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(ECON198)[200X](f)final~3270^_10018.pdf
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Department of Economics, HKUST
ECON 198 Microeconomic Theory I
Note: This set of solutions serves only as guidelines for grading. Giving the same answers as suggested below is no guarantee of full credits. Detailed explanation is required.
Final Examination
Solutions

1. (a) Indifference curves are convex to the origin.
As more and more of one good is consumed, we can expect that a consumer will prefer to give up fewer and fewer units of a second good to get additional units of the first one.
(b) No, because Pokemon cards are not homogeneous. The 100th Pokemon card is different from the other 99 cards.
2. Agree.
For the ordinary (uncompensated) demand curve customarily used, utility changes along the curve. Therefore, the area under the ordinary demand curve does not really measure the total valuation. Only the compensated demand curve, which holds the utility constant, measures the total valuation.
U ''(W ) WU ''(W )
3. r(W ) =. rr(W ) =.
U '(W ) U '(W )
(a) r(W ) = 0 rr(W) = 0
1 W
(b) r(W ) = rr(W ) =
2(1 +W ) 2(1 +W )
1 W
(c) r(W ) = rr(W ) =
(1+W ) (1 +W ) 22W
(d) r(W ) = rr(W ) =
(1+W ) (1 +W )
Rankings according to r(W ):
r(W) in (d) > r(W) in (c) > r(W ) in (b) > r(W ) in (a)

Rankings according to rr(W ):
rr(W ) in (d) > rr(W) in (c) > rr(W) in (b) > rr(W ) in (a)
Hence, the answer does not depend on which measure of risk aversion we use.

4. <Proof>
Risk Averse U (EV ) > EU
11

U (w) > U (w + h) + U (w . h)
22 1 121 12
U (w) > [U (w) +U '(w)h + U ''(w)h ] + [U (w) .U '(w)h + U ''(w)h ]
2 22 2 12
U (w) > U (w) + U ''(w)h
2
U ''(w) < 0
Diminishing Marginal Utility

w-h w w+h
5. False.
A risk averse individual may place a bet on HKs horse racing if he/she thinks the expected value of the gamble is greater than zero and the expected utility of gambling is greater than the utility of not gambling.
i.e. U (w . p + a) + (1. )U (w . p) > U (w)
C subjective probability of winning of the individual
p C price of the gambling
a C prize of the gambling

6. (a) C (d)
px py I x* y* Utility
Base year \$5 \$4 \$60 4 10 7.37(=U0)
Following year \$10 \$2
No adjustment \$60 2 20 9.28(=U1)
CPI adjustment \$60(=I1) 2 20 9.28(=U2)
True COLA \$47.62(=I*) 1.59 15.87 7.37(=U3)

I1 is the amount of income with which the consumer can afford to buy the initial consumption bundle under the new prices.
I* is the amount of income with which the consumer can achieve the initial level of utility under the new prices.
12
. 1 I * .3 . 2 I * .3
. .. .= 7.37
. 3 10 .. 32 . . I* = \$47.62
(e) U1 = U2 > U0 = U3 y

1.59 2 4 6 12 x
I1
(f) = 1.26 Substitution bias = 26%
I *
(g) The consumer is over-subsidized.
7.
If the Chinese University paid for the editorial boards legal fees, it would set a dangerous precedent that the cost of the reckless behavior of students would be covered by the