Quiz 2 Solutions  Upton
Microeconomics Fall 2016
Suppose that the daily market demand curve for tacos in Upton is Q(P ) = 1750 250P . Price (P ) is
measured in dollars per taco and quantity (Q) is measured in tacos per day. The total cost curve of a typi
Quiz 1 Solutions  Nate
Microeconomics Fall 2016
Nate snacks on cashews (x) and macadamia nuts (y) when he watches TV. His preferences over these two
goods can be represented by the utility function U (x, y) = 0.25 log x + 0.75 log y where x represents th
Name_
Marta buys donuts (x) and bagels (y) on her way to school. Her preferences over these
two goods can be represented by the utility function
where x represents
U ( x , y ) y 3e x
the number of donuts and y represents the number of bagels.
a) (5 points
Additional Questions for the final on the Stackelberg Model
1. On Homework 11, in question 4 you analyzed the impact of two different market structures
(competition and a cartel) for the vitamin market. Here you will look at a third, the Stackelberg
model
Additional Questions for the final on the Stackelberg Model
1. On Homework 11, in question 7 you analyzed the impact of two different market structures
(competition and a cartel) for the silicon market. Here you will look at a third, the Stackelberg model
Name_
Phyllis drinks both coffee (x) and milk (y). Her preferences over these two goods can be
represented by the utility function U(x,y) = x + 3y1/2 where x represents the number of
pounds of coffee and y represents the number of quarts of milk.
a) (5 po
A)
marginal
2
&3 form
firms
inverse
MC
Max
Mc
demand
market
in
's
problem
Tlz+3
,
720
Qztz
0.5
=
03=2 P
Qzt
=
( Qus
:
2P

market demand
base
cartel
QE
:
ME)
:
the Cartel
of
came
a
=
Qi =P
:
the Cartel Quz
of
came
deduced
=
:
of each firm
curve
)
Mala
fir
Solutions for Sample Final Questions
Fall 2008
Problem 1
Suppose that the following production function represents a firms ability to manufacture pencils:
f(L,K) = 31/2K1/4L1/4.
a) Show that this production function exhibits decreasing returns to scale.
f
Quiz 2 Solutions  Rosedale
Microeconomics Fall 2016
Suppose that the daily market demand curve for pizza in Rosedale is Q(P ) = 440 10P . Price (P ) is
measured in dollars per pie and quantity (Q) is measured in pies per day. The total cost curve of a ty
Quiz 1 Solutions  Ophelia
Microeconomics Fall 2016
Ophelia buys both ham (x) and cheese (y) for her sandwiches. Her preferences over these two goods can be
represented by the utility function U (x, y) = min[2x, y] where x represents the number of slices
Name_
Suppose that daily demand in Oceanside for ice cream is QD (P ) = 120050P . Price (P)
is measured in $ per gallon and quantity (Q) is measured in gallons per day. Suppose that
the total cost curve for a typical ice cream parlor is C(Q) = 0.1Q2 + 12Q
Name_
Luis receives a weekly allowance to purchase soda (x) and juice (y) at school. His
preferences over these two goods can be represented by the utility function
U(x,y) = 0.25x + ln y where x represents the number of cans of soda and y represents
the n
Name_
Suppose that daily demand in Patchogue for storage shed rentals is QD(P) = 670 50P.
Price (P) is measured in $ per shed and quantity (Q) is measured in sheds per day.
Suppose that the total cost curve for a typical mini storage company is C(Q) = 0.0
Name_
Suppose that the daily market demand curve for taxi rides in Syosset is QD (P ) =
2900200P . Price (P ) is measured in dollars per ride and quantity (Q) is measured in rides
per day. The total cost curve of a typical cab company is C(Q) = 0.01Q2 + 9
Lecture 5: Demand Analysis
Chapters 6 & 8, Varian
A big picture
1. Consumers Optimal Choice
2. Comparative Statics: how does the
optimal choice change as prices and
incomes change
a CobbDouglas Example.
Suppose that the consumer has
CobbDouglas preferen
Lecture 3: Consumer Problem
Chapters 2 & 5, Varian
Consumers problem
l Choose the best from the set of feasible
alternatives.
Example
l a consumer has $100 to spend on beer and
water
l the price of beer is $ 2 per can
l the price of water is $ 1 per bottl
Lecture 2: Preference and
Utility Representation
Theorems
Chapters 3 & 4, Varian
Modelling Individual Player
n
Choose the best from the set of feasible
alternatives.
Rationality
lPostulate:
A decisionmaker always chooses its most
preferred alternative fro
Lecture 4:
Solving Consumer Problem
Chapter 5, Varian
Consumer Problem: General
l
Max
s.t.
U(x1,xn)
x1 0, , xn 0 and
p1x1 + + pnxn m.
This is a constrained maximization problem.
Questions:
1) Existence of a solution
2) Uniqueness of the solution
3) Proper
Supplemental Material to Lecture 4:
Solving Consumers Problem Using
Lagrange Multipliers
UN3211
September 17, 2017
I
You need to know
I
I
I
the ideas/intuition behind the method
how to use it to solve problems
The mathematical proofs behind the method is
ECON 3211: Problem Set 4 Solutions
Question 1
a. The supply curve of the individual firm is S(p) = p2 . If there are n firms in the industry,
.
the industry supply curve is Y = nS(p) = np
2
b. The smallest price is p = 2.
c. Guess at p = 2. This gives D(2
ECON 3211: Problem Set 5 Solutions
Question 1
a. Yes, there are two: (U, R) and (D, L). To see this, notice that no player has an incentive
to deviate in either of those scenarios.
b. Yes, there is one. Finding the equilibrium amounts to finding the proba
Problem Set 3 Solution
(1)(a)
MRS =
MU1
x
= 2
MU 2
x1
At the optimum,
MRS =
p1
p2
Therefore,
x2*
p
1
* = 1 =
2
x1
p2
x1* = 2 x2*
In the meantime, given that the income is $40,
x1* + 2 x2* = 40
4 x2* = 40
x2* = 10
x1* = 2 x2* = 20
Accordingly, Mark will
ECON 3211: Final 2015 Solutions
Question 1
a. mc(y) = 2y + 3, avc(y) = y + 3, ac(y) = y + 3 +
c
1
y
mc
atc
avc
q
b. For a perfectly competitive firm, p = mc(q) = p = 2y + 3.
p
S
q
c. The monopolist will set M R(q) = M C(q) = 500 4q = 2q + 3 = 497 = 6q =
q
Solutions for Problem Set 2
1
Question 2
Part a
U (9, 10) = 4 9 + 10 = 12 + 10 = 22
Part b
4 x1 + x2 = 22 = x2 = 22 4 x1
2
Part c
1
41x 2
2
2
M Ux
2
= 2 1 = = =
M RS =
M Uy
1
x1
3
9
Part d
M RS =
M Ux
2
=
M Uy
x1
Question 3
Part a
U (9, 10) = (9 + 2)(10
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Introduction to Statistics (with calculus)
Statistics W1211 Spring 2016
Section 002: TR 11:40am12:55pm; 309 Havemeyer
Instructor:
Ronald Neath
[email protected]
Office hours:
Time and location to be announced
Course description: This is a first course
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Intermediate Microeconomics
W3211
Lecture 8:
Market Demand
Columbia University, Spring 2015
Pietro Ortoleva
[email protected]
Note
n
This corresponds to Chapter 15 of the book
n
Notice: WE ARE JUMPING!
From Individual to Market Demand
Functions