This document provides a case study and questions about the bottled water market. Key points include: - Demand and supply graphs are used to show the impact of increases in gasoline prices on the equilibrium price and quantity of bottled water. - Elasticity is discussed, showing how a more inelastic demand curve results in a smaller change in equilibrium quantity compared to a more elastic curve. - Regression analysis is performed to estimate demand equations for summer and winter. Supply is also estimated. - Graphs are drawn and analyzed to illustrate changes in demand vs. quantity demanded and changes in supply vs. quantity supplied from changes in input prices like gasoline. - Simplified demand and supply equations are

1. Case Study # 1: Bottled Water (70 points total)
Fill in Answers below
Refer to case study for scenario and detailed instructions
Names of TeamMembers: ___________________________________________
1. (2pts) Use a Supply and Demand graph of the bottled water market to explain the impact of
an increase in the price of gasoline on the equilibrium P & Q of bottled water.
 (1pt) Shift the appropriate curve in the appropriate direction.
 (1pt) Use words to explain what happened.
Bottled Water
P S2 S1
D
Q
When the price of gasoline increases, there will be a leftward
shift in supply. The equilibrium price of bottled water will
increase, and the equilibrium quantity of bottled water will
decrease. This is because gasoline is an input in the production
and delivery of bottled water, so bottled water will become more
expensive to produce.
2. (4pts) Use a Supply and Demand graph of the bottled water market to explain how elasticity
affects the impact of an increase in the price of gasoline on the equilibrium P & Q of bottled
water
 (0.5pts) Draw a relatively steep demand curve and a regular supply curve (the supply
curve can be the same as in question 1). [Again, just free draw them]. Label equilibrium
P & Q.
 (0.5 pts) Draw a new flatter demand line that goes through the initial equilibrium point.
 Shift the same curve as in question #1 to show the impact of the gasoline price increase.
 (0.5pts) Label the new equilibrium P & Q for the steep Demand line.
 (0.5pts) Label the new equilibrium P & Q for the flatter Demand line.
E1
E2
P*1
P*2
Q*2 Q*1

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 (2pts) Comparing the two equilibriums, explain how elasticity impacts the magnitude of
the adjustment in P & Q when the price of gasoline increases. Be sure to specify which
D curve is relatively elastic and which is relatively inelastic.
The D1 curve is relatively inelastic, because a change in the equilibrium price
caused a relatively small change in the equilibrium quantity demanded. The D2
curve is relatively elastic, because a change in the equilibrium price caused a
relatively large change in the equilibrium quantity demanded.
P
Q
3. (8pts) Estimate the demand equation for bottled water.
a. Use Excel to estimate the regression equation for summer (first set of columns):
i. Check Results:
 (1pt) Look at your t-stats and/or your P-values. Are all of your slope coefficients
significantly different from zero? Explain. If they are not, eliminate the
insignificant variables, and re-estimate your demand equation. (Note: you always
want to include a constant, even if it is not significantly different from zero.)
All of the slope coefficients are significantly different from zero. This
implies that all of these variables have a significant effect on the demand for
bottled water.
S1
D1
E1
Q*1
P*1
D2
S2
E2
Q*2
P*2
P*3
Q*3
E3

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SUMMARY OUTPUT
Regression Statistics
Multiple R 0.961621208
R Square 0.924715348
Adjusted R Square 0.922267066
Standard Error 14.59608966
Observations 128
ANOVA
df SS MS F Significance F
Regression 4 321869.462 80467.3655 377.6997852 4.7852E-68
Residual 123 26204.63751 213.0458334
Total 127 348074.0995
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 267.7675919 27.42306288 9.764321114 5.05688E-17 213.4853204 322.0498634 213.4853204 322.0498634
Pbw -24.56448529 2.798672436 -8.777191992 1.17091E-14 -30.10428578 -19.02468481 -30.10428578 -19.02468481
Pmachine 21.386875 5.160496989 4.144344052 6.2909E-05 11.17198763 31.60176237 11.17198763 31.60176237
Ppopcorn -57.2359375 12.90124247 -4.436467079 2.0051E-05 -82.77315594 -31.69871906 -82.77315594 -31.69871906
Income 19.2874375 0.516049699 37.37515503 5.26776E-69 18.26594876 20.30892624 18.26594876 20.30892624
SUMMARY OUTPUT
Regression Statistics
Multiple R 0.97221859
R Square 0.945208987
Adjusted R Square 0.943427166
Standard Error 13.74265172
Observations 128
ANOVA
df SS MS F Significance F
Regression 4 400741.8557 100185.4639 530.4734264 1.5938E-76
Residual 123 23229.83857 188.8604762
Total 127 423971.6942
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 219.2680303 25.81962779 8.492300204 5.52344E-14 168.1596603 270.3764004 168.1596603 270.3764004
Pbw -52.62149265 2.63503318 -19.96995448 2.07074E-40 -57.83737926 -47.40560603 -57.83737926 -47.40560603
Pmachine 17.561625 4.85876111 3.61442446 0.000437256 7.944005297 27.1792447 7.944005297 27.1792447
Ppopcorn -30.90359375 12.14690278 -2.544154203 0.012192366 -54.94764301 -6.859544493 -54.94764301 -6.859544493
Income 20.0541375 0.485876111 41.27417884 6.4521E-74 19.09237553 21.01589947 19.09237553 21.01589947
ii. (2pts) Cut and Paste your final regression results for summer here:
b. (2pts) Use Excel to estimate the same regression equation as in part “a” but for winter
Cut and Paste your final regression results for winter here:

