1.
Every morning Professor Gordon buys a bagel and a cup of coffee from
Peabody’s.
At Peabody’s the price of bagels is $2.00 and the price of a cup of coffee is
$1.00.
a.
Assuming that Professor Gordon has $20 to spend on coffee and bagels, sketch her
budget constraint, putting coffee on the xaxis and bagels on the yaxis.
Clearly label a)
the xintercept, b) the yintercept, c) and the slope of the budget constraint.
b.
Now, suppose that Peabody’s wants to encourage customer loyalty.
To do so they start
the following program: every time someone purchases 10 cups of coffee, they get the
11
th
cup for free.
Sketch Professor Gordon’s new budget constraint under the
assumption that she still has $20 to spend on coffee.
As above, put coffee on the xaxis
and bagels on the yaxis.
Clearly label a) the xintercept, b) the yintercept, c) and the
slope of the budget constraint.
In addition, if there are any changes in the slope of the
budget constraint, clearly identify the coordinates (i.e. the points) where those changes
occur.
NOTE:
Think about this one carefully.
a.
coffee
bagels
20
10
slope=1/2
b.
coffee
bagels
22
10
slope=1/2
10 11
21
5
3.
Suppose that George is currently consuming 4 apples and 4 bananas. If the price of
apples is .25 and George spends $6 on apples and bananas, then what is the price of bananas?
Use the budget constraint equation to obtain:
P1*X1+P2*X2=M.
Let apples be X1 and
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bananas be X2.
This gives us .25*4+P2*4=6. Solving for P2 we get that P2=1.25.
So the price
of bananas =1.25.
4.
Suppose Dave has $100 to spend on entertainment every month and that Dave’s favorite
forms of entertainment are movies and concerts.
a.
If the price of movies is $10 and the price of concerts is $20, draw Dave’s budget
constraint for entertainment, putting movies on the horizontal axis. Clearly label a) the
xintercept, b) the yintercept, c) and the slope of the budget constraint.
b.
Now suppose that the local theatre where Dave always goes to watch movies offers the
following special deal:
Anyone who goes to more than 4 movies a month, can see any
remaining movies in that month for half price.
Draw Dave’s new monthly budget
constraint for entertainment. Clearly label a) the xintercept, b) the yintercept, c) and
the slope of the budget constraint.
In addition, if there are any changes in the slope of
the budget constraint, clearly identify the coordinates (i.e. the points) where those
changes occur.
a.
Recall the budget constraint equation P1*X1+P2*X2=M. If the price of movies
is 10 and the price of concerts is 20 we have 10*X1+20*X2=100.
If we solve for X2 we
have the equation X2= .1/2X1 + 5. The slope of the line is then given by P1/P2
= 10/20
=1/2. If he spent all his income on movies he would be able to buy I/P1 or 100/10 = 10
Movies.
If he spent all his money on concerts he would be able to buy 5 concerts.
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 Spring '08
 TANG
 Microeconomics

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