Econ 310: Microeconomic Theory II
Queen University
s
Fall 2014
Time and Location:
Monday, 1:00pm - 2:30pm; Wednesday, 11:30am - 1:00pm; at BioSci 1103.
Instructor: Professor Amy Sun
O ce: Dunning Hall 309; Phone: 613-533-2267
Email: [email protected]

Econ 310: Microeconomic Theory II
Assignment 1
Due: 3:00pm, Monday, October 6, 2014
[Note: A student must work individually and independently on all the assignments.]
For all the questions in this assignment, apply the notations used in class.
1. Consider

Production Theory
Terminology
Production function: f : Rn ! R+;
+
y = f (x) ;
where x
0 is the vector of n inputs and y
0 is the output.
Assumption 2 (Properties of the production function): Assume that
the production function f : Rn ! R+ is continuous, s

Prot maximization
The prot function is dened as:
(p; w)
max
x 0; y 0
py
w x
s:t: f (x)
y;
where p is the output price.
Because the objective function is strictly decreasing in x, the constraint
must hold with equality: f (x) = y . Using the constraint to

Consumer Theory
Goal: To examine consumer behavior
Plan: To derive demand function by studying
a model of utility maximization
with economic constraints
Preliminaries
Notations:
xi: quantity of good i
x = (x1; x2;
n
; xn)T : consumption/commodity bundle

Comparing the consumer optimization problems
s
Utility-Maximization
Problem
v (p;y ) =
"
max u (x)
x
s.t. p x y
Cost-Minimization
#
e (p; u) =
"
min p x
x
s.t. U (x) u
Homogeneity
v (tp; ty ) = v (p; y )
e (tp; u) = t e (p; u)
Monotonicity
strictly increa

Properties of the indirect utility function
Theorem 1 If u is continuous and strictly increasing, then v (p;y ) is
1. continuous;
2. homogeneous of degree 0 in (p;y ), i.e. v (tp;ty ) = v (p;y ) for any t > 0;
3. strictly increasing in y ;
4. decreasing i

Cost-minimization problem
Sometimes a consumer may want to choose the consumption bundle that
minimizes his total expenditure in order to achieve a particular utility level.
Expenditure function, e (p; u), is the minimum amount of money required to achiev

ECON 310
Microeconomic Theory II
Fall 2014
Objective of Study
A more rigorous take on the microeconomic theories;
To illustrate how to apply math techniques to study microeconomic issues
Topics
consumer theory
production theory
equilibrium concept and soc

Optimization
Applications of optimization in microeconomics:
utility maximization subject to the budget constraint
prot maximization, or cost minimization
choice between nancing methods
incentive problems
game theory: duopoly pricing; coordination game; a