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SUMMARY OUTPUT
Regression Statistics
Multiple R 0.960744373
R Square 0.92302975
Adjusted R Square 0.922421289
Standard Error 56.95252604
Observations 256
ANOVA
df SS MS F Significance F
Regression 2 9841001.633 4920500.817 1516.992123 1.3178E-141
Residual 253 820628.3262 3243.590222
Total 255 10661629.96
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 14.29152721 19.084377 0.748860034 0.454637216 -23.29295486 51.87600927 -23.29295486 51.87600927
Pbw00 391.1787388 7.724768027 50.63954509 2.041E-134 375.965698 406.3917796 375.965698 406.3917796
Pgas -69.66924762 3.017724012 -23.08668631 3.21834E-64 -75.61230743 -63.72618781 -75.61230743 -63.72618781
c. (3pts) Write out the demand equations for summer and winter using the estimated betas
from your regression results:
Demand in Summer: QBW = 267.77 – 24.56PBW + 21.39Pmachine – 57.24Ppopcorn + 19.29I
Demand in Winter: QBW = 219.27 – 52.62PBW + 17.56Pmachine – 30.90Ppopcorn + 20.05I
4. (4pts) Estimate the supply of bottled water.
a. (2pts) Use Excel to estimate the regression equation for Supply
Cut and Paste your final regression results for supply here:
b. (2pts) Write out the supply equation using the estimated “betas.”
Supply: QBW = 14.29 + 391.18PBW – 69.67Pgas
5. (9pts) Use graphs to explain the impact from a change in one of the slope coefficients. Also,
distinguish between a change in demand vs a change in quantity demanded and a change in
supply vs a change in quantity supplied.
a. Use the framework below to answer the following questions:
P P
D1 D
Q D2 Q

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Bottled water Vending machine soft drinks
i. (0.5pts) Label each axis and draw one Demand curve for the bottled water market
and one Demand curve for the vending machine soft drink market (do not draw
supply curves). [Again, you are free drawing here]
ii. (0.5pts) What does the positive sign of b2 tell you about the relationship between
bottled water and the competitor's vending machine soft drinks?
There is a positive relationship between bottled water and machine
soft drinks. As the price of soft drinks increases, the demand for
bottled water will also increase. This implies that they are substitute
goods.
iii. (2pts) Suppose that the price of vending machine soft drinks increases. How does
this affect each demand curve? Demonstrate this change on each demand curve
in the graphs above. Explain your logic.
With an increase in the price of vending machine soft drinks, there
will be a decrease in the quantity demanded of soft drinks; therefore,
there will be an increase in demand of bottled water. There is a
movement along the demand curve for soft drinks, while there is a
shift in the entire curve for bottled water.
b. Use the framework below to answer the following questions:
P P
D2 D1 D
Q Q
Bottled water Popcorn
i. (0.5pts) Label each axis and draw one Demand curve for the bottled water market
and one Demand curve for the popcorn market (do not draw supply curves).
ii. (0.5pts) What does the negative sign of b3 tell you about the relationship between
bottled water and popcorn?
There is a negative relationship between bottled water and popcorn.
They are complementary goods.
iii. (2pts) Suppose the price of popcorn increases. Demonstrate this change on the
demand curves in the graphs above. Explain your logic.
With an increase in the price of popcorn, there is a movement upward
along the demand curve for popcorn. Since popcorn and bottled water

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are complementary goods, as the price of popcorn increases, the
demand curve for bottled water will shift to the left.
c. Use the framework below to answer the following questions:
P P
S2 S1 S
Q Q
Bottled water Gasoline
i. (0.5pts) Label each axis and draw one Supply curve for the bottled water market
and one Supply curve for the gasoline market (do not draw demand curves).
ii. (0.5pts) What does the negative sign of c2 tell you about the relationship between
bottled water and gasoline?
As the price of gasoline increases, the supply of bottled water
decreases. This tells us that gasoline is an input in the production of
bottled water.
iii. (2pts) Suppose the price of gasoline increases. Demonstrate this change on the
supply curves in the graphs above. Explain your logic.
With an increase in the price of gasoline, there is an upward
movement along the supply curve for gasoline. As the price of gasoline
increases, the supply curve for bottled water will shift leftward.
6. (6pts) Recall the demand equations estimated from question #3.
 Pmachine = $2
 Ppopcorn = $1
 Income = $35
a. (2pts) Use the regression equation for summer demand in question #3c and plug in the
values above. Compute the new constant for the simplified summer demand equation.
Show your work.
b. (1pt) Write the simplified demand equation for summer:
Q1 = 267.77 – 24.56PBW + 21.39($2) – 57.24($1) + 19.29($35)
Q1 = 267.77 – 24.56PBW + 42.78 – 57.24 + 675.15
Q1 = 928.46 – 24.56PBW

