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
Syllabus
CHM_2041.0001
Chemistry Fundamentals IB
Fall 2016
Instructor:
Dr. Alejandra Branham
Office and Office Hours: PSB 248
, Tuesday and Thursday 6:00 PM to 7:30
PM
Lecture Time:
Tuesday and Thursday from 4:30 PM to 5:50 PM
Location:
CB2-101
E-mail:
al
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
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
Midterm Exam
1. Consider the functions:
v1 (p, w) = (w p2 )
v2 (p, w) = (w + p2 )
p p
12
p p
12
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 the
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
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 ,
Practice Exam Questions 2
1. There is a household who maximizes discounted utility
u(c1 ) + u(c2)
and faces budget constraints, w = L + s + c1 and rL + s = c2 , where c1 is consumption in
period 1 and c2 is consumption in period 2, where w is wealth, and
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
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 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 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
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
UCF - CHEMISTRY FUNDAMENTALS 1A - PROF. BEAZLEY
UCF PROF. BEAZLEY PRACTICE TEST 3
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UCF - CHEMISTRY FUNDAMENTALS 1A - PROF. BEAZLEY
PRACTICE TEST: UCF PROF. BEAZLEY PRACTICE TEST 3
PRACTICE: There are two different common crystalline fo