Econ 701/311 Homework 1
Due online Wednesday night September 21 at midnight.
1. Suppose u(x) = 3 x1 + x2 .
(a) Draw the indifference curve through x = (1, 1). Are preferences convex?
(b) Will an optimizing consumer with positive wealth consume both goods,

Econ 701/311 Homework 1 Solutions
1. Suppose u(x) = 3 x1 + x2 .
(a) Draw the indifference curve through x = (1, 1). Are preferences convex?
Yes, preferences represented by u(x) = 3 x1 + x2 are convex, because the set of points
above the indifference curve

Lecture 3
Indirect Utility, Expenditure, Demand
Last time, we defined the consumer problem
max u(x)
s.t.
pxm
and noted two of its main implications: (i) if preferences are LNS, then the budget constraint holds
with equality at the solution; and (ii) if tw

Lecture 2
1
Utility Maximization
The Consumer Problem
Wednesday, we.
posited a consumer with preferences over a choice set X = <k+
defined what it meant for preferences to be well-behaved (and some other properties)
proved that if preferences are well

Lecture 5
1
Working backwards
Revisiting Slutsky
Monday, we derived the Slutsky Equation
xj
pi
=
hj
xj
xi
pi
m
I interpreted the first term as a substitution effect, and the second term as an income
effect or wealth effect. Some people asked why.
For mo

Lecture 4
1
Properties of h and the Slutsky Equation
From last week.
First of all: last lecture was more proof- and math-heavy than I wanted
I should have done fewer proofs (two not three).
and gone slower and more carefully through the two I did
Writ

Introduction
Story 1: Tesla
This is the Tesla Roadster.
All-electric car, based on the Lotus Elise, introduced in 2008.
Cost $110,000 at the time. I believe they initially had a range around 100 miles on a charge,
but subsequent improvements have boosted

Recall that in todays lecture, we stated the following theorem:
Theorem 1. If preferences are complete, transitive, continuous, and strictly monotonic, then
there exists a continuous function u such that u(x) u(y) if and only if x y.
We proved it by defin