ECO 7404, Homework 1
Len Cabrera
2.1. (a) Represent the following game in extensive form. Firm A decides whether to enter firm B's industry. Firm B observes this decision. If firm A enters, then the t
Consumer Theory - Preferences & Choice Functions
What's First - arguments for and against presenting consumer theory first or production first Production - easier; clearer results Consumer - more fund
Homogeneous Product Oligopoly
Industrial Organization - study of markets without perfect competition
Results aren't very general because they're sensitive to model assumptions (which results
from real
Product Differentiation
Solutions to Bertrand "Paradox" (i.e., p = MC with only 2 firms)
Capacity Constraints - proposed by Edgeworth; result in Bertrand-Edgeworth Cycles - for
some prices you want to
Vertical Differentiation Models
Vertical Differentiation - consumers agree on ideal product, but vary on willingness to pay
(because of preferences or income);
Guille: "faster is better, but different
Monopolistic Competition Models
Chamberlinian Models - monopolistic competition; assumes varieties (products) are
"located" symmetrically and each faces a downward sloping demand curve (so any brand
c
Entry and Exit, Strategic Moves
(Tirole Chpt 8)
Oligopoly - what'd different between oligopoly and monopoly, perfect competition and
monopolistic competition? Firms play a game. in many cases the firm
Dynamic Price Competition
(Repeated Games)
Varian - model of sales with informed and uninformed consumers; Hamilton says we covered it
previously, but I couldn't find in anywhere (we did cover it in G
ECO 7938, Problem Set 1
Len Cabrera
1.1. In the Bertrand model with increasing marginal cost, each firm would prefer to
charge a price greater than p * where p * satisfies S1 ( p*) + S 2 ( p*) = D( p*
ECO 7938, Problem Set 2
Len Cabrera
1.6. If P (Q) = 1 Q , show that Tiroles solution (p. 219) satisfies this property (i.e.,
Cournot equilibrium quantity depends only on the average of marginal costs
ECO 7938, Problem Set 3
Len Cabrera
2.1. Given identical, constant marginal cost and quadratic transportation costs td 2 , find
the equilibrium locations for two firms when they can choose any point o
ECO 7115, Consumer Theory Problems
Len Cabrera
1. Assume an individual consumes only two commodities, apples and oranges. The
individual picked a bundle with 6 apples and 0 oranges (6,0) over one with
ECO 7115, Midterm Review
Len Cabrera
Fall 1989 Midterm, Problem #4
F(X,Y) is a function of the variables X and Y. An individual chooses the variable X to
maximize F while taking the variable Y as give
Consumer Theory - Utility Representation & Ordinary Demand Utility Representation
Utility Representation, U(x) - use function to represent preferences so we can use optimization for proofs; function c
Consumer Theory - Indirect Utility Function
Indirect Utility Function - V(P,I) Max U(x) st Px I and x 0; optimized value function (i.e., solve the maximization problem, then plug solution back into U(
Consumer Theory - Expenditure Function & Compensated Demand
Expenditure Function - E(P, u) Min Px st U(x) u and x 0; optimized value function of the dual to the utility maximization problem (i.e., Px
Consumer Theory - Summary
Summary of Properties - define a "standard consumer" Preferences
1 2
Choice Function - C(A,R) C(A,R) cfw_x A: x R y y A Theorems: 1,2 (acyclic) + A finite 1,2,3 + A compact C
Consumer Theory - Random Topics
"Random topics. in no particular sensible order" -Slutsky
Consumer Surplus
Diamond-Water Paradox - by many forms of measurement, diamonds are more valuable than water;
Production Theory
Different From Consumer Theory - easier because no income effects because producers can sell output Selling Output - consumers output is happiness or utils which can't be sold; produ
ECO 7115, Problem Set 1
Len Cabrera
1. A firm has two identical plants and a fixed amount of labor. The firm wishes to
maximize output from both plants.
Production:
Yi f (li ) , l i 0 , f (0) = 0 , an
ECO 7115, Homework
Len Cabrera
Prove that quasiconvexity is a valid (i.e., invariant) property for utility representations
using the determinant of the bordered hessian for the two commodity case.
Sta
ECO 7938, Problem Set 4
Len Cabrera
4.1. In the timing Cournot game (incumbent has no fixed costs and sets quantity first,
then entrant decides whether to enter and pays fixed cost if its quantity is
Externalities and Public Goods Basics
(Mas-Colell Chpt 11)
Externality - present whenever the wellbeing of a consumer or the production possibilities of a
firm are directly affected by the actions of
Private Provision of Public Goods
Bergstrom, Blume, & Varian. "On the Private Provision of Public Goods." Journal of Public
Economics. Vol. 29, 1986, 25-49.
BBV - most important paper on this subject;
ECO 7415, Homework 2
Len Cabrera
1. Calculate the probability density function, expected value and variance of the following:
(a) Y = 2X 2 + 1, where X follows a uniform distribution on the interval [
ECO 7415, Homework 3
Len Cabrera
1. The following data show the number of A's obtained in a population of 5 students enrolled in
an Accounting PhD program at the Micanopy Institute of Technology.
Stud
ECO 7415, Homework 5
Len Cabrera
1. In order to be able to work at home, Professor Slutsky needs to provide his cat Flash with
cat toys that that he will leave him alone. There are two types of cat to
ECO 7415, Homework 6
Len Cabrera
1. Assume that the following data come from the linear model:
y i = 0 + 1 xi + i
i ~ N (0, 2 ) i = 1,2,.,n
y
-6.1
-0.5
7.2
6.9
-0.2
-2.1
-3.9
3.8
x
-2.0
0.6
1.4
1.3
0
ECO 7415, Midterm
Len Cabrera
1. A multiple choice exam has N questions, each of which has k possible answers. A student
knows the correct answer to n of these questions. For the remaining N - n quest