University of Waterloo
Department of Economics
ECON 357 - Environmental Economics
Midterm Exam Sample- Answers
Question 1
Note whether the statements below are true, false, or ambiguous. For each case, clearly explain your
answer.
a. The Pareto criterion
University of Waterloo
Department of Economics
ECON 357 - Environmental Economics
Practice problem set I- Answers
1. The local government of the city of Water Valley is considering cleaning up a browneld site so that
the land can be used as a park. The si
University of Waterloo
Department of Economics
ECON 357 - Environmental Economics
Midterm Exam Sample
Question 1
Note whether the statements below are true, false, or ambiguous. For each case, clearly explain your
answer.
a. The Pareto criterion used as a
Econ 211 Winter 2014 Final Exam
Instructions: NO electronic aids of any type are permitted. Answer seven (7)
of the following ten (10) questions. All questions are of equal weight. Indicate
clearly on the rst page of your booklet which questions you want
Econ 211 Spring 2013 Final Exam
Instructions: NO electronic aids of any type are permitted. Answer seven (7)
of the following ten (10) questions. All questions are of equal weight. Indicate
clearly on the rst page of your examination which questions you w
Economics 211
Assignment 5
Must be handed in, in class, Thursday July 24th 2014
Name:
Student Number:
1
Please print this assignment and then answer all questions in the space provided. Please write clearly and concisely.
1. Consider a price-taking, prot-
Economics 211
Assignment 4
Must be handed in, in class, Tuesday July 15th 2014
Name:
Student Number:
1
Please print this assignment and then answer all questions in the space provided. Please write clearly and concisely.
1. Prove the n by n symmetric matr
Economics 211
Prot functions
Consider a price-taking, prot-maximizing rm that produces output q using two inputs.
Denote the production function by f (z1 , z2 ). Let (p, w1 , w2 ) equal the rms maximum
prot as a function of the output price, p, and input
Economics 211
A Note on Chapter 7: a 3 by 3 example to solve equations by the
row-echelon method
Suppose we want to solve the following system of 3 equations in 3 unknowns.
a11 x1 + a12 x2 + a13 x3 = z1
a21 x1 + a22 x2 + a23 x3 = z2
a31 x1 + a32 x2 + a33
Economics 211
Assignment 3
Must be handed in, in class, Tuesday June 17th 2014
Name:
Student Number:
1
Please print this assignment and then answer all questions in the space provided. Please write clearly and concisely.
1. Use the notes on chapter 6 to n
Economics 211
Test 2
Thursday 6th March 2014
Name:
Student Number:
Please turn o all electronic devices computers, cell phones, calculators.
1
Answer all questions. Each question is worth 10 marks.
1. Let f be a real-valued dierentiable function: [c, d] .
Economics 211
Assignment 2
Must be handed in, in class, Thursday 22 May 2014
Answer all questions in the space provided.
Please write clearly and concisely.
Name:
Student Number:
1
1. Let u : 2 be the utility function for some consumer who always prefers
Economics 211
Cramers Rule
.
Consider the system of linear equations Ax = b where A is n by n, and x and b are n by
1 column vectors. If the determinant of A is not zero we have seen that the solution for x is
A1 b where
1
A
1
=
det(A)
c11 c21 . . . cn1
Economics 211
Test 2
Thursday 3rd July 2014
Name:
Student Number:
Please turn o all electronic devices computers, cell phones, calculators.
1
Answer all questions. Each question is worth 10 marks.
1. Let f be a real-valued dierentiable function: [c, d] .
The envelope theorem
Suppose we have a value function dened by
V (a) =
Max or Min
f (x, a),
x
and f attains its max or min at a point where f /x = 0, then
f (x(a), a)
.
a
Why is this true? Let x(a) be the function that gives the optimal value of x for eac
Economics 211
Notes on chapter 6
Suppose we want to maximize f : [a, b] , a, b , a < b. Assume f possesses rst
and second derivatives and f is strictly concave, that is, f (x) < 0, for x [a, b]. Denote
the optimal value x [a, b]. Show: (i) x = c if f (c)
Economics 211
Notes on Quadratic Forms
.
Quadratic forms and their properties are used to state the second-order conditions for
functions of two or more variables. If A is an n by n matrix and x is an n by 1 column vector
then the quadratic form of A and
Economics 211
Test 1
Thursday 29th May 2014
Name:
Student Number:
Please turn o all electronic devices computers, cell phones, calculators.
1
Answer all questions. Each question is worth 10 marks.
1. Let, X, the set for the following questions, be n . Usi
Economics 211
Assignment 1
Must be handed in, in class, Thursday 15 May 2014
Answer all questions in the space provided.
Please write clearly and concisely.
1. Assume a, b, p1 , p2 are positive real numbers and w is a nonnegative real number. Solve
the fo
Economics 211
Some notes on chapters 3 and 4
The text denes a sequence as a function whose domain is the natural numbers cfw_1, 2, 3, . . .
(page 62). So if the range is n we could write the sequence as a countable subset of n .
cfw_a1 , a2 , a3 , . . . c