ECON 705 Assignment: LSUS Enrollment, Demand, and Regression Analysis

This economics assignment analyzes LSUS undergraduate enrollment data, tuition, and fees from 2004 to 2017. It calculates annual elasticities for headcount and credit hours, determining the impact of tuition on enrollment. The assignment also includes an OLS regression to estimate a demand function, calculate point price elasticity, and analyze the effects of price and income changes on quantity demanded. Furthermore, the document explores seasonal adjustments in monthly data using regression models and forecasts sales based on the estimated equations. The student calculates and interprets various elasticities, including own-price, income, and cross-price elasticities, and determines revenue-maximizing strategies. The solution demonstrates the application of economic principles to real-world data analysis, providing a comprehensive understanding of demand, elasticity, and regression analysis.

Running head: ECONOMICS ASSIGNMENT
Economics Assignment
Name of the Student
Name of the University
Course ID

1ECONOMICS ASSIGNMENT
Table of Contents
Answer 1..........................................................................................................................................2
Answer 2..........................................................................................................................................2
Answer a......................................................................................................................................2
Answer b......................................................................................................................................3
Answer c......................................................................................................................................4
Answer d......................................................................................................................................5
Answer e......................................................................................................................................5
Answer f.......................................................................................................................................6
Answer 3..........................................................................................................................................7
Answer 4........................................................................................................................................11
Answer a....................................................................................................................................11
Answer b....................................................................................................................................11
Answer c....................................................................................................................................12
Answer d....................................................................................................................................13
Answer e....................................................................................................................................13
Answer f.....................................................................................................................................13

2ECONOMICS ASSIGNMENT
Answer 1
Year
undergrad
enrollment
total LSUS credit hour
production
undergrad tuition
and fees
Price vs
headcount
Price vs
credit hour
2004 3,910 101,868 1545
2005 3,940 100,181 1621 0.159 -0.348
2006 3,594 92,486 1667 -3.283 -2.855
2007 3,556 92,123 1667
2008 3,903 94,639 1751 1.893 0.548
2009 4,220 101,972 1867 1.217 1.163
2010 4,058 98,137 2062 -0.394 -0.386
2011 4,134 98,372 2247 0.216 0.028
2012 4,124 93,163 2472 -0.025 -0.570
2013 3,674 85,292 2803 -0.920 -0.703
2014 3,202 87,907 3084 -1.438 0.316
2015 2,775 91,021 3355 -1.697 0.414
2016 2,587 94,077 3417 -3.830 1.803
2017 2,637 115,340 3417
Aver
age -0.737 -0.054
The average elasticity of undergraduate enrollment with respect to tuition fees is -0.737.
The same for credit hours is -0.054. Therefore, with increase in tuition fees enrollment and credit
hours though reduces but not as much as tuition fees. Increase in tuition fees thus can be a
effective way of increasing revenue of LSUS.
Answer 2
Answer a
The result of OLS estimation is given below
Regression Statistics
Multiple R 0.98
R Square 0.97
Adjusted R Square 0.96
Standard Error 0.03

3ECONOMICS ASSIGNMENT
Observations 5
ANOVA
df SS MS F Significance F
Regression 1 0.076 0.076 87.886 0.003
Residual 3 0.003 0.001
Total 4 0.079
Coefficients
Standard
Error t Stat P-value Lower 95% Upper 95%
Intercept 16.8049 0.8909 18.8632 0.0003 13.9697 19.6401
Q -0.0025 0.0003 -9.3747 0.0026 -0.0033 -0.0016
The estimated demand function is
P=16.8049−0.0025 Q
The obtained value of R square from the OLS regression is 0.98. That is quantity
demanded can explain 98 percent variation in price. This indicates the model is a good fit model.
From the 95 percent confidence interval it can be said that we are 95 percent confident that
estimated coefficient will lie between -0.0033 and -0.0016.
From the estimated demand function, the inverted demand function can be obtained as
P=16.8049−0.0025 Q
¿ , 0.0025 Q=16.8049−P
¿ , Q= 16.8049
0.002 − 1
0.002 P
¿ , Q=6788.46−403.96 P