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c. (2pts) Use the regression equation for winter demand in question #3c and plug in the
values above. Compute the new constant for the simplified winter demand equation.
Show your work.
d. (1pt) Write the simplified demand equation for winter:
Q2 = 219.27 – 52.62PBW + 17.56($2) – 30.90($1) + 20.05($35)
Q2 = 219.27 – 52.62PBW + 35.12 – 30.90 + 20.05
Q2 = 243.53 – 52.62PBW
7. (13pts) Graph the simplified demand curves created in question 6.
P
Q1: summer
Q
a. Think about this graph carefully.
 (1pt) We need to think carefully about the constant term. When P = 0, Q1 =928.46 .
Label that point on the graph.
 (1pt) When Q1 = 0, P = 37.8 . Label that point on the graph.
b. What do you expect to happen to demand during the winter period?
 (1pt) When P = 0, Q2 = 243.53 . Show that point on the graph.
 (1pt) When Q2 = 0, P = 4.63 . Show that point on the graph.
 (1pt) Show the winter demand line on the graph above.
c. (1pt) Did you just illustrate a movement along a demand curve or a shift in demand?
Briefly explain.
Illustrated in the graph above is a shift in demand. Weather is a non-price
variable, meaning a change in the weather leads to a shift in the demand
curve, not a movement along the curve. In the winter months, there will be a
lesserdemand for bottled water at every price.
d. Use Excel to create a graph showing the two demand lines.
ii. (2pts) Graph Q1 and Q2 against price (PBW).
928.46243.53
37.8
4.63
Q2: winter

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 Cut and paste your graph here:
e. (1pt) Looking at your graph, Excel put which variable on the vertical axis? Quantity .
f. (1pt) Think about the equation for Q1. If the excel graph were extended, where would it
cross the Q1 axis? (ie., what is the Q1 intercept) (write the number) 928.46 .
g. (1pt) Think about the equation for Q2. If the excel graph were extended, where would it
cross the Q2 axis? (ie., what is the Q2 intercept) (write the number) 243.53 .
h. (2pts) How does the Excel graph compare with the graph you drew in part “a” above?
The Excel graph reversed the vertices of the graph, causing the demand curve to
appear much flatter than it actually is. In addition, the Excel graph did not include
intercepts.
8. (8pts) Graph the simplified supply curve when gas prices are $2.50 per gallon (Q3).
a. (2pts) Refer back to the supply curve you estimated in question #4. Plug in the value for
the price of gas, calculate the new constant term and write out the simplified supply curve
(Q3).
Q3 = _______________________________________________
c. (2pts) Create an Excel graph with supply and both demand curves:
 Insert your graph here:
d. (2pts) Now suppose the price of gas increases to $3 per gallon. Refer back to the supply
curve you estimated in question #4. Plug in this new value for the price of gas, calculate
the new constant term and write out the new simplified supply curve (Q4).
Q4 = _______________________________________________
f. (2pts) Create two Excel graphs
 The first graph will show two supply lines (Pgas = 2.5 and Pgas = 3), along with
summer demand (Q1).

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 The second graph will show two supply lines (Pgas = 2.5 and Pgas = 3), along with
winter demand (Q2).
 Insert your graphs here:
9. (8pts) Use the equations for Q1, Q2, Q3, and Q4 to compare the impact of the gasoline price
increase on P&Q in the two situations.
a. Rewrite the equations for Q1-Q4 so they are all in one place.
b. (3pts) Use algebra to solve for the equilibrium P and Q for summer with gas prices at
$2.5 and $3. Show your work.
c. (3pts) Use algebra to solve for the equilibrium P and Q for winter with gas prices at $2.5
and $3. Show your work.
d. (2pts) Fill in the table below:
summer winter
Magnitude of the change in P
Magnitude of the change in Q
10. (8pts) Compute the elasticity of demand in the summer and in the winter when the price of
gas is $2.50.
a. (5pts) Use this information to make the calculations necessary to fill in the following
table (show calculations):
C1 C2 C3 Elasticity of
demand
Regression
equation
coefficient of
Pbw
(this is ∆Q/∆P)
Equilibrium P
(when Pgas =
$2.50)
Equilibrium Q
(when Pgas =
$2.50)
C1*(C2/C3)
Summer
winter
Calculations:

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b. (3pts) Now that you have used Excel to estimate the supply and demand curves and
you have used this information to calculate the elasticity of demand for the summer
and winter equilibria, are your Excel results consistent with the prediction from your
hand-drawn graph in question #2? Explain.