Jonathan Eaton
Economics 1130
Spring 2015
Problem Set 2 (Nonhomotheticity) Eaton Answers
1. Weve introduced the general utility function and a utility function with the Cobb-Douglas functional form.
A
Table 1. Quintiles of income before taxes: Average annual expenditures and characteristics, Consumer Expenditure Survey, 2011
Item
Number of consumer units (in thousands)
Lower Limit
All consumer
unit
%
%
%
%
%
%
Profit Maximizing Machine Number
Jonathan Eaton
March 1, 2014
1 unit of revenue produced Leontief with 1 worker and 1 machine
output price is 1 and labor is a sunk cost
uses MATLAB's binop
A Note on Matrices
Economics 1130
It is often convenient to organize variables in MATLAB into matrices. A matrix is a rectangular object with a positive integer number of rows and columns.
Associated
General Equilibrium
Economics 1130
Spring 2014
The Physical World
goods i = 1; :; N (e.g., i = sox, personal training sessions, etc.)
factors k = 1; :; K (e.g., k = labor,capital, land)
1 representati
A Note on Lagrangian Maximization
Economics 1130
With one constraint the constrained maximization problem can be stated
as:
max
x1 ;x2 ;:;xn
f (x1 ; x2 ; :; xn ) s.t. g(x1 ; x2 ; :; xn )
0
(1)
Lets as
A Simple General Equilibrium
Example
Economics 1130
Spring 2014
The Environment
Goods 1 and 2
Factors labor and land
Preferences
Cobb Douglas with share 1/2:
1=2
1=2
U (C1; C2) = C1 C2
where Ci is con
Market Failure
Economics 1130
Spring 2014
Time and Uncertainty
Can be accommodated in competitive equilibrium by labeling goods not
only by physical characteristics but by date and by state of nature
Jonathan Eaton
Economics 1130
Spring 2014
Practice Problems: Not to be handed in
1. It takes 1 worker on 1 year to produce 100 units of good 0; which is produced competitively. The economy
measures al
Economics 1130
Problem Set 3
Due: April 3, 2014 at the beginning of class.
Instructions: You may work in groups.
1. A city has a downtown where all the jobs are. A job downtown pays a wage w: Business
%
%
%
%
%
%
Profit Maximizing Machine Number Varying Labor
Jonathan Eaton
March 1, 2014
1 unit of revenue produced Leontief with 1 worker and 1 machine
output price is 1 and labor is a sunk cost
uses
Jonathan Eaton
Economics 1130
Spring 2014
Problem Set 2 (revised February 26)
Due: Tuesday, March 4
Instructions: You may work in groups. Make sure that your answer has the name of each participant on
Jonathan Eaton
Economics 1130
Spring 2014
Problem Set 4
Due: Thursday, May 1. You may work in groups.
1. A monopolist (say Picasso) can sell a product either in period 1 or in period 2: The good is du
First and Second Welfare Theorems
Economics 1130
Spring 2014
The Primitives of the Economy
i = 1; :; N goods;
k = 1; :; K factors.
h = 1; :; H households with utility functions dened over consumption
A Note on Homotheticity
Economics 1130
A characteristic of a function that is useful in thinking about utility functions or production functions is homotheticity. A function h(x1 ; x2 ; :; xn ) is
hom
Games and Oligopoly
Economics 1130
Spring 2014
Components of a game
Players (A,B)
Strategies (Up, Down for A, Left, Right for B)
Payos to each players as a function of the strategies both choose
Order
Economics 1130
Spring 2015
Midterm 1: Eaton Answer
A consumer has a utility function over consumption of goods 0; 1; and 2 (in amounts C0 ; C1 ; and C2 ; respectively)
of the form:
(
1)=
(
1)=
C1
+ C2
Economics 1130
Spring 2015
Midterm 2: Eaton Answers
As a potential entrepreneur you can set up a rm that has a production function:
Q = AL
(1)
where Q is your output and L is your input of labor. You
Jonathan Eaton
Economics 1130
Spring 2015
Economics 1130
Problem Set 1: Eaton Answer
We are going to add land as a factor production. Say that Freddy has 2 acres of land as well as his 1 unit of
labor
Economics 1130
Spring 2015
Midterm 3: Eaton Answer
Consider an economy that can produce two goods x and y. There are two factors of production, skilled labor S
and unskilled labor U: The production fu
The Elements of the Economy
Economics 1130
Spring 2014
The Things in the Economy
Goods (and services) apricots, bananas, personal training sessions, magazines, video games,.
Factors of production (wha
On the Size Distribution of Business Firms
Author(s): Robert E. Lucas, Jr.
Reviewed work(s):
Source: The Bell Journal of Economics, Vol. 9, No. 2 (Autumn, 1978), pp. 508-523
Published by: RAND Corpora
Introducing
MATLAB
For Economics
What is MATLAB?
MATrix LABoratory
Computer Environment & Language
1 million users in mainly engineering, science &economics
In Econ: Bridges theory and practice
Outlin
Firms
Economics 1130
Spring 2014
The Firm-Size Distribution
(Axtell)
The Pareto Distribution
Wilfredo Pareto (1848-1923) Italian, but spent most of his life at the
University of Lausanne in Switzerlan
The Theory of the Producer
Economics 1130
Spring 2014
Technology: The Production Function
K inputs (factors of production) used in amount xk can produce output
y:
y = f (x1; x2; :; xK )
Examples of in
The Constant Elasticity of
Substitution (CES) Production or
Utility Function
Economics 1130
Spring 2014
Preliminary 1: The Leontief Production or Utility Function
Utility Function Version
Parameters a
Monopolistic Competition
Economics 1130
Spring 2014
History
The background: Joan Robinson (1933), Edward Chamberlin (1936), and
Avinash Dixit and Joseph E. Stiglitz (1977)
The undergraduate picture an
Uncertainty
Economics 1130
Spring 2014
Weve Done it Already
Dene a good according to the state of nature s = 1; :; S in which it
appears as well as its physical characteristics. The states are exhaust