4ECONOMICS ASSIGNMENT
Answer b
Q=6788.46−403.96 P
dQ
dP =−403.96
Estimates for point price elasticity
P Q Point price elasticity
$8.64 3306 ($1.056)
$8.55 3337 ($1.025)
$8.42 3376 ($0.998)
$8.37 3397 ($0.986)
$8.29 3451 ($0.961)
Answer c
The point price elasticity as P = $8.64 is – 1.056.
At P = $ 8.32
Q=6788.46− ( 403.96× 8.32 )
¿ 6788.46−3360.95
¿ 3427.51
Point price elasticity= dQ
dP × P
Q
¿−403.96 × 8.32
3427.51
¿−403.96∗0.0024

5ECONOMICS ASSIGNMENT
¿−0.981
Answer d
At P = $8.55, the estimated price elasticity of demand is computed as – 1.035. The
elasticity measure greater than 1 implies demand at this price is relatively elastic in nature. The
company therefore should lower the price to increase the revenue.
At P = $8.32, the demand is relative price inelastic as obtained from the measured
elasticity of – 0.98. Therefore, in order to maximize revenue at this price the company should
increase price.
Answer e
P=16.8049−0.0025 Q
TR=P × Q
¿ ( 16.8049−0.0025Q ) ×Q
¿ 16.8049 Q−0.0025 Q2
MR= d ( TR )
dQ
¿ d ( 16.8049 Q−0.0025Q2 )
dQ
¿ 16.8049−0.005Q

6ECONOMICS ASSIGNMENT
3280 3300 3320 3340 3360 3380 3400 3420 3440 3460
($2.00)
$0.00
$2.00
$4.00
$6.00
$8.00
$10.00
Price, Marginal Revenue
P MR
Quantity
P, MR
Answer f
TR=16.8049Q−0.0025Q2
The first order condition for revenue maximization is
d ( TR )
dQ =0
¿ , 16.8049−0.005 Q=0
¿ , 0.005 Q=16.8049
¿ , Q=3360.98 3361
Revenue maximizing price
P=16.8049−0.0025 Q
¿ 16.8049− ( 0.0025× 3361 )
¿ 16.8049−8.4025

7ECONOMICS ASSIGNMENT
¿ 8.40
Revenue earned
Revenue=3361× 8.40
¿ 28232. 4
At P = $8.64, Q = 3298.246
Revenue = ($8.64 * 3298.246) = $28497
At P = $8.32, Q = 3427.51
Revenue = ($8.32 * 3427.51) = $28517
Answer 3
Estimated correlation between adjusted and unadjusted adjusted monthly data is 0.97
Apr-01 Jan-04 Oct-06 Jul-09 Apr-12 Dec-14 Sep-17 Jun-20
0
20
40
60
80
100
120
140
Scatterplot of unadjusted monthly data

8ECONOMICS ASSIGNMENT
Apr-01 Jan-04 Oct-06 Jul-09 Apr-12 Dec-14 Sep-17 Jun-20
0
20
40
60
80
100
120
140
Scatterplot of Seasonally adjusted Monthly
data
The scatterplot of adjusted and unadjusted monthly data show that after seasonal
adjustment the series become smoother. That is the seasonal adjustment reduces fluctuation in
the given series.
The result four regression is given below
Seasonally unadjusted monthly as the dependent, and t and t2 as the independents
Regression Statistics
Multiple R 0.916499
R Square 0.839970
Adjusted R Square 0.838131
Standard Error 10.845438
Observations 177
ANOVA
df SS MS F Significance F
Regression 2 107425.305 53712.652 456.649 0.000
Residual 174 20466.492 117.624
Total 176 127891.797

