06	83	965
Aug-06	88	1035
Sep-06	80	1016
Oct-06	74	941
Nov-06	71	1003
Dec-06	71	998
Jan-07	66	891
Feb-07	68	828
Mar-07	80	833
Apr-07	83	887
May-07	79	842
Jun-07	73	793
Jul-07	68	778
Aug-07	60	699
Sep-07	53	686
Oct-07	57	727
Nov-07	45	641
Dec-07	44	619
Jan-08	44	627
Feb-08	48	593
Mar-08	49	535
Apr-08	49	536
May-08	49	504
Jun-08	45	487
Jul-08	43	477
Aug-08	38	435
Sep-08	35	433
Oct-08	32	393
Nov-08	27	389
Dec-08	26	377
Jan-09	24	336
Feb-09	29	372
Mar-09	31	339
Apr-09	32	337
May-09	34	376
Jun-09	37	393
Jul-09	38	411
Aug-09	36	418
Sep-09	30	386
Oct-09	33	396
Nov-09	26	375
Dec-09	24	352
Jan-10	24	345
Feb-10	27	336
Mar-10	36	381
Apr-10	41	422
May-10	26	280
Jun-10	28	305
Jul-10	26	283
Aug-10	23	282
Sep-10	25	317
Oct-10	23	291
Nov-10	20	287
Dec-10	23	326
Jan-11	21	307
Feb-11	22	270
Mar-11	28	300
Apr-11	30	310
May-11	28	305
Jun-11	28	301
Jul-11	27	296
Aug-11	25	299
Sep-11	24	304
Oct-11	25	316
Nov-11	23	328
Dec-11	24	341
Jan-12	23	335
Feb-12	30	366
Mar-12	34	354
Apr-12	34	354
May-12	35	370
Jun-12	34	360
Jul-12	33	369
Aug-12	31	375
Sep-12	30	385
Oct-12	29	358
Nov-12	28	392
Dec-12	28	399
Jan-13	32	446
Feb-13	36	447
Mar-13	41	444
Apr-13	43	441
May-13	40	428
Jun-13	43	470
Jul-13	33	375
Aug-13	31	381
Sep-13	31	403
Oct-13	36	444
Nov-13	32	446
Dec-13	31	433
Jan-14	33	443
Feb-14	35	420
Mar-14	39	405
Apr-14	39	403
May-14	43	451
Jun-14	38	418
Jul-14	35	402
Aug-14	36	456
Sep-14	37	470
Oct-14	38	476
Nov-14	31	442
Dec-14	35	497
Jan-15	39	515
Feb-15	45	540
Mar-15	46	480
Apr-15	48	502
May-15	47	502
Jun-15	44	480
Jul-15	43	506
Aug-15	41	518
Sep-15	35	456
Oct-15	39	482
Nov-15	36	504
Dec-15	38	546
Jan-16	39	505
Feb-16	45	517
Mar-16	50	532
Apr-16	55	576
May-16	53	571
Jun-16	50	557
Jul-16	54	628
Aug-16	46	575
Sep-16	44	558
Oct-16	46	575
Nov-16	40	571
Dec-16	39	561
Jan-17	45	573
Feb-17	51	587
Mar-17	61	632
Apr-17	56	598
May-17	57	635
Jun-17	56	619
Jul-17	48	572
Aug-17	45	556
Sep-17	50	637
Oct-17	49	626
Nov-17	50	711
Dec-17	45	630
Jan-18	48	590
Feb-18	54	618
Mar-18	66	679
Apr-18	61	642
May-18	62	662
Jun-18	56	636
Jul-18	52	628
Aug-18	47	593
Sep-18	46	595
Oct-18	43	554
Nov-18	44	625
Dec-18	38	546
Jan-19	49	591
Feb-19	57	638
Mar-19	68	705
Apr-19	64	695
May-19	56	602
Jun-19	66	763
Jul-19	55	669
Aug-19	57	720
Sep-19	56	715
Oct-19	55	721
Nov-19	50	710
Dec-19	49	693
Jan-20	59	685
Feb-20	63	699
Mar-20	59	609
Apr-20	52	569
May-20	64	696
Jun-20	79	936
Jul-20	85	1019
Aug-20	81	1029
Sep-20	77	988
Oct-20	78	1027
Nov-20	61	863
Dec-20	63	873
Jan-21	77	901
Feb-21	70	765
Mar-21	83	850
Apr-21	74	810
May-21	65	715
Jun-21	61	716
Jul-21	62	760
Aug-21	55	690
Sep-21	58	742
Oct-21	51	680
Nov-21	54	772
Dec-21	61	830
Jan-22	70	810
Feb-22	71	773
Mar-22	68	707
Apr-22	56	611
May-22	58	636
Jun-22	48	563
Jul-22	44	543
Aug-22	51	638
Sep-22	44	567
Oct-22	43	577
Nov-22	41	582
Dec-22	47	636
Jan-23	55	649
Feb-23	56	625
Mar-23	62	640
Apr-23	60	679
May-23	67	710
Jun-23	58	683
Jul-23	60	728
Aug-23	52	654
Sep-23	55	698
Oct-23	51	676
Nov-23	42	615
Dec-23	50	664

4. Your company, which specializes in running shoes for men who are growing increasingly follicly-challenged (BalderDash), has the following demand function:

Q = a + bP + cM + dR

where Q is the quantity demanded of BalderDash's most popular shoes, P is the price of that product, M is consumer income, and R is the price of a related product. The regression results are:

Adjusted R Square	0.7796
Independent Variables	Coefficients	Standard Error	t Stat	P-value
Intercept	21,055.04	1428.27	14.74	8.1E-16
P	-83.912	19.079	-4.398	0.000
M	0.0266	0.013	2.064	0.047
R	-16.6	10.664	-1.556	0.129

1. Discuss whether you think these regression results will generate good sales estimates for BalderDash.

Now assume that the income is $69,100, the price of the related good is $39, and BalderDash chooses to set the price of its product at $54.

b. What is the estimated number of units sold given the data above? (round to nearest unit; no decimals)

c. What are the values for the own-price, income, and cross-price elasticities?

d. If P increases by 6%, what would happen (in percentage terms) to quantity demanded?

e. If M increases by 2%, what would happen (in percentage terms) to quantity demanded?

f. If R decreases by 3%, what would happen (in percentage terms) to quantity demanded?