C what bundle would bernice choose if she faced the

(c) What bundle would Bernice choose if she faced the original prices and
had just enough income to reach the new indifference curve?
(3 , 3) .
Draw with red ink the budget line that passes through this bundle at
the original prices. How much income would Bernice need at the original
prices to have this (red) budget line?
$9.

186 CONSUMER’SSURPLUS (Ch. 14)
(d) The maximum amount that Bernice would pay to avoid the price
increase is
$3.
This is the (compensating, equivalent) variation in
income.
Equivalent.
(e) What bundle would Bernice choose if she faced the new prices and had
just enough income to reach her original indifference curve?
(4 , 4) .
Draw with black ink the budget line that passes through this bundle at
the new prices. How much income would Bernice have with this budget?
$16.
(f) In order to be as well-off as she was with her original bundle, Bernice’s
original income would have to rise by
$4.
This is the (compensating,
equivalent) variation in income.
Compensating.
Calculus
14.6 (0) Ulrich likes video games and sausages. In fact, his preferences
can be represented by u ( x, y ) = ln( x + 1) + y where x is the number of
video games he plays and y is the number of dollars that he spends on
sausages. Let p
x
be the price of a video game and m be his income.
(a) Write an expression that says that Ulrich’s marginal rate of substi-
tution equals the price ratio. ( Hint: Remember Donald Fribble from
Chapter 6?)
1 / ( x + 1) = p
x
.
(b) Since Ulrich has
quasilinear
preferences, you can solve this
equation alone to get his demand function for video games, which is
x = 1 /p
x
− 1 .
His demand function for the dollars to spend on
sausages is
y = m − 1 + p .
(c) Video games cost $ . 25 and Ulrich’s income is $10. Then Ulrich de-
mands
3
video games and
9.25
dollars’ worth of sausages.
His utility from this bundle is
10.64.
(Round off to two decimal
places.)
(d) If we took away all of Ulrich’s video games, how much money would
he need to have to spend on sausages to be just as well-off as before?
$10.64.

NAME 187
(e) Now an amusement tax of $.25 is put on video games and is passed
on in full to consumers. With the tax in place, Ulrich demands
1
video game and
9.5
dollars’ worth of sausages. His utility from this
bundle is
10.19.
(Round off to two decimal places.)
(f) Now if we took away all of Ulrich’s video games, how much money
would he have to have to spend on sausages to be just as well-off as with
the bundle he purchased after the tax was in place?
$10.19.
(g) What is the change in Ulrich’s consumer surplus due to the tax?
− . 45
How much money did the government collect from Ulrich by
means of the tax?
$.25.
Calculus
14.7 (1) Lolita, an intelligent and charming Holstein cow, consumes
only two goods, cow feed (made of ground corn and oats) and hay. Her
preferences are represented by the utility function U ( x, y ) = x − x
2
/ 2+ y ,
where x is her consumption of cow feed and y is her consumption of hay.