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Department of Economics, HKUST
ECON 198

Prof. S. F. Leung

Final Examination
This is a closed book examination. You have 180 minutes to complete the test. Write coherently, lucidly, and legibly. Always explain your answer. The maximum score for this exam is 180 points. Points are marked next to the questions (the numbers in brackets refer to the points for each subquestion) and may be served as a rough guide to how much time you should allocate on each question. Points will be deducted for irrelevant materials. Use mathematics and/or diagrams wherever appropriate to support your answer.
This examination contains 11 questions.
You may find the following formulas useful:
dyn n.1 dy
= ny , where n is a constant.
dx dx
ln() 1 dy
= , y > 0.
dx ydx
1. (10) [5, 5]
What is diminishing marginal rate of substitution (DMRS)? Why is it a reasonable assumption of consumer behavior?

Suppose that a complete collection of Pokemon cards contains 100 cards and a consumer has already obtained 99 cards. In order to complete his collection, he is willing to pay a lot of money to obtain the 100th Pokemon card. The amount is larger than that he paid for the first card. Does his behavior contradict the assumption of diminishing marginal rate of substitution? Explain.


Consider a consumers ordinary demand curve for a good X. For any given quantity x, the area under the curve does not really measure the consumers total valuation of these xunits of good. Do you agree? Discuss.


Let W = wealth, rank the following utility functions in terms of the degree of risk aversion. Prove your answer. Does the answer depend on which measure of risk aversion you use?
() =+W,

UW 1

() =


UW() =ln(1 +W),

UW() =. .


Prove or disprove: An individual is risk averse if and only if he/she has diminishing marginal utility of income.


(30) [3, 3, 5, 5, 6, 5, 3]

Prove or disprove: A risk averse individual will never place any bet on Hong Kongs horse racing.

Consider a world with only two goods xand y. Consumers have the same utility function
1/3 2/3
(, )=x
Uxy y
and the same budget constraint
pxpy I 60 .
+ ==
The table below shows that the prices of x and y in the base year were $5 and $4, respectively. In the following year, the prices changed to $10 and $2, respectively.
px py I x * y * Utility
Base year $5 $4 $60 ? ? ?
Following year $10 $2
No adjustment $60 ? ? ?
CPI adjustment $? ? ? ?
True COLA $? ? ? ?

Copy the table to your answer book.
Fill in all the ? cells in the second row (Base year) and show your calculations.

If there is no adjustment to income, what will be the ? cells in the fourth row (No adjustment)? Explain.

To compensate the consumer for t