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
PROBLEM SET 5
(1) Consider the following game:
U
D
L
2, 1
0, 0
R
0, 0
1, 2
(a) Are there Nash Equilibria in pure strategies? If so, what are they?
(b) Are there Nash Equilibria in mixed strategies? If so, what are they?
(2) Consider the following game:
U
Intermediate Microeconomics
W3211
Lecture 21:
Oligopoly
Columbia University, Spring 2015
Pietro Ortoleva
[email protected]
Where in the book?
n
This corresponds to Chapter 27 of the book
Oligopoly
n
A monopoly is an industry consisting a single
Intermediate Microeconomics
W3211
Lecture 22:
Externalities
Columbia University, Spring 2015
Pietro Ortoleva
[email protected]
Where in the book?
n
This corresponds to Chapter 34 of the book
Externalities
n
An externality is a cost or a benefit
PROBLEM SET 2
(1) Consider the utility function U (x1 , x2 ) = 4 x1 + x2 .
(a) What is the utility of the bundle U (9, 10)?
(b) What is the equation of the indifference curve going through that bundle?
(c) What is the MRS at that bundle?
(d) Can we derive
PROBLEM SET 3
(1) Joe Grad has just arrived at the big U. He has a fellowship that covers his tuition
and the rent on an apartment. In order to get by, Joe has become a grader in
intermediate price theory, earning $100 a month. Out of this $100 he must pa
Sample Questions 2, Spring 2015
1. A competitive firm has the following short-run cost function: c(y) = y 3 3y 2 + 7y + 12.
(a) What is the firms marginal cost function?
(b) What is the firms average variable cost function?
(c) Sketch the marginal cost an
Example questions, Spring 2015
2
1
1. Consider an individual with a utility function U (x1 , x2 ) = (x1 + 4) 3 (x2 + 6) 3 . Prices
are p1 and p2 and his income is m.
(a) Compute the marginal rate of substitution.
(b) Compute the demand of x1 as a function
PROBLEM SET 4
(1) Consider a competitive industry with a large number of firms, all of which have
identical cost functions c(y) = y 2 + 1 for y > 0 and c(0) = 0. Suppose that initially
the demand curve for this industry is given by D(p) = 52 p. (The outpu
Chapter 18
Externalities and Public Goods
Chapter Outline
18.1 Externalities 18.2 The Inefficiency of Competition with Externalities Supply-and-Demand Analysis Cost-Benefit Analysis 18.3 Market Structure and Externalities Monopoly and Externalities M
Chapter 19
Asymmetric Information
Chapter Outline
19.1 Problems Due to Asymmetric Information 19.2 Responses to Adverse Selection Controlling Opportunistic Behavior Through Universal Coverage Equalizing Information 19.3 How Ignorance About Quality Dr
Chapter 4
Consumer Choice
Chapter Outline
4.1 Preferences Properties of Consumer Preferences Preference Maps 4.2 Utility Utility Function Ordinal Preference Utility and Indifference Curves Utility and Marginal Utility Utility and Marginal Rates of Su
PART TWO Answers to Problems 1 in Text
1
This section provides answers to problems not already solved in the text.
Chapter 2
Answers to Problems in the Text
1. When Japan discovered the StarLink, demand for U.S. corn fell. As a result the supply o
Chapter 5
Applying Consumer Theory
Chapter Outline
5.1 Deriving Demand Curves 5.2 How Income Changes Shift Demand Curves A Rise in Income Shifts the Demand Curve Consumer Theory and Income Elasticities 5.3 Effects of a Price Change Income and Substit
PART THREE Answers to Study Guide Exercises
Chapter 2
1. True. See Figure 2.1 and assume that the demand curve is D0. The quantity demanded falls from Q2 to Q1, but the actual amount bought rises from Q0 to Q1 as producers move from point A to point
Chapter 20
Contracts and Moral Hazards
Chapter Outline
20.1 Principal-Agent Problem A Model Types of Contracts Efficiency 20.2 Production Efficiency Efficient Contract Full Information Asymmetric Information 20.3 Trade-Off Between Efficiency in Produ
Chapter 6
Firms and Production
Chapter Outline
6.1 The Ownership and Management of Firms Ownership of Firms The Management of Firms What Owners Want 6.2 Production Production Functions Time and the Variability of Inputs 6.3 Short-Run Production: One
Chapter 3
Applying the Supply-and-Demand Model
Chapter Outline
3.1 How Shapes of Supply and Demand Curves Matter 3.2 Sensitivity of Quantity Demanded to Price Price Elasticity of Demand Elasticity Along the Demand Curve Other Demand Elasticities 3.3
Chapter 2
Supply and Demand
Chapter Outline
2.1 Demand The Demand Curve The Demand Function Summing Demand Curves 2.2 Supply and demand The Supply Curve The Supply Function Summing Supply Curves Effects of Government Import Policies on Supply Curves
PART ONE Teaching Aids
Chapter 1
Introduction
Chapter Outline
1.1 Microeconomics: The Allocation of Scarce Resources Trade-offs Who Makes the Decisions Prices Determine Allocations 1.2 Models Simplifications by Assumption Testing Theories Positive V