Homework 5 - Solutions
Exercise 1
Gentle Charlie consumes only apples and bananas. His utility function is
U
(
x
A
, x
B
) =
x
A
x
B
(where
x
A
and
x
B
are the number of apples and bananas consumed in a day). The price of
apples is $1, the price of bananas is $2, and Charlie’s income is $40 a day. The price of bananas
suddenly falls to $1.
(a) How many apples and bananas did Charlie consume per day before the price change?
On a graph below, use black ink to draw Charlie’s original budget line and put the label
A

on his chosen consumption bundle.
(b) If, after the price change, Charlie’s income had changed so that he could exactly afford
his old consumption bundle, what would his new income have been?

(c) Does the substitution effect of the fall in the price of bananas make him buy more ba-
nanas or fewer bananas?
What is the exact amount of the change in the amount of bananas consumed?

1

(d) After the price change, how many apples and bananas does Charlie buy?
Use blue ink to draw Charlie’s actual budget line after the price change. Put the label
C

on the bundle that he chooses after the price change. Draw three horizontal lines on your
graph, one from
A
to the vertical axis, one from
B
to the vertical axis, and one from
C
to
the vertical axis. Along the vartical axis, label the income effect, the substitution effect, and
the total effect on the demand for bananas. Is the blue line parallel to the red line or the