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 two firms simultaneously decide whether to advertise. Ot
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 fundamental; production relies on consumer; underlies welfa
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 world being complicated, not from "bad" modeling)
Issu
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 undercut and for others (i.e., low price firm near cap
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 rates of return for speed"
Quality - look at scale wit
Monopolistic Competition Models
Chamberlinian Models - monopolistic competition; assumes varieties (products) are
"located" symmetrically and each faces a downward sloping demand curve (so any brand
can raise price and not lose all of its sales
Monopolist
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 has an effect on the
game to be played
Problem - descr
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 Game Theory; see "Applications
of Nash Equilibrium" p.1)
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*) . Prove this
for the proportional-rationing case.
Not
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 and not on
the distribution of these costs, as long as
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 on the
unbounded line.
Delivered
cost
Assume firms locat
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 5 apples and
3 oranges (5,3). The individual then chos
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 given. If F has a unique interior maximizing
value of X for
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 contains information about preferences but function itse
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(x) to get V(P,I); lists the solutions to the maximizati
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 = I trying to minimize what consumer would have x2 x2 I
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(A,R) C(A,R) xPz xRz
Complete: x P y or y P x or x I y
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; paradox because water is more important for life to exi
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; producers can sell their output so it's measurable it's mean
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 , and f ' (li ) > 0
Labor:
l1 + l 2 L
A. Set this up as a m
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.
Start with a general utility representation, U(x), where x
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 positive), what
happens if the incumbent can reduce its
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 another agent in the economy
Directly Affected - not th
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; also applies to giving to any charity, political party
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 [0,1]
(b) Y = X 2, where X has a standard normal distrib
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.
Student
Number of A's
Alma
3
Bud
0
Carmella
1
Dora
3
Elmer
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 toys that Professor Slutsky
is trying to choose between:
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
0.0
-1.6
-1.7
0.7
Find the maximum likelihood estimates
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 questions, he checks
the answers completely at random. To ta