Managerial Economics (MBA 775)
Name:
Instructions: Answer all the questions in the space provided. You may work on the problems with other
class members, but please write up your own answers. Show your work where possible. The homework is
credit/no credit. Questions will not be graded, but problems will be worked in class. Due before the Week 2
Live Session.
1. Use the data from the minivan example (posted on the course website) to answer the following questions
about “our” minivan manufacturer:
a. What is the cross-price elasticity of demand (with respect to Chrysler) in Nashville, TN?
In general, the cross price elasticity tells us how the quantity of our minivan sold reacts to changes to the price
of another good. In this scenario, we want to see how our quantity reacts to changes in the price of Chrysler
given the current set of market conditions in Nashville.
We will use the formula for elasticity from the async material based on using the demand function. We can
see that below. We multiple the coefficient on price (3.00) times price over the estimated quantity in Nashville.
The price, in thousands from the data is 20.44. What is missing is the estimated quanity.
Nashville
Nashville
EQ
Our Minivan
, PChrysler
= α Chrysler Price
PChrysler
Nashville
Qˆ Our Minivan
α Chrysler Price = 3.00 from regression
Nashville
PChrysler = 19.05 from data
We get the estimated quantity by using the estimated demand function from the async material and plugging
in the data for Nashville. We can see this below. The average price of minivans there was 20.31 (or $20,310)
and the average income was 33.48 (or $33,480), etc…. Plugging in all the data we get the estimated quantity
sold in Nashville of 30.55.
Nashville
Qˆ Our Minivan =−6.66 + ( −5.22 * 20.31) + ( 0.45 * 33.48 ) + ( 0.93 * 23.91)
+ (1.77 * 27.56 ) + ( 3.00 *19.05 ) + ( 0.96 * 0.12 )
Nashville
Qˆ Our Minivan = 30.55
Now we have all the numbers to plug into our equation and we can see that the estimated elasticity is 1.87.
Nashville
Nashville
EQ
Our Minivan
, PChrysler
=α Chrysler Price
PChrysler
Nashville
Qˆ Our Minivan
=3.00 ×
19.05
30.55
1.87
=
This elasticity tells us that if Chrysler raises the price of their minivans 1% in Nashville, then our sales will
increase by 1.87% in Nashville, all else being equal.
b. Which market is more sensitive to changes in the price of the minivan that our company produces: Water
Mills, NY, or Denver, CO?
Now we are going to follow similar steps to part a, but now we are calculating the own price elasticity of
demand for Water Mills and Denver. That will let us know which consumers are more sensitive to the changes
in the price of the minivans that we sell.
Again we have the base equation for own price elasticity in Water Mills. Now we are using the coefficient on
our own price (-5.22) and the average price for Water Mills from the data (23.06).
Watermills
Watermills
EQ
Our Minivan
, POur Minivan
= α Our Minivan Price
POwn Minivan
Watermills
Qˆ Our Minivan
α Our Minivan Price = −5.22 from regression
Watermills
POwn Minivan = 23.06 from data
Again we need to calculate the estimated quantity using the data from Water Mills. This estimated quantity is
9.53.
Watermills
Qˆ Our Minivan =−6.66 + ( −5.22 * 23.06 ) + ( 0.45 * 40.37 ) + ( 0.93 *10.3 )
+ (1.77 *19.36 ) + ( 3.00 * 23.61) + ( 0.96 * 3.88 )
Watermills
Qˆ Our Minivan = 9.53
Putting this all together we get an estimated own price elasticity of -12.63 for Water Mills.
Watermills
Watermills
EQ
Our Minivan
, POur Minivan
Watermills
EQ
Our Minivan
, POur Minivan
=
α Our Minivan Price
POwn Minivan
Watermills
Qˆ Our Minivan
= −5.22 ×
23.06
9.53
=
−12.63
= −12.63
Now we go through the same steps to calculate the own price elasticity for Denver which is -5.09.
