GS/ECON 5010
APPLIED MICROECONOMICS October 2005
Answers to Midterm Exam
Q1. State and prove Roys Identity (the relation between a consumers indirect utility function and her Marshallian demand functions). A1. Roys Identity : xM (p, y) = i v(p, y) v(p, y)
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PART II
MARKETS AND
WELFARE
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CHAPTER 4
PARTIAL EQUILIBRIUM
In previous chapters we studied the be
GS/ECON 5010 Midterm Exam
APPLIED MICROECONOMICS Answers to Midterm October 2004
Q1. Derive a consumers Marshallian (uncompensated) and Hicksian (compensated) demand functions for all three commodities, if her preferences can be represented by the utility
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PART I
ECONOMIC AGENTS
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CHAPTER 1
CONSUMER THEORY
In the rst two chapters of this volume, we will explore
GS/ECON 5010
section B
Midterm Exam
APPLIED MICROECONOMICS
October 24 2012
2:30 3:30 pm
Do all 3 questions. All count equally.
1. Derive the Slutsky equation, which shows the relationship between the derivatives
of the Marshalllian and Hicksian demand fun
GS/ECON 5010
section B
Midterm Exam
APPLIED MICROECONOMICS
October 23 2013
2:30 3:30 pm
Do all 3 questions. All count equally.
1. What is a consumers expenditure function, if her (direct) utility function is
U (x1 , x2 ) = log (x1 ) + log (x2 )
(where log
Revealed Preference
W ARP : If a consumer is observed to make a bunch of choices, choosing xi when the prices are pi, then pi xi pi xj pj xj < pj xi for any distinct observations i and j (1)
SARP : There is no cycle of any length M , such that
pi xi pi xi
GS/ECON 5010 section B
Assignment 1
due : Wednesday October 2
F2013
before class (2.30 pm)
Do all 5 questions. Each counts 20%.
1. Are the preferences described below strictly monotonic? Convex? Explain briey.
The person consumes only bread and cheese. Ea
Basic Concepts
players : whoever are making the strategic choices .(firms, or consumers, or governments, or . . .) payoffs : what the players care about . (profit, or utility, or prestige, or . . .) actions : what the players choose (output levels, or pri
Collusion
q i : output of rm i in the industry J : number of rms in the industry prot of rm j j (q 1, q 2, . . . , q J ) with j <0 i=j i q special case : homogeneous products Q q1 + q2 + + qJ i.e. : perfect substitutes
Typeset by FoilTEX 1
so that
j = p
Cost Minimization
Given an output level y, what is the minimum cost of producing it?
minimize
wx
subject
to
f (x) y
(1)
the cost function C(w, y) is the cost of the input bundle x which solves minimization problem (1) The levels x of the quantities of the
YORK UNIVERSITY
Faculty of Graduate Studies
Final Examination
December 12, 2013
Economics 5010 BF3.0 : Applied Microeconomics
S. Bucovetsky
time=2.5 hours
Do any 6 of the following 10 questions. All count equally.
1. Prove that the Hicksian (compensated)
What is an Equilibrium Price Vector?
its a vector p such that Z(p) = 0 where Z(p) is a vector of excess demands in general equilibrium, we are looking for prices that clear all n markets there are n prices : (p1, p2, p3, . . . , pn) and n markets to clear
Gambles
g (p1 a1, p2 a2, . . . , pn an) means : g is a gamble, in which the outcome a1 will arise with the probability p1, the outcome a2 will arise with the probability p2, and so on if, for example g 1 (0.5 100, 0.5 0) and g (0.2 100, 0.8 g 1) then g is
CES : Expenditure Function and Hicksian Demands
expenditure minimization minimize p x subject to
n
[
i=1
x]1/ u i
(1)
so the Lagrangean is
n
p x + [u [
i=1
x]1/] i
(2)
with rstorder conditions
n
pi = [
k=1
x ]1/1x1 i k
i = 1, 2, . . . , n
(3)
Typeset by
Constant Elasticity of Substitution [CES] Preferences
u(x) = (x + x + + x )1/ n 2 1 where < < 1 and = 0
marginal utilities
1 u = (x1 + x + + x )1/1x1 n 2 i xi
Typeset by FoilTEX
1
rstorder conditions for utility maximization
(x+x+ +x )1/1x1pi = 0 i = 1
GS/ECON 5010
section B
Answers to Assignment 4
November 2013
Q1. What does the contract curve look like for a 2person, 2good exchange economy, with a
total endowment of E1 units of good 1 and E2 units of good 2, if the preferences of the two people
could
GS/ECON 5010
section B
APPLIED MICROECONOMICS
Answers to Midterm Exam
October 2013
Q1. What is a consumers expenditure function, if her (direct) utility function is
U (x1 , x2 ) = log (x1 ) + log (x2 )
(where log denotes the natural logarithm, and where 0
Cournot Oligopoly
quantities are strategic variables meaning : each firm chooses a quantity q i to produce each firm's price is then determined by the market demand "standard" case : homogeneous output products of each firm in the industry are perfect sub
An Exchange Economy
no production : just reallocation of given aggregate quantities of goods e = (e1, e2, . . . , en) : aggregate endowment vector : aggregate quantities of each good I : number of people an allocation x is a list of I consumption bundles
Coalitions and Blocking
"barter" exchange economy now people own the endowments so that
I
e
i=1
ei
ei is person i's endowment vector people could form coalitions to exchange their endowments if S cfw_1, 2, 3, . . . , I is a coalition, what allocations can
Solution Concepts for Games in Strategic Form
solution? prediction of what happens in the game so far. games with dominant strategy example : Prisoners' Dilemma (e.g. 3) : t is a strictly dominant strategy for player 1, L is a strictly dominant strategy f
Nash Equilibrium
terminology : let S be player 1s set of strategies (e.g. S = cfw_t, m, b), and let T be player 2s set of strategies let u1(s, t) be player 1s payoff, when she plays s S, and when player 2 plays a strategy t T strategy s is called a best r
Games in Extensive Form
the extensive form of a game is a "tree" diagram except that my trees grow sideways any game can be represented either using the extensive form or the strategic form but the extensive form is probably the most useful tool to analyz
Games of Incomplete Information
complication : a player might not know which node she is at what? example : player 1 moves rst, but player 2 does not actually observe what action player 1 takes so he doesnt know if he is at node L or R in the game, if L a
Games in Strategic Form : Examples
Example 1 : A ZeroSum Game
1\2 t b
L
R
(4, 6) (6, 4) (6, 4) (4, 6)
Example 2 : A Coordination Game
1\2 t b
L (5, 5) (0, 0)
R (0, 0) (5, 5)
Example 3 : Prisoners Dilemma
1\2 t b
L (2, 2) (0, 7)
R (7, 0) (6, 6)
GS/ECON 5010
section B
Answers to Assignment 1
F2013
Q1. Are the preferences described below strictly monotonic? Convex? Explain briey.
The person consumes only bread and cheese. Each kilo of bread contains 500 calories and 50
grams of protein. Each kilo
GS/ECON 5010
section B
Answers to Assignment 3
November 2013
Q1. What is the equation of the shortrun supply curve of a rm which has a shortrun total
cost function with the equation
T C (q ) = (q 12)2 q + 48q + 100
where q is the quantity of output produc
GS/ECON 5010
section B
Answers to Assignment 2
October 2013
Q1. Could the function
v (p, y ) =
1
(p1 )2 + (p2 )2
[y +
6p3 ]
p1 + p2
p3
be an indirect utility function for some consumer with wellbehaved preferences? Explain.
(You can assume that the perso