Unit 9: Externalities
Prof. Antonio Rangel
February 19, 2014
1
Public bads
1.1
What is an externality?
An externality arises when the actions of one economic actor aect
DIRECTLY the utility function or production function of another economic actor (i.e.
Unit 7: Imperfect Competition I monopoly
Prof. Antonio Rangel
February 5, 2014
1
Monopoly without price discrimination
1.1
Basic model
Model of the consumers is as before:
C consumers
Ui (q, m) = Bi (q) + m
wi endowment of m-good
price takers
utilit
Unit 3: Producer Theory
Prof. Antonio Rangel
December 13, 2013
1
Model of the rm
1.1
Key properties of the model
Key assumption: rms maximize prots subject to
Technological constraints: natural limits to production, given existing technology
Economic c
Unit 8: Imperfect Competition II oligopoly
and monopolistic competition
Prof. Antonio Rangel
December 23, 2014
1
Oligopoly
Oligopoly: more than one rm, but not enough for perfect competition
Firms have some market power
Intermediate case between monopo
Unit 6: Government policy in competitive
markets II Distribution & incidence
Prof. Antonio Rangel
December 23, 2014
1
Endogenous income and inequality
1.1
Simple model
There are two markets and two goods:
Labor market: consumers sell labor l at wage w t
Unit 5: Government policy in competitive
markets I Eciency
Prof. Antonio Rangel
December 23, 2014
1
Pareto optimal allocations
1.1
Preliminaries
Big picture
Consumers: 1, . . . , C, each w/ Ui , Wi
Firms: 1, . . . , F , each w/ Cj ()
Consumers and rms
Unit 1 : Principles of Optimizing Behavior
Prof. Antonio Rangel
December 23, 2014
1
Introduction
Most models in economics are based on the assumption that economic
agents optimize some objective function.
Ex 1. Consumers decide how much to buy by maximi
Unit 4: Competitive Markets
Prof. Antonio Rangel
December 23, 2014
1
Allocations
1.1
What is an allocation?
Framework:
Look at market for single good x in isolation
1, . . . , C = consumers in market (xed)
1, . . . , F = rms in market (xed)
All rms a
SYLLABUS
Principles of Economics with Calculus
CaltechX Ec1011x
Prof. Antonio Rangel
Winter 2015
About this course. This course provides a quantitative and model-based introduction to basic
economic principles, and teaches how to apply them to make sense
Unit 2: Consumer Theory
Prof. Antonio Rangel
December 23, 2014
1
Consumer demand
1.1
The experienced utility function
Suppose that the consumer only cares about two goods:
x, good of interest, measured in units
m, a measure of all other consumption in
Final Solutions
Principles of Economics for Scientists
Caltech/Coursera
Winter 2013
Prof. Antonio Rangel
Question 1: Solution
Solving the utility maximization problem for a typical consumer, we
get that his demand function is given by q D (p) = A/p. Summ
SOLUTIONS to nal exam
Principles of Economics with Calculus
Caltech/edX
Spring 2014
Prof. Antonio Rangel
Question 1: Solution
Consumers problem before change:
max 8 x + sx x
x0
The FOC for this problem is
4(1 + s)
1=0
x + sx
Solving for x yields
x = 16(1
Solutions to Final Exam
Principles of Economics with Calculus
Caltech/edX
Winter 2015
Prof. Antonio Rangel
Problem 1: Solution
The consumers problem is:
max ln x 2 x
x0
The FOC for this problem is
1
1
=0
x
x
Solving the FOC for x gives the solution x = 1
Final Exam
Principles of Economics with Calculus
Caltech/edX
Spring 2014
Prof. Antonio Rangel
Question 1
Consider the problem of a rational consumer with an experienced utility
function given by 8 x + m. Let p = $1 p/unit denote the market price of
good
Final Exam
Principles of Economics for Scientists
Caltech/Coursera
Winter 2013
Prof. Antonio Rangel
Question 1.
Consider a competitive market with 1000 identical consumers and 10
identical rms. Each consumer utility function is given by
U (q, m) = A log(
Tips on how to use the problem set grader
Follow these tips to ensure that your answers are graded correctly by the
edX system:
Enter formulas as you would enter them into a calculator or spreadsheet. If the answer is
m2
2
enter
m^2/sqrt(2)
or
m^2/2^(1/2