Denver
Denver
EQ
Our Minivan
, POur Minivan
= α Our Minivan Price
POwn Minivan
Denver
Qˆ Our Minivan
α Our Minivan Price = −5.22 from regression
Denver
POwn Minivan = 22.50 from data
Denver
Qˆ Our Minivan =
−6.66 + ( −5.22 * 22.50 ) + ( 0.45 * 29.28 ) + ( 0.93 * 20.93 )
+ (1.77 * 28.39 ) + ( 3.00 * 20.25 ) + ( 0.96 * 3.77 )
Denver
Qˆ Our Minivan = 23.06 sum(regression coefficients* data values in Denver)
Denver
Denver
EQ
Our Minivan
, POur Minivan
Denver
EQ
Our Minivan
, POur Minivan
= α Our Minivan Price
POwn Minivan
Denver
Qˆ Our Minivan
= −5.22 ×
22.50
23.06
=
−5.09
= −5.09
If we raise prices 1% in Water Mills, sales would decrease by an estimated 12.63%. If we raise prices 1% in
Denver, sales would decrease by an estimated 5.09%. Therefore, consumers in Water Mills are more sensitive
to the price of our minivan.
2. The following quote is from a recent MSN Money article on Clorox’s 2012 4th quarter financial results:
Sales of Clorox cleaning products alone jumped 15% to $425 million and increased income
28%. Household sales surged 7% and profits rose 65% as both prices and demand increased and
a germ-averse public stocked up.
Between strains of flu not covered by this year's flu shot and an absolutely grotesque norovirus
import from Australia that's been putting gastrointestinal systems to the test, it's been a tough
few weeks fraught with peril and hand washing for the average American.
Suppose an enterprising manager wanted to use changes in the 4th quarter to calculate the own-price
elasticity of demand for Clorox cleaning products. The manager has data on changes in price and changes
in quantity sold during the quarter.
a. What would be the main challenge they would face in calculating a reliable estimate of elasticity?
This is similar to the cruise ship example we looked at in the async material. In order to calculate own
price elasticity it must be the case the only relevant factors that are changing are quantity and price. In
this case demand also increased. Thus it would be difficult to separate the effect of the price change from
the change in demand. As it is we do not know how much more quantity would have increase if price did
not go up.
b. Suppose for the 3rd quarter this challenge did not exist, rather the challenge was one of the data
availability. All the manager knows, a few minutes before a quickly called meeting to discuss 3rd quarter
results, is that the price of a pack of 35-count Clorox Wipes increased by 12% while revenue from those
wipes increased by 5%. Calculate the own-price elasticity of demand for Clorox Wipes in this quarter.
Own price elasticity is defined as EQX PX =
%∆QX
. The problem here is that we are given the change in
%∆PX
price and the change in revenue. Thus we have to use the relationship between quantity, price and revenue
to calculate the change in quantity.
Here’s the fancy algebra way to do that (where P is the price at the beginning of the quarter and P’ is the
price at the end):
Rev= P × Q and P’ = P · 1.12 and
Q’ =
R’ = R · 1.05. This means that
R 1.05
R’
1.05
(by rearranging) so ×
=×
=×
Q
Q 0.9375 =×
Q (1 − 0.0625)
P 1.12
P’
1.12
This means that Q decreased by 6.25%. Now we can calculate the elasticity.
EQX PX =
%∆QX −0.0625
=
= −0.521
%∆PX
0.12
Another way to get to the same conclusion is to construct the following table where the second row gives us
price, quantity and revenue before the price increase and the second row gives us the new price and revenue.
Before Price Increase
After Price Increase
Price
Quantity
Revenue
10
100
1,000
11.20
1,050/11.2 =93.75
1,050
Notice that we assume that before the price change the price is $10 and quantity sold is 100. Multiplying the
two gives us a revenue of $1,000. After the 12% price increase the new price would be $11.20. We also know
that revenue goes up by 5% so that we have $1,050.
To get the quantity after the price change we divide the new revenue by the new price to get a quantity of 93.75.
Thus quantity has decreased by 6.25 units (100-93.75). Thus the percentage change in quantity is 6.25/100 =
6.25%. This is the same as what we found above using algebra.