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
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 go
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, Wal
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
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 o
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 functi
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 )
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 functio
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
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, transi
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
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 ration
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 ration
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 t
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
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 h
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-maxim
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
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 L
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 )
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
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 rationa
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 )
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 fun
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 fun
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.