Let’s examine the history of LSUS undergraduate enrollment vs. its tuition and fees. Download the “A3Q1 LSUS enrollment data” Excel file (in CSV format if you don’t have Excel); in it you will see historical information on LSUS undergraduate enrollment, total credit hour production, and tuition and fees. (If you wish, you can verify or look up additional informationhere, here, andhere.)
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 from 2006-2007 and 2016-2017, since the elasticity calculation will be trying to divide by zero; just delete those error values in your Excel table so that the cells are blank. The first headcount elasticity will be calculated based on the 2000 and 2001 values of tuition and headcount and should be about -0.008; the first credit hour elasticity will also be based on the 2000 and 2001 values and should be about 0.359). Calculate the average annual elasticity for headcount (from 2000-2017), and the average annual elasticity for credit hour (from 2000-2017).
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:
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=$13.75? What is the point price elasticity of demand when P=$11.83?
d. To maximize total revenue, what would you recommend if the company was currently charging P=$13.20? If it was charging P=$11.83?
e. Use your first demand function to determine an equation for TR and MR as a function of Q, and create a graph of P and MR on the vertical and Q on the horizontal axis.
What is the total-revenue maximizing price and quantity, and how much revenue is earned there? Compare that to the TR when P = $13.75 and P = $11.83.
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 – Seasonal Factors, Total (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 November 2018. 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 167 (Nov. 2018); make a t2 column too (since, if you look at the data, you can see sales are 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. 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. Bob’s Underground, a limited liability corporation specializing in new rap artists (B.U. LLC, rap) has the following demand function:
Q = a + bP + cM + dR
where Q is the quantity demanded of the most popular product B.U. sells, P is the price of that product, M is income, and R is the price of a related product. The regression results are:
Adjusted R Square
Discuss whether you think these regression results will generate good sales estimates for B.U. LLC, rap.
Now assume that the income is $57,600, the price of the related good is $15, and B.U. chooses to set the price of its product at $13.50.
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 4%, what would happen (in percentage terms) to quantity demanded?
e. If M increases by 3%, what would happen (in percentage terms) to quantity demanded?
f. If R decreases by 5%, what would happen (in percentage terms) to quantity demanded?