Intermediate Microeconomics
October 15, 2003
Due:
Prof.Li-Chen Hsu
1.
October 22, 2003
Problem Set #1
(10 points) Suppose that the budget equation is given by p1 x1  p2 x2  m . The
government decides to impose a lump-sum tax of u, a quantity tax on good 1 of t, and an
ad valorem subsidy on good 2 of s.
a) What is the formula for the new budget line?
b) If p1  5 , p2  10 , m  100 , u  10 , t  5 , s  10% , please draw the original
and new budget line and their slopes.
2.
(10 points) While traveling abroad, Mike spent all of the money in his purse to buy 5
plates of spaghetti and 6 oysters. Spaghetti cost 8 units of the local currency per plate
and he had 94 units of currency in his purse. If s denotes the number of plates of
spaghetti and o denotes the number of oysters purchased.
a) The set of commodity bundles that he could just afford with the money in his purse
is described by what equation?
b) If the number of plates of spaghetti is restricted to be less than 10 and the number of
oysters is restricted to be less than 8, please draw the budget set.
3.
(12 points) Draw the indifference curve for the following cases.
a) Average is indifferent to extreme.
b) $10 coin and $50 coin. (perfect substitutes)
c) A individual likes to eat two toasts with one egg. (perfect complements)
4.
(12 points) According to the previous question b) and c), please show:
a) The utility functions.
b) The MRS , MU x and MU y .
5.
.
(10 points) Draw graphs with quantities of pepperoni pizza on the horizontal axis and
quantities of anchovy pizza on the vertical axis to illustrate the following situations. In
each case draw two different indifference curves and make a little arrow pointing in the
direction of greater preference.
a) Mikeyu loves pepperoni pizza and hates anchovy pizza.
b) Colorking hates pepperoni pizza and is completely indifferent about anchovy pizza.
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6.
(6 points) Kobe has indifference curves with the equation x 2  10  6 x1 3 . If good 1 is
drawn on the horizontal axis and good 2 on the vertical axis, what is the slope of Kobe’s
indifference curve when his consumption bundle is (8, 9)?
7.
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(10 points) GiGi consumes goods x and y. GiGi’s utility function is U ( x, y )  x y .
a) What are the MU x , MU y and MRS ?
b) If GiGi’s utility function becomes U ( x, y)  x 4 y 4 , What are the MU x , MU y and
MRS ?
c) Are the MRS of a) and b) the same or different? Why?
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8.
(12 points) Bush’s utility function is U ( x, y )  y  3x 2 , please answer the following
questions:
a) What are the MU x , MU y and MRS ?
b) Try to explain the meaning of MRS of this preference form.
c) Bush has 25 units of x and 12 units of y. If his consumption of x is reduced to 0, how
many units of y would he need in order to be exactly as well off as before?
9.
(12 points) Webber’s utility function is U ( x, y )  xy . Which of the following utility
functions is the one that would and would NOT represent Webber’s preferences? Why?
a) V ( x, y)  2 x 3 y 3  10
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b) V ( x, y)  0.5 x 2 y 2  20
c) V ( x, y )  4 xy(1  xy)
d) V ( x, y )  2 /(1  4 xy)
e) V ( x, y )  ln xy
f) V ( x, y)  e  xy
10. (6 points) Is the following statement true or false? Briefly explain your answer.
a) If there are two goods, if a consumer prefers less of each good to more, and if she
has a diminishing marginal rate of substitution, then her preferences are convex.
b) A consumer has preferences represented by the utility function
U ( x, y)  8( x 2  2 xy  y 2 )  40 . For this consumer, goods x and y are perfect
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substitutes.
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