Econ 415/615-01
Mathematical Economics I
Problem Set I
Lau
One-variable calculus
1
c)
y f ( x) 3x5 2 x 0.2
ln( x 1)
y f ( x)
x
3
y f ( x) x ax 2 e2 x
d)
y f ( x) 2 x 2 ( x 2 ax 0.5 ) 2 2ax 2.5
a)
b)
f)
x2 2
y f ( x)
4x
y f ( x) ( x 2 ax)( x3 bx c ) x5 a
Econ 415/615-01 Mathematical Economics I
Instructor:
Fall 2016
Prof. Man-lui Lau (R 6:309:15 pm)
Office:
Cowell 404
Office Hrs: T and R 4-6 pm or by appointment
Phone #:
415-422-6730 (office)
Email:
[email protected]
Pre-requisite: Econ 120
Econ 101
Econ 102
Econ 415/615 Mathematics for Economists
Lecture Notes
I.
Lau
Economic application of one-variable calculus
$
TR2
the slope of this tangency line is the MR @ Q1
TR1
TR
Q
Mathematically, MR lim
Q 0
MR
Q1
TR dTR
Q
dQ
TR
Q
Q
Q2
As Q becomes smaller, the angl
Econ 415/615-01
Mathematical Economics I
Problem Set II
Lau
Multi-variable calculus
1.
2.
Find the partial derivatives of the following functions:
y f ( x, z ) x 2 z 3 ln( x 1) e3 z
a)
b)
y f ( x, z ) ( x 5) a ( z b)c
c)
y f ( x, z ) ln( x z ) ( xz ) 2
d)