9ECONOMICS ASSIGNMENT
Coefficients
Standard
Error t Stat P-value Lower 95% Upper 95%
Intercept 122.516 2.473 49.532 0.000 117.634 127.398
t -1.764 0.064 -27.488 0.000 -1.890 -1.637
t^2 0.008 0.000 23.502 0.000 0.008 0.009
Seasonally unadjusted monthly as the dependent, and t, t2, and D as the independents
Regression Statistics
Multiple R 0.9308
R Square 0.8664
Adjusted R Square 0.8641
Standard Error 9.9390
Observations 177
ANOVA
df SS MS F Significance F
Regression 3 110802.187 36934.062 373.888 0.000
Residual 173 17089.609 98.784
Total 176 127891.797
Coefficients
Standard
Error t Stat P-value Lower 95% Upper 95%
Intercept 117.7976 2.4061 48.9576 0.0000 113.0485 122.5467
t -1.7528 0.0588 -29.7958 0.0000 -1.8689 -1.6367
t^2 0.0081 0.0003 25.4242 0.0000 0.0075 0.0088
D 8.7428 1.4953 5.8468 0.0000 5.7914 11.6943
Seasonally adjusted monthly as the dependent, and t and t2 as the independents
Regression Statistics
Multiple R 0.93575
R Square 0.87562
Adjusted R Square 0.87419
Standard Error 9.22042
Observations 177

10ECONOMICS ASSIGNMENT
ANOVA
df SS MS F Significance F
Regression 2 104143.922 52071.961 612.495 0.000
Residual 174 14792.820 85.016
Total 176 118936.742
Coefficients
Standard
Error t Stat P-value Lower 95% Upper 95%
Intercept 121.2348 2.1029 57.6522 0.0000 117.0844 125.3852
t -1.7328 0.0545 -31.7668 0.0000 -1.8404 -1.6251
t^2 0.0080 0.0003 27.1155 0.0000 0.0075 0.0086
Seasonally adjusted monthly as the dependent, and t, t2, and D as the independents
Regression Statistics
Multiple R 0.935808
R Square 0.875737
Adjusted R Square 0.873582
Standard Error 9.242868
Observations 177
ANOVA
df SS MS F Significance F
Regression 3 104157.248 34719.083 406.401 0.000
Residual 173 14779.494 85.431
Total 176 118936.742
Coefficients
Standard
Error t Stat P-value Lower 95% Upper 95%
Intercept 121.5312 2.2376 54.3135 0.0000 117.1147 125.9477
t -1.7335 0.0547 -31.6863 0.0000 -1.8414 -1.6255
t^2 0.0081 0.0003 27.0468 0.0000 0.0075 0.0086
D -0.5492 1.3906 -0.3950 0.6934 -3.2940 2.1955

11ECONOMICS ASSIGNMENT
For the first model, the adjusted R square is 0.84. That means t and t2 can explain 84
percent variation in the series. The overall model is statistically significant as obtained from the
significant F value. Finally, the p value for both the independent variable is 0.000. As the p value
is lower than significance level, the null hypothesis of no significant relation between
independent and dependent variable is rejected implying both the variables are statistically
significant.
For the second model, the adjusted R square value is 0.86. The three independent
variables t, t2 and D thus can explain 86 percent variation of the dependent variable. The model
has overall significance and also the independent variables have individual significance.
The third and fourth model that is model that is adjusted series is better compared to
unadjusted series because of a higher value of adjusted R square. The adjusted R square value for
third and fourth model is 0.87. The third and fourth though are almost similar, it is however
better to use third model for forecasting. This is because in the third model, both the independent
variables are statistically significant. In contrast, the dummy variable is insignificant in the fourth
model. Therefore, the third model is more suitable for forecasting.
The estimated equation that can be used to forecast sales is
Sales=121.2348−1.7328 t +0.0080 t2
Answer 4
Answer a
From the regression result, the value of adjusted R Square is obtained as 0.7583. This
shows price, income and price of the related good can together explain 75 percent variation in