ECON110-L1, L2 Introductory Microeconomics
* The numbers in  indicates the points of each question (total 200 points), and the numbers in () indicates
the module objectives corresponding to each problem.
1. Suppose there are two goods, apple and banana, and Alice’s preferences over the two goods are
represented by a utility function U(x,y)=xy that is, her total utility of consuming x apples and y bananas is
xy. Her income today is $120, and both apple and banana are $2 each. Suppose she cannot save her income
for the future.
(1)  How many apples and bananas should Alice consume in order to maximize her utility? (8.1)
(2)  If the price of apple increases to $3, how many apples and bananas will Alice consume? (8.1)
(3)  Calculate the price elasticity of demand for apple as the price increases from $2 to $3. (4.1)
(4)  Calculate the cross elasticity of demand for banana as the price of apple increases from $2 to $3.
(5)  In (2), how much is due to the substitution effect? (9.3)
Answer: (1) From 2x+2y=120 and MUx/Px=MUy/Py, x=y=30.
(2) From 3x+2y=120 and MUx/Px=MUy/Py, x=20 and y=30.
(5) Let M be a hypothetical income. Then, the consumer chooses x=M/6 and y=M/4. For the consumer to
be indifferent between this and the one in (1), M^2=24*(30)^2. Therefore, M=60
, which implies that
. The substitution effect is 10
their savings into the partnership to buy equipment and initial inventory. They rented a building for
$90,000 a year, and hired two employees for an annual wage of $40,000 each. Case and Bond believed that
the best alternative investment of their money would be government bonds, which could yield an annual
return of 8 percent. To run the store, Case quit her previous job, at which she earned $100,000, but her
former boss told her that she was welcome to return anytime. Bond kept his job with the government, but
gave up 6 hours of leisure each week (for 50 weeks), the time he used to spend playing golf. Bond used to