Consider a consumer who consumes two goods, x and y, with a daily income of I=100

.

On Monday the price of x is px=1 and the price of y is py=2

.

On Tuesday the price of x is px=2 and the price of y is py=1

Below are different consumption decisions by different consumers. All of them are facing the same prices and income. We say that a utility function is "consistent" with the participant's choices if maximizing the function on any given day yields that participant's actual choice on that day.

Question 4

Daniel chose the bundle (x,y)=(100,0)

on Monday, and the bundle (x,y)=(0,100)

on Tuesday.

a.

The utility function u(x,y)=xy

is consistent with these choices

b.

There do not exist strictly convex preferences that are consistent with these choices.

c.

The utility function u(x,y)=3x+y

is consistent with these choices.

d.

There may exist a strictly convex utility function that is consistent with these choices, but it is not one of the answers provided.

e.

The utility function u(x,y)=x-y

is consistent with these choices.

f.

The utility function u(x,y)=y-x

is consistent with these choices

g.

The utility function u(x,y)=x+y

is consistent with these choices.

Question 5

Alice chose the bundle (x,y)=(0,50)

on Monday, and the bundle (x,y)=(0,100)

on Tuesday.

Question 5Answer

a.

The utility function u(x,y)=xy

is consistent with these choices

b.

There may exist a strictly convex utility function that is consistent with these choices, but it is not one of the answers provided.

c.

The utility function u(x,y)=2x+y

is consistent with these choices.

d.

The utility function u(x,y)=x+y

is consistent with these choices.

e.

The utility function u(x,y)=x-y

is consistent with these choices.

f.

The utility function u(x,y)=y-x

is consistent with these choices

g.

There do not exist strictly convex preferences that are consistent with these choices.

h.

The utility function u(x,y)=3x+y

is consistent with these choices.

Question 6

Benjamin chose the bundle (x,y)=(50,25)

on Monday, and the bundle (x,y)=(25,50)

on Tuesday.

a.

The utility function u(x,y)=xy

is consistent with these choices

b.

The utility function u(x,y)=x-y

is consistent with these choices.

c.

There do not exist strictly convex preferences that are consistent with these choices.

d.

The utility function u(x,y)=y-x

is consistent with these choices

e.

The utility function u(x,y)=2x+y

is consistent with these choices.

f.

The utility function u(x,y)=3x+y

is consistent with these choices.

g.

There may exist a strictly convex utility function that is consistent with these choices, but it is not one of the answers provided.

h.

The utility function u(x,y)=x+y

is consistent with these choices.

Question 7

Charlotte chose the bundle (x,y)=(25,37.5)

on Monday, and the bundle (x,y)=(37.5,25)

on Tuesday

a.

There may exist a strictly convex utility function that is consistent with these choices, but it is not one of the answers provided.

b.

The utility function u(x,y)=2x+y

is consistent with these choices.

c.

The utility function u(x,y)=xy

is consistent with these choices

d.

There do not exist strictly convex preferences that are consistent with these choices.

e.

The utility function u(x,y)=x+y

is consistent with these choices.

f.

The utility function u(x,y)=3x+y

is consistent with these choices.

g.

The utility function u(x,y)=y-x

is consistent with these choices

h.

The utility function u(x,y)=x-y

is consistent with these choices.