Chapter 2: The Budget Constraint
1. In 1965 Congress extended the Social Security program to include Medicare, a
compulsory hospitalization insurance plan covering doctors’ fees for people over
65. A similar program is available to low income individuals. Suppose that if
an individual is eligible for the program, then by paying an extra $20 per month
she obtains an extra $200 of medical benefits. (She can pay an extra $20 for
$200 of benefits only once per month.)
(a) If an individual’s cash income is $500 per month and she is not eligible for
the medical program draw her budget line (the value of non-medical goods
consumed per month will be measured on the vertical axis, and the value
of medical goods on the horizontal axis).
(b) Draw the individual’s budget line on this graph if she is eligible for the
medical benefits and her cash income is still $500 (hint: a budget line can
have kinks).
2. Joe College has a money income of $M. Joe consumes only Pizza and Beer
which have prices of pZ = $1 and pB = $1, respectively.
(a) Graph Joe’s budget set. Put the quantity of Beer on the horizontal axis.
(b) Joe’s parents are considering giving Joe a gift of $G < $M. However, they
are concerned that he might drink too much beer. They decide that the
gift will be reduced by $1 for every $1 that Joe spends on beer. (If Joe
spends more than $G on beer then the gift is reduced to zero. Assume that
his parents can monitor his beer consumption.) Graph Joe’s new budget
set on the same graph as (a).
(c) Joe’s parents reason that “None of our gift is used to purchase beer since
the gift is reduced by $1 for every $1 that Joe spends on beer.” Suppose
that Joe chooses a consumption bundle “x” in (a) which exhausts his
income. Could there be a consumption bundle “y” in (b) which has more
pizza and more beer than x? (In other words, is it possible that Joe’s
consumption of beer is greater in (b) than in (a)?)
(d) Suppose instead that Joe’s parents offer the gift of $G only if he agrees
to become a teetotaler. (In other words, if he gives up drinking.) Graph
Joe’s budget set before he has decided whether or not to accept the gift.
Could there be a consumption bundle “z” which is affordable given this
new budget set, and which has more pizza and more beer than x?
3. Jane Consumer has an income of $100 which she spends on phone calls to New
York city and to Boston.
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(a) The long distance carrier ABC charges a $25 connection fee. The price is
a $1 per minute calling either Boston or N.Y.C. Sketch Jane’s budget set
if she chooses ABC as her long distance carrier. (Graph minutes to Boston
on the horizontal axis.)
(b) XYZ charges $2 per minute when calling either Boston or N.Y.C. However,
XYZ will give a 50% discount on calls made to the city that is called the
most. (For example, the bill for 10 minutes of calls to N.Y.C. and 15
minutes of calls to Boston is 2 × 10 + 1 × 15 = 35.) If each city is called
equally often, then the discount applies to only one city. XYZ charges no
connection fee. Sketch Jane’s budget set if she chooses XYZ as her long
distance carrier.
(c) Sketch Jane’s budget set given that she can choose either company as her
long distance carrier.
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