Problem Set 8: Decision under Uncertainty
1. Let X be a random variable taking values x [0, 1]. Let an agents Bernoulli utility function
be u(x) = x where 0 < < 1. Let the probability distribution of X be P r[X x; ] = F (x; ) =
x1+ where = 0.
i. Character
Running head: GLOBALIZATION: WHO IS IT REALLY GOOD FOR?
Globalization: Who is it really good for?
Michaela Livengood
University of Southern Indiana
1
GLOBALIZATION
2
Globalization: Who is it really good for?
World income distribution is obviously effected
Problem Set 5: Expenditure Minimization, Duality, and Welfare
1. Suppose you were given the following expenditure function:
e(p, u) = up p
1 2
+
where 0 < , < 1 and + = 1. Derive Hicksian demand, Walrasian demand, and the indirect
utility function. What
Problem Set 8: Decision under Uncertainty
1. Let X be a random variable taking values x [0, 1]. Let an agents Bernoulli utility function
be u(x) = x where 0 < < 1. Let the probability distribution of X be P r [X x; ] = F (x; ) =
x1+ where 0.
i. Characteri
Problem Set 2: The implicit function and envelope theorems
2. (i) A monopolist faces inverse demand curve p(q, a), where a is advertising expenditure, and
has costs C (q ). Solve for the monopolists optimal quantity, q (a), and explain how the optimal
qua
Problem Set 1 - selected answers
2. (i) A function is Lipschitz continuous on (a, b) if, for all x and x in (a, b), |f (x ) f (x )| <
K |x x |, where K is nite. Show that a Lipschitz continuous function is continuous. Provide an
example of a continuous fu
Problem Set 3: Unconstrained maximization in RN
2. (i) Find all critical points of f (x, y ) = (x2 4)2 + y 2 and show which are maxima and which
are minima. (ii) Find all critical points of f (x, y ) = (y x2 )2 x2 and show which are maxima
and which are m
Problem Set 4: Equality-Constrained Maximization
1. Consider the maximization problem
max x1 + x2
x1 ,x2
subject to
x2 + x2 = 1
1
2
Sketch the constraint set and contour lines of the objective function. Find all critical points of the
Lagrangian. Verify w
Problem Set 7: Welfare and Producer Theory
1. For utility function u(x1 , x2 ) = (x1 1 )x2 and budget constraint w = p1 x2 + p2 x2 , derive the
agents money-metric utility function. Provide a general expression for EV and CV , and compute
these for change
Problem Set 6: Consumer Theory
1. Preferences are lexicographic on R2 if (x1 , x2 ) (y1 , y2 ) whenever (i) x1 > y1 or (ii) x1 = y1
and x2 y2 . Show that lexicographic preferences are complete, transitive, strongly monotone, and
strictly convex.
i. To sho
Problem Set 5: Inequality-Constrained Maximization
I was going to mention this in class, but KKT multipliers must be positive if you write the
constraint as hk (x) 0. Why? Lets relax the constraint by to hk (x) 0. Then the
Lagrangian is
L = f (x) g(x) 1 h
Midterm Exam
1. Consider the functions
e1 (p, u) = up p
12
1
pp
u12
e2 (p, u) =
+
+
= up p K
12
=
1
ppK
u12
where > 0, > 0, and + = 1.
i. What properties must expenditure functions derived from rational, continuous, locally non-satiated preferences satisf
Midterm Exam
1. Consider the functions
e1 (p, u) = up p
12
1
pp
u12
e2 (p, u) =
+
+
= up p K
12
=
1
ppK
u12
where > 0, > 0, and + = 1.
i. What properties must expenditure functions derived from rational, continuous, locally non-satiated preferences satisf
Midterm Exam
1. Consider the inequality constrained maximization problem
max log(x) + log(y )
x,y
, > 0, subject to the inequality constraints
x, y 0
where
x2 + y 2 1
y (1 2t)x + t
1/2 < t < 1 (note that if x = 1/ 2, then (1 2t)x + t = 1/ 2)
a. Sketch the
Problem Set 4: Basic Consumer Theory
Recommended MWG questions (Not to be turned in) : 2E8, 2F16, 2F17, 3B2, 3C2, 3D8, 3E4,
3G1, 3G7, 3G14
1. Preferences are lexicographic on R2 if (x1 , x2 ) (y1 , y2 ) whenever (i) x1 > y1 or (ii) x1 = y1
and x2 y2 . Sho
Absolute Advantage and Comparative Advantage
Worksheet
Assume that there are two nations in the world, Ireland and Switzerland, and that each
country can produce only two products. Each country uses half of its resources on each
product. They can produce
AP Economics:
Costs FRQ
December 5, 2013
Monopoly FRQs
1. The graph below shows the demand and cost curves of a firm that does not price
discriminate.
(a) Suppose the firm produces at the profit-maximizing output. Using the labeling on the
graph, identify
Problem Set 1 Selected answers
1. (i) Suppose x is a local maximizer of f (x). Let g() be a strictly increasing function. Is
x a local maximizer of g(f (x)? (ii) Suppose x is a local minimizer of f (x). What kind of
transformations g() ensure that x is al
Lecture 3
Replacement of lecture and tutorial
No classes 28/3 1/4
Friday 25/3: public holiday
For students with lecture or tutorial on Fridays:
Stream 3: Replacement lecture
Wed 23/3, 6-8pm, ABS Lecture Theatre 1110
Friday tutes: Replacement mass tut
Practice Exam Questions 1
1. There is a rm that produces quantities of two goods, q1 and q2 . The price of good 1 is
p1 and the price of good 2 is p2 . The rms cost structure is
C(q1 , q2 ) = c1 (q1 ) + c2 (q2 ) q1 q2
where C(q1 , q2 ) > 0 for all q1 , q2
Midterm Exam
1. Consider the functions
e1 (p, u) = up p
1 1
1
p p
u 1 1
e2 (p, u) =
+
+
= up p K
1 1
=
1
p p K
u 1 1
where > 0, > 0, and + = 1.
i. What properties must expenditure functions derived from rational, continuous, locally non-satiated prefere
Midterm Exam
1. Consider the functions
e1 (p, u) = u(p + p )1/
1
2
e2 (p, u) =
1
(p + p )1/
2
u 1
where < < 1 and not equal to zero.
i. What properties must expenditure functions derived from rational, continuous, locally non-satiated preferences satisfy
Practice Exam Questions 1
1. There is a rm that produces quantities of two goods, q1 and q2 . The price of good 1 is
p1 and the price of good 2 is p2 . The rms cost structure is
C(q1 , q2 ) = c1 (q1 ) + c2 (q2 ) q1 q2
where C(q1 , q2 ) > 0 for all q1 , q2
Midterm Exam
1. Consider the indirect utility function
v(p, w) = (w px x )
(1 )1
p p1
x y
where (0, 1) and w > px x .
i. Derive the Walrasian demand functions, x(p, w).
ii. Derive the expenditure function, e(p, u).
iii. Derive the Hicksian demand functio
Midterm Exam
1. Consider the indirect utility function
v(p, w) = (w px x )
(1 )1
p p1
x y
where (0, 1) and w > px x .
i. Derive the Walrasian demand functions, x(p, w).
ii. Derive the expenditure function, e(p, u).
iii. Derive the Hicksian demand functio
Midterm Exam
1. Consider the functions:
v1 (p, w) = (w p2 )
v2 (p, w) = (w + p2 )
p p
1 2
p p
1 2
Assume + = 1 and w > p2 .
i. List the characteristics a valid indirect utility function must have. Explain why v1 () and v2 () either do or
do not meet t