PROBLEM SESSION #4 Suggested Solutions in Red
Application of Regression Analysis to Managerial Economics
Q.1
You are the CEO of a regional telephone company . You picked up the October 6 th
edition of your local newspaper and began reading on page D1:
The Federal Government completed the biggest auction in history today, selling
off part of the nation’s airwaves for $7 billion to a handful of giant companies
that plan to blanket the nation with new wireless communications networks for
telephone and computers…..
You read the article with interest because your firm is scrambling to secure loans to
purchase one of the licenses the FCC plans to auction off in his region next year. The
region serviced by his firm has a population that is 7% greater than the average where
the licenses have been sold before, yet the FCC plans to auction the same number of
licenses. . This troubled you, since in the most recent auction 99 bidders coughed up a
total of $7billion – an average of $70.7 million for a single license.
Fortunately for you, the newspaper article contained a table summarizing the price paid
per license in 10 different regions, as well as the number of licenses sold and the
population of each region. You quickly entered this data into your spreadsheet, clicked
the regression tool button, and found the following relation between price of a license,
the quantity of licenses available and regional population size (price and population
figures are in millions)
ln P = 2.23 – 1.2 ln Q + 1.25 ln Pop
Based on your analysis, how much money do you expect your company will need to buy
a license?
Since this is a log-log model, the coefficients are elasticities. The coefficient of ln Pop is 1.25  the
percentage change in price resulting from a one percentage change in population. Since the
population in the relevant region is 7% higher than the average, this means price will have to change
by 1.25(7%) = 8.75%.
The CEO should expect to pay a price which is 8.75% higher than the average price paid in the auction.
Since the price paid was $70.7m, the expected price need to win the auction in his region = 70.7(1.085)
= $76.9 million
Q.2
You manage a brewing company that sells its microbrew in seven provinces. However, you are interested in the
demand and pricing strategy for your brew in British Columbia. The company’s marketing department has
collected data from its distributors in BC. The data consists of quantity of your microbrew (Qx), price (per case) of
your microbrew (Px), the price of product Y (Py), the price of product Z (Pz), and income levels. Your boss wants
you to develop a pricing strategy (reduce price, increase price or maintain price) because your competitors drop
their prices which resulted in a loss of revenue for your firm. Using the data, you obtained the regression results in
Exhibit A below
a.
Evaluate the overall fit of the estimated regression equation. (2 lines)
Roughly 80% of the variation in our quantity sold can be explained by changes in Px, Py and Pz and
Incomes. If we base our conclusions solely on this, then the model is a good fit
b.
c.
d.
e.
Which of the explanatory variables have real effects on your demand? Why? (2 lines)
Px and Pz since their t-ratios fall in the critical regions and lead to a rejection of the null of no
significant relationship with Qx.
Suppose you expect price of Y to fall by 10% and price of Z to fall by 10% as well, what is the
predicted change in the quantity demand of your product X. (3 lines)
[(-0.58*10) + (1.20*10)]%
What pricing strategy would you propose (be specific) to counteract the actions taken by the producers of
product Y and product Z in question (c) above so that the quantity demanded of your product X remains
the same as before their actions? (3 lines)
Change your price by -{[(-0.58*10) + (1.20*10)]%/2.02}
Should you be concerned if macroeconomic forecasts predict a recession? Why or why not? Explain. (2
lines). No really, because incomes are insignificant (|t ratio| less than 1.96) so a recession will not have
any significant effect plus incomes elasticity<1.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.90850899
R Square
0.82538859
Adjusted R Square
0.79745077
Standard Error
0.05997329
Observations
30
ANOVA
df
Regression
Residual
Total
4
25
29
Coefficients
Intercept
lnPx
lnPy
lnPz
lnincome
-3.24323769
-2.02041877
-0.58293365
1.20954497
0.32286375
SS
0.42505154
0.08991989
0.51497143
MS
0.106263
0.003597
F
29.54377
Standard
Error
3.74299952
0.43904185
0.56015006
0.17969263
0.41551418
t Stat
P-value
-0.86648
-4.60188
-1.04067
6.731188
0.761016
0.394467
0.000248
0.307987
0.014422
0.035639
Q.3
You gave your intern data on quantity demanded (Qx), price of your product (Px), price of a substitute
(Py), price of a complement (Pz), average Income levels (Income) and your advertising budget
(Advertising) to estimate a demand function for your company and present the results to your
regional manager. A week after her presentation, you received the following note from your boss.
“One of your MBA interns sent this spreadsheet in response to the question I asked regarding the
potential impact (on our sales) of the following simultaneous events predicted for next year: 7% drop in
our competitor’s prices, 12% increase in our collaborator’s prices, 9% decline in incomes and a 5% cut in
our advertising budget.
This is absolutely nuts – do they not teach people how to speak in words anymore? Can you help me
out?” All I need to know are
a. Summarize her findings and tell me what these numbers mean. The spreadsheet is
absolute gibberish to me.
EXPLAIN THE COEFFICIENTS. CHECK THE SIGNS, EXPLAIN R-SQUARED. EXPLAIN
SIGNIFICANCE OF EACH VARIABLE TO VARIATION IN OUR QTY.
b. In very simple words and numbers, tell me what will be the total effect of the events I
described above on our quantity sold next year.
(-7%*1.583)+(12%*-1.212)+(-9%*0.332)+(-5%*1.45)
And next time, please do your job rather than send an intern to me. Thank you
SUMMARY
OUTPUT
Regression Statistics
R Square
0.825
Adjusted R Square
0.797
Observations
300
Intercept
ln Px
ln Py
ln Pz
ln Income
ln Advertising
Coefficients
-3.24
-2.020
1.583
-1.212
0.332
1.452
Standard Error
3.74
0.44
1.56
0.250
0.042
0.867
t Stat
-0.87
-4.60
1.012
-4.848
7.904
1.67
P-value
0.394
0.000
0.330
0.000
0.000
0.095