Download Intermediate Microeconomics December 10, 2003

Intermediate Microeconomics
December 10, 2003
Due: December 17, 2003
Prof. Li-Chen Hsu
Problem Set #3
1.
(20 points) Is the following statement true or false? Briefly explain your answer.
(a) The SARP says that if a consumer bought x when he could have afforded y and
bought y when he could have afforded z, then he will buy x whatever he can afford z.
(b) When prices are ($4, $2), Jolin chooses the bundle (9, 18), and when prices are ($1,
$3), she chooses the bundle (8, 14). Then the bundle (8, 14) is revealed preferred to
the bundle (9, 18), and she violates WARP.
(c) Jay spends his entire income on two goods. One of them is a Giffen good. If the
price of the Giffen good rises, demand for the other good must fall.
(d) An inferior good must be a Giffen good.
2.
(8 points) In 1991, good x cost $5 and good y cost $1. They now cost $9 and $5
respectively. In 1991 the consumption bundle of x and y was 4 x’s and 5 y’s. It is now 9
x’s and 7 y’s. Calculate the Laspeyres and Paache index of current prices relative to 1991
prices rounded to two decimal places.
3.
(8 points) When the prices were ($5, $1), Yuki chose the bundle ( x, y )  (6, 4) . Now at
the new prices, ( Px , Py ) , she chooses the bundle ( x, y )  (5, 7) . For Yuki’s behavior to be
consistent with the WARP, what is the relation between Px and Py ?
4.
(12 points) If we know that Kidd chooses the bundle (100, 100) when prices are (100,
100) and he chooses the bundle (120, k) when prices are (100, 80). What range of k
would you conclude if his behavior violates WARP?
5.
(12 points) You are given the following information about a consumer’s purchases. He
consumes only two goods, x and y.
Year 1
Year 2
Year 3
Quantity
Price
Quantity
Price
Quantity
Price
x
7
4
6
2
8
p x3
y
9
2
8
4
6
p 3y
What’s the condition for the consumer’s preferences to satisfy SARP?
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6.
(20 points) Suppose O’neal has a utility function U ( x, y )  xy .Originally his income is
$100, the price of x and y are $4 and $5. Please answer the following questions.
(a) What are the optimal choices of x and y?(3 points)
(b) If the price of x falls to $2, please calculate the substitution effect.(4 points)
(c) By (b), please calculate the income effect.(4 points)
(d) Is x a normal good and ordinary good? Why? (3 points)
(e) Draw a graph to show the situation from (a) to (d).(6 points)
7.
(12 points) Please use the Slutsky decomposition to draw the graphs of (a) perfect
complement, (b) perfect substitutes, (c) quasilinear preferences and denote the
SE(substitution effect), IE(income effect) and TE(total effect).
8.
(8 points) What is the Hicks substitution effect? What are the differences between
Slutsky and Hicks substitution effect? Please draw graphs to explain it.
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