R2
cfw_xn
xn ! x & c n ! c
R
k xy
xn yn k=k xy
=k x(y
xn yn k=k x(y
xyn + xyn
yn ) + (x
xn )(yn
y) + (x
|x | k y
cfw_xn
9N1 st.8n
xy
N1 k x
xn yn k<
X
S
8n
N
kx
9N2 st.8n
xn k
ky
cfw_cn
yn ) + (x
xn )(yn
yk+kx
xn )(yn
yn k
cfw_xn
yn k<
3(|x| + 1)
xn

E CONOMICS 526 M IDTERM
O CTOBER 5 TH , 2015
Answer two of the three problems each from problems 1-3 and problems 4-6. Each problem
is worth 25 points. Answering more than four problems will not increase your grade. If you
try working on more than four pr

Problem Set 5 : Suggested Solutions
Zhengfei Yu
November 5, 2015
1. Please refer to the solution of Q13 in nalReview.pdf.
2.
1. Let A be continuous at 0 and v 2 V . Take any > 0. Then by continuity at 0, there
exists such that if kxk < , then kAx A0k < .

P ROBLEM S ET 3 S OLUTIONS
YAWEN L IANG
D UE : M ONDAY, O CTOBER 19 TH
U NIVERSITY OF B RITISH C OLUMBIA
E CONOMICS 526
Problem 1. Suppose an unemployed worker receives a wage offer independently distributed
uniformly on [0, w] each period. If the worker

P ROBLEM S ET 2
PAUL S CHRIMPF
D UE : M ONDAY, S EPTEMBER 28 TH
U NIVERSITY OF B RITISH C OLUMBIA
E CONOMICS 526
Problem 1 (Based on exercise 1.3 from [?]). A monopolist produces output y at cost C (y), faces
demand D ( p), and must pay a tax t per unit s

E CONOMICS 526 M IDTERM R EVIEW
M IDTERM IS ON O CTOBER 5 TH , 2015
1. F ORMAT
Answer two of the three problems each from problems 1-3 and problems 4-6. Each problem
is worth 25 points. Answering more than four problems will not increase your grade. If yo

E CONOMICS 526 F INAL R EVIEW
F INAL IS ON N OVEMBER 9 TH , 2015
1. F ORMAT
Answer two of the three problems each from problems 1-3 and problems 4-6. Each problem
is worth 25 points. Answering more than four problems will not increase your grade. If you
t

E CONOMICS 526 M IDTERM
O CTOBER 6 TH , 2014
Answer two of the three problems each from problems 1-3 and problems 4-6. Each problem
is worth 25 points. Answering more than four problems will not increase your grade. If you
try working on more than four pr

E CONOMICS 526 F INAL
N OVEMBER 9 TH , 2015
1. F ORMAT
Answer two of the three problems each from problems 1-3 and problems 4-6. Each problem
is worth 25 points. Answering more than four problems will not increase your grade. If you
try working on more th

E CONOMICS 526 F INAL R EVIEW
F INAL IS ON N OVEMBER 9 TH , 2015
1. F ORMAT
Answer two of the three problems each from problems 1-3 and problems 4-6. Each problem
is worth 25 points. Answering more than four problems will not increase your grade. If you
t

E CONOMICS 526 F INAL
N OVEMBER 12 TH , 2014
1. F ORMAT
Answer two of the three problems each from problems 1-3 and problems 4-6. Each problem
is worth 25 points. Answering more than four problems will not increase your grade. If you
try working on more t

P ROBLEM S ET 4
PAUL S CHRIMPF
D UE : M ONDAY, O CTOBER 26 TH
U NIVERSITY OF B RITISH C OLUMBIA
E CONOMICS 526
Problem 1. For each of the following sets in R2 state whether it is open, whether it is closed, and
whether it is compact. Briey justify your an

P ROBLEM S ET 5
PAUL S CHRIMPF
D UE : AT TA TUTORIAL ON M ONDAY, N OVEMBER 2 ND
U NIVERSITY OF B RITISH C OLUMBIA
E CONOMICS 526
Problem 1. Let X be a metric space with metric d X and Y be a compact metric space with metric
dY . Dene a metric on the produ

P ROBLEM S ET 2
PAUL S CHRIMPF
D UE : M ONDAY, S EPTEMBER 28 TH
U NIVERSITY OF B RITISH C OLUMBIA
E CONOMICS 526
Problem 1 (Based on exercise 1.3 from [Tirole(1988)]). A monopolist produces output y at cost
C (y), faces demand D ( p), and must pay a tax t

P ROBLEM S ET 3
PAUL S CHRIMPF
D UE : M ONDAY, O CTOBER 19 TH
U NIVERSITY OF B RITISH C OLUMBIA
E CONOMICS 526
Problem 1. Suppose an unemployed worker receives a wage offer independently distributed uni
formly on [0, w] each period. If the worker accepts

P ROBLEM S ET 1
PAUL S CHRIMPF
D UE : M ONDAY, S EPTEMBER 21 ST
U NIVERSITY OF B RITISH C OLUMBIA
E CONOMICS 526
Problem 1 ([Dixit(1990)] exercise 2.2). A consumer can buy two goods, x and y, at prices p and q.
She has income I, and her utility function i