NAME:
Micro II Midterm, October 15, 2007
You have until 2:50 to complete this exam. Answer all four questions. You may use results
covered in class, the textbook, or your homework to answer the questions. To insure maximum credit, be sure to explain your
Homework #5
6.2 Suppose there are 3 states, s = 1, 2, 3.
Dene lotteries L1 = (1/2, 1/2, 0), L2 =
(0, 1/3, 2/3) and L3 = (2/3, 0, 1/3). Can (1/3, 1/3, 1/3) be written as a compound lottery
based on L1 , L2 , and L3 ? If so, demonstrate how.
Answer: We must
Micro I Midterm, February 23, 2012
1. There are two goods. Suppose a consumer has the convex utility function u(x1 , x2 ) = x1 + x2 and
2
consumption set X = R2 . Let prices be p = (1, p)
0 and income be m > 0. Suppose further that
+
u 0. If possible for
Micro I Final, April 26, 2012
1. Suppose that a gambler discounts future utility at rate > 0 per period, yielding discount factor = 1/(1 + ) < 1
and has felicity function u(c) = c1 /(1 ) where > 0 and = 1. In that case, the sum of disconted felicity can
b
NAME:
Micro II Midterm, October 15, 2007
You have until 2:50 to complete this exam. Answer all four questions. You may use results
covered in class, the textbook, or your homework to answer the questions. To insure maximum credit, be sure to explain your
Micro II Midterm, October 15, 2007
1. There are two consumer and two goods. The indirect utility functions of the consumers are v1 (p, m) =
(p1 + m)/(p1 + p2 ) and v2 (p, m) = (p2 + m)/(p1 + p2 ). If these are the only consumers, is market demand
a functi
Micro II Final, December 12, 2007
You have until 3:00 to complete this exam. Answer all ve questions. You may use results covered in class, the textbook,
or your homework to answer the questions. To insure maximum credit, be sure to explain your answers.
Micro II Final, December 12, 2007
1. A lottery pays $10 with probability .1 and $0 with probability .9. The consumers utility function is
u(c) = c where 0 < < 1.
a) Compute the certainty equivalent of this lottery as a function of .
Answer: Expected utili
NAME:
Micro I Midterm, February 26, 2008
You have until 6:15 to complete this exam. Answer all four questions. You may use results you recall from
class, the textbook, or your homework to answer the questions. To insure maximum credit, be sure to
explain
Micro I Midterm, February 26, 2008
1. Suppose the expenditure function is e(p, u) = p1 +
p1 p2 + u(p1 + p2 ) for u 0.
a) Find the Hicksian demand functions.
Answer: Using the Shephard-McKenzie Lemma, we nd h1 (p, u) = 1 + u + (1/2) p2 /p1 and
h2 (p, u) =
Homework #4
5.8 Let f : R+ R+ be continuous and concave. Dene F (x1 , x2 ) = x2 f (x1 /x2 ). Let
T = cfw_(x1 , x2 , y ) : y F (x1 , x2 ). Show that T is an constant returns production set.
Answer: Let (x1 , x2 , y ) T and > 0. Then y F (x1 , x2 ) = x2 f (
Homework #2
2.3 When L = 2, let utility have the Leontief form u(x) = mincfw_x1 , 2x2 . Suppose wealth is
m = 2 and prices are p = (1, 0). Does the utility maximization problem have a solution?
If so, nd it. If not, explain why theorem 2.1 does not apply.
Homework #1
2
1.4 On R2 , dene x y if both x1 + x2 > y1 + y2 and x1 x2 > y1 y2 . Is
+
complete? Justify your answers either by proof or counter-example.
transitive? Is it
Answer: Consider x = (20, 0.01), y = (19, 0.1) and z = (1, 1). Then x1 + x2 = 20.01
Micro II Midterm, October 15, 2007
1. There are two consumer and two goods. The indirect utility functions of the consumers are v1 (p, m) =
(p1 + m)/(p1 + p2 ) and v2 (p, m) = (p2 + m)/(p1 + p2 ). If these are the only consumers, is market demand
a functi
Micro II Final, December 12, 2007
You have until 3:00 to complete this exam. Answer all ve questions. You may use results covered in class, the textbook,
or your homework to answer the questions. To insure maximum credit, be sure to explain your answers.
Micro II Final, December 12, 2007
1. A lottery pays $10 with probability .1 and $0 with probability .9. The consumers utility function is
u(c) = c where 0 < < 1.
a) Compute the certainty equivalent of this lottery as a function of .
Answer: Expected utili
NAME:
Micro I Midterm, February 26, 2008
You have until 6:15 to complete this exam. Answer all four questions. You may use results you recall from
class, the textbook, or your homework to answer the questions. To insure maximum credit, be sure to
explain
Micro I Midterm, February 26, 2008
1. Suppose the expenditure function is e(p, u) = p1 +
p1 p2 + u(p1 + p2 ) for u 0.
a) Find the Hicksian demand functions.
Answer: Using the Shephard-McKenzie Lemma, we nd h1 (p, u) = 1 + u + (1/2) p2 /p1 and
h2 (p, u) =
NAME:
Micro I Final, April 22, 2008
You have 2 hours to complete this exam. Answer all ve questions. You may use results covered in class,
the textbook, or your homework to answer the questions. To insure maximum credit, be sure to explain
your answers. E
NAME:
Micro II Final, April 28, 2011
You have 2 hours to complete this exam. Answer all ve questions. You may use results covered in
class, the textbook, or your homework to answer the questions. To insure maximum credit, be sure to
explain your answers.
Micro II Final, April 28, 2011
1. Consider a two-person, two-good exchange economy. Consumer i has utility ui (xi ) = maxcfw_xi , xi .
12
The endowments are 1 = (3, 1) and 2 = (0, 2).
a) Find all the equilibria of this economy.
Answer: Due to strong monot