课程名称︰个体经济学上
课程性质︰经济系大二必修
课程教师︰黄贞颖
开课学院：社会科学院
开课系所︰经济学系
考试日期（年月日）︰2021/01/11
考试时限（分钟）：180
试题 :
There are 10 questions in the exam, and each worth 10 credits.
1. Albert has 10000 dollars. There is an investment opportunity
Albert considers. In a good state, the return rate is 20%.
Every dollar invested becomes 1.2 dollar. In a good state, the
return rate is -20%. Every dollar invested becomes 0.8 dollar.
The probability of a good state is 0.55. The probability of a
bad state is 0.45. Albert cannot borrow to invest. Hence the
amount he invests in this opportunity is between 0 to 10000 do-
llars.
(a) If Albert invests 1000 dollars. What is his final income
in a good state? What is his final income in a bad state?
(b) Suppose Albert invests m dollars. Write down his final in-
come in a good state and that in a bad state.
(c) By varying m, we can draw Albert's budget line segment. Re-
member that Albert cannot borrow to invest. Hence, 0 <= m
<= 10000. In your diagram label Albert's final income in
a good state on the X-axis. Label his final income in a bad
state on the Y-axis. What is the slope of the budget line
segment? Illustrate his budget line segment by a diagram.
(d) Denote Albert's final income in a good state by x and that
in a bad state by y. Suppose Albert's utility is:
u(x, y) = x^(0.55) * y^(0.45)
Is Albert's utility function an expected utility function?
Can you apply a monotonic transformation to make his util-
ity function become an expected utility function? Does he
behave like an expected utility maximizer? Briefly explain.
(e) Continue from above. Is Albert risk averse? How much will
Albert invest in this opportunity? Briefly explain.
(f) Continue from above. But now assume that because of a bad
shock, in a bad state, the return rate becomes -22%. Every
dollar invested becomes 0.78 dollar. How will Albert's bud-
get line segment change? What is its slope now? Illustrate
this change by a diagram.
(g) Continue from above. Compare the new situation with a bad
shock to the original situation, how much will his final
income in a good state change? Briefly explain your calcu-
lation.
(h) Continue from above. Decompose your answer in (g) to
Slutsky substitution effect and income effect. Briefly ex-
plain your calculation.
2. True or False: You need to explain briefly your answers.
(a) In the CAPM model, if stock A has the same standard devia-
tion of return as stock B, and has lower expected return
than stock B, then no one would want to hold stock A
because all money invested in stock A should go to stock B.
(b) If apples are a normal good for a net supplier of apples,
then it is possible that when the price of apples increases,
his demand for apples increases as well.