Question EC 340: Homework Set #1 Due Date: Sept. 22, 2014

02 Jun Question EC 340: Homework Set #1 Due Date: Sept. 22, 2014

Question
EC 340: Homework Set #1

Due Date: Sept. 22, 2014

Problem #1

Consider the following demand function

Q =A ?BP.

Find the price elasticity of demand. Illustrate how the elasticity changes as the price changes.

Problem #2

Give an example of a demand function characterized by a constant price elasticity equal to 5.

Problem #3

Consider the set, X, of pairs of ( a , b ) , where a and b are integers not smaller than 0 and not bigger than

9. Define the preferences over elements of X as

?

?

?a , b

?

?

? ? ?

?

? c , d

?

?

? ?? { a >c

a =c b ?d .

Can you think of a utility function that represents ?.

Problem #4

Consider the following utility function

U ( x 1 , x 2 ) = x 1

x 2 ?12.

Which of the following functions represents the same preferences as the above utility function. Justify your

answer.

a ) V ( x1 , x2 ) = ? ( x1x2) ?1 b ) V ( x1 , x2 ) =x1 +x2 +4

c ) V ( x1 , x2 ) =x1x2

2 d ) V ( x1 , x2 ) =e

x 1x 2 ?167

Problem #5

Imagine that preferences of a given individual are represented with

U ( x 1 , x 2 ) =x ?

1 x 1??

2 +5.

Assume that the prices of the two goods consumed by this individual are given by p1 and p2

. Furthermore,

assume that the individual earns income I.

i) Derive the demands of the individual for the two goods.

ii) Verify that the demands happen to be homogenous of degree 0.

iii) Plot the two demands as a function of income.

Problem #6Imagine that preferences of a given individual are represented with

U ( x 1 , x 2 ) =x 1 + x 2.

Assume that the prices of the two goods consumed by this individual are given by p1 and p2

. Normalize the

price of the first good to 1, i.e., set p1 =1. Furthermore, assume that the individual earns income I.

i) Derive the demands of the individual for the two goods.

ii) Plot the two demands as a function of income.