Intermediate Microeconomics
Homework Set 1: Budget Set and Preferences
Due 09/17 (Beginning of class)
Exercise 1
You have an income of $50 to spend on two commodities. Commodity 1 costs $12 per
unit and commodity 2 costs $5 per unit.
(1) Write down your budget equation.
(2) Suppose the government taxes $2 per unit on commodity 1 and %5 per price on
good 2. Write down your new budget equation.
Exercise 2
A consumer consumes one consumption good x and hours of leisure h. The price
of the consumption good is 1. The consumer earns wage rate s per hour for the first
eight hours of work, and s
0 > s for additional overtime hours. He also faces a tax rate
per dollar on labor income earned above amount M. Draw the budget set.
Exercise 3
You have an income of $100 to spend on two commodities. The price of commodity
2 is constant at $1. But the price of commodity 1 decreases if you buy more than 20
units. More precisely, p1 = $2 if 0 ≤ x1 ≤ 20, and p1 = $1 if x1 > 20. Draw your
budget constraint.
Exercise 4
(1) Christopher takes (x1, x2) to be at least as good as (y1, y2) if and only if x1 ≥ y1
and x2 ≥ y2. Show which condition his preferences violate.
(2) Explain how it would be possible to cheat someone who had intransitive preferences. Be explicit about what you would offer him, and what he would do in
response.
(3) A household formed by Mom (M), Dad (D), and Child (C) is deciding what to
do on Friday evening. The alternatives are attending an opera (O), a rock concert
(R), or an ice-skating show (I). The three members of the household have individual
preferences: O M R M I, I D O D R, R C I C O. The household makes
decisions by majority voting: An option is chosen if and only if at least two people
vote for it. Show which condition the majority rule violates.
Exercise 5
1
(1) John’s preferences are the type of perfect complements in which the locus of
kinks is given by 2x1 = x2. Which does he prefer, (3, 7) or (10, 2)?
(2) Martina’s preferences are the type of perfect substitutes. Suppose that she is
indifferent between (5, 1) and (2, 7). What is her marginal rate of substitution of
good 2 for good 1?
Exercise 6
Denise chooses an alternative in the set X = {x1, . . . , x20}. Show that if her preferences  are complete, transitive and reflexive, then there exists an alternative she
prefers to all others: That is, there is x
∗ ∈ X such that x
∗  x for all x ∈ X