Sam, Ivy, Avery,
and Claire are all students at Mount Holyoke College. During their first few
weeks on campus as first year students, they all developed a love for the Chef
Jeff cookies and the other goods sold at Uncommon Grounds. They then had to
learn to manage their love for baked treats throughout the semester based on
their own preferences and budgets.
Sam, a Mount
Holyoke Student, loves to visit Uncommon Grounds. She enjoys nothing more than
finishing her Friday morning class and then on her route back to Rockies, she
stops by Uncommon Grounds for a strong cup of their “Fogbuster” coffee and a
delicious chocolate chunk Chef Jeff cookie.
She has quite
particular tastes and would not enjoy her chocolate chunk cookie without a cup
of coffee. She only consumes the cup of coffee and cookie together. For her
they are the Perfect Compliments to
each other. For example, when she orders two cookies she would also order two
cups of coffee because she would not consume them independent of each other.
Therefore her Optimal Consumption Bundles would be
one cookie and one coffee, two cookies and two coffees, three cookies and three
coffees, and so on. We can draw a line connecting her OCBs which we can call
the Income Offer Curve. As she has
30 Dining Dollars each semester, her budget line will be 30 dollars.
Theoretically, her consumption of cookies and coffee will be proportionate a
every income level. To describe how her demand for each good changes with her
income level, we can use quantity of goods consumed and income level to draw an
Engle Curve.
During the reading
days before her finals, Ivy, an international Mount Holyoke student, decides to
spend all of her dining dollars at Uncommon Grounds. She does not want to spend much more than her dining dollars
and she has spent $10 in Blanchard Café during the semester, so her budget constraint is fixed at $20. Since Ivy does not like coffee, tea or
ice-cream, she decides to buy Chef Jeff cookies, which cost about $1.25 each, and
smoothies, which costs about $4 per cup.
Now she definitely
does not want to spend all her budgets on 16 cookies or 5 cups of
smoothies. If she buys 4 cups of
smoothies, she only has $4 left to buy 3 or 4 cookies, which are not enough for
her. Therefore, she would rather
forgo a smoothie to buy more cookies, so that she can have 3 cups of smoothies
and 6 or 7 cookies. However, she
still wants more cookies. Therefore,
she chooses to buy 2 cups of smoothies and 10 cookies, and she feels that she
has made the best choice.
The graph below
shows Ivy’s indifference curves and budget line. Ivy’s optimal
consumption bundle, which consists of 2 cups of smoothies and 10 cookies is
represented by the red dot at the tangency between her budget line and one of
her indifference curves.
Claire, a student
at Mount Holyoke, loves Chef Jeff cookies. It doesn’t matter what type of
cookie it is, Claire will eat it. However, she does have two favorites. She
loves the chocolate chunk cookies and the Oreo cookies. Whenever she passes
Uncommon Grounds, in the student center, she stops for one of these cookies.
She does limit herself to her $30 dining dollars budget though, so that she
doesn’t spend all of her money on Chef Jeff cookies. Because the cookies are
$1.25 each, she can consume 24 cookies throughout the semester, if she does not
use her dining dollars budget for any other good.
Sometimes she stops at
Uncommon Grounds and they are selling both chocolate chunk cookies and Oreo
cookies. Other days she stops and they’re only selling one type of cookie. It
doesn’t matter to Claire though, she is equally happy with either, for her,
they are perfect substitutes.
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As shown on the
graph, Claire has many different optimum
consumption bundles. She would be happy consuming 8 chocolate chunk cookies
and 16 Oreo cookies (the blue dashed line). Claire would also be happy buying
16 chocolate chunk cookies and 8 Oreo cookies (the green dashed line), and
would be happy consuming both 12 chocolate chunk cookies and 12 Oreo cookies
(the red dashed line).
Avery has a severe
nut allergy. While growing up, visiting a cafe like Uncommon Grounds was like
touring a minefield. Happily, just in time for her High School graduation in
2010, a miracle over the counter drug called Nutsafe appeared on the market in the form of a pill to be taken
daily. Ever since then, food establishments have become a much safer place for
Avery. While attending Mount Holyoke College, she even developed a taste for
Chef Jeff cookies.
Depending
on the cookie and because all of the cookies are made and sold in a not quite
nut free environment, Avery can only consume so many cookies before she notices
a slight anaphylactic reaction. One could even conceptualize the limitations on
her cookie consumption as a budget
constraint.
Avery
absolutely loves Chef Jeff cookies. She likes to mix and match cookie types
each time she visits Uncommon Grounds and has a few favorite combinations that
also work with her nut allergy. Avery knows that after taking one dose of Nutsafe, she can consume a maximum of 6
cookies, given that they don’t explicitly contain nuts. Because she isn’t
particularly picky about how many of each cookie she eats, she treats chocolate
chip and Heath Bar Chef Jeff cookies as perfect
substitutes. Avery’s nut budget
constraint takes the form of: 6=x+y,
After taking one
dose of Nutsafe, Avery’s budget is a
maximum of 6 nutless cookies. With every additional dose of Nutsafe she can consume an additional 6
nutless cookies. Chocolate chip and Heath Bar Chef Jeffs are not just perfect substitutes
for Avery, their individual health and monetary costs are also exactly the
same. This implies however, that Avery prefers no one combination of chocolate
chip and Heath Bar Chef Jeff cookies to another. In other words, it is the case
that every bundle of goods represented in the above scatter plot could be
called Avery’s Optimal Consumption
Bundle.
We can also
approach this idea from a mathematical angle. The Marginal Rate of Substitution of the Indifference Curve along which Avery’s nutless cookie budget
constraint lies is -1. After rearranging the nutless cookie budget constraint,
we see that y=6−x. The slope of her budget constraint equals -1, or ,−P-x./,P-y.
= −1, which is exactly equal to the MRS of the above depicted IC. In other
words, −M,U-x./M,U-y. = −1 = −,P-x./,P-y..
These pieces of information tell us that Avery’s entire nutless cookie budget
constraint intersects with the above shown IC, which has a utility for Avery
equal to 6 nutless cookies.
Avery has also
found that she can increase her resistance to nuts by taking additional Nutsafe pills. This enables her to eat a
proportionately larger number of cookies. She only does this occasionally
however, because the long term effects of overusing Nutsafe haven’t yet been determined. As a runner on the Mount
Holyoke College cross country team though, Avery readily doubles, and even
triples her cookie consumption, showing a homothetic
preference for Chef Jeff cookies,
1 Dose Nutsafe
→ 6=x+y, 2 Doses Nutsafe → 12=2x+2y, 3 Doses Nutsafe → 18=3x+3y
Avery loves
cookies and never hesitates to buy six at a time. As a senior, she requires
lots of cookies to keep her company on lonely nights researching her thesis in
the library. Luckily for her, she has enough money saved in the bank to support
her Chef Jeff habit through these stressful times.
As shown in the
above examples, Sam, Ivy, Avery, and Claire each have their own unique
preferences. They each figured out a way to manage their own personal budgets
while still maximizing their utility of cookie, smoothie, and coffee
consumption. Students, faculty, and staff are all familiar with this struggle
as they pass Uncommon Grounds. In its own right, it is practically a Mount
Holyoke tradition.
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