EC349 – Assignment One

Answer ALL of the following questions:
1.考虑具有以下两个时期的实用程序功能的使用者：
𝑢（𝑐1，𝑐2
）=𝑐1𝑐2
0.6

a）确定𝑐1和𝑐2的值，以使该用户的效用函数最大化。

b）现在假设政府对消费者实行贷款限制，以便

（10分）
c）以图形方式显示您在a）和b）中的答案。 （5分）
2.您可以访问两个风险资产，股票1和股票2，它们的信息是

ID以52结尾，所以这里的相关系数

a）如果该基金平均投资于股票1和股票2，则预期为

b）使用以上信息来计算投资权重，预期收益

c）假设您可以使用无风险资产并获得4％的回报，并且您的均值偏好效用函数为𝑈（𝐸（𝑟𝑝），𝜎𝑝
2
）=𝐸（𝑟𝑝）-
3
2
𝜎𝑝
2
portfolio and the corresponding utility level? (10 marks)
Page 2 of 2
3. Consider the five stocks as follows:
Stock Beta βi Actual return (%)
1 0.9 12
2 1.3 13
3 0.5 11
4 1.1 12.5
5 1 12
The expected return for the market is 12% and the risk-free rate is 8%.
a) What is market risk premium? Calculate the expected rate of return for each stock.
(10 marks)
b) Determine which stocks are traded at fair value, undervalued, and overvalued.
What investment decisions should be made based on the information given?
4. Consider a single-owner firm, the transformation curve is:
(𝐾1 + 1)
2 + 𝐾2
2 = 21
if the initial resources 𝐾1 = 5 and the market interest rate is 10%.
a) Solve for the wealth maximisation problem and illustrate in a diagram your
b) Work out the utility maximisation problem if the consumer’s utility function is
𝑈 = 𝑐1𝑐2
0.5
. (10 marks)

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