EC202
UNIVERSITY OF WARWICK
Test 1 2013/14
Microeconomics 2
Time Allowed: 45 minutes
Answer both questions; the two questions carry equal weight.
When the time is up, please close your answer book and wait for it to be collected by an
invigilator. All answer books must be collected.
Approved hand calculators may be used.
1. A consumer lives for two periods and faces earnings uncertainty in the second period. Her
first period earnings are E1 = 1 with certainty; her second period earnings are E 2 with
probability 1/2 and they are E 2 < E 2 with probability 1/2, where (1/2) E 2 + (1/2) E 2 = 1
(i.e. second-period earnings are a random variable but they average to unity).
Assume that the rate of interest, r, is zero. If the consumer saves an amount s out of
her earnings in the first period, her first period consumption is c1 = E1 − s = 1 − s, her
second-period consumption when her earnings are high is c2 = E 2 + s, and her secondperiod consumption when her earnings are low is c2 = E 2 + s.
The consumer’s intertemporal preferences under uncertainty are represented by
EU (c1 , c2 , c2 ) = ln c1 + δ (1/2) ln c2 + (1/2) ln c2 .
Assume δ = 1 (i.e. the rate of time preference is zero).
(a) Derive the coefficient of relative risk aversion, −c u00 (c)/u0 (c) (where u(c) = ln c)
(10 points).
(b) How much will the consumer save in period 1 when E 2 = E 2 = 1?
(20 points)
(c) How much will the consumer save in period 1 when E 2 = 3/2 and E 2 = 1/2?
(20 points)
(Continued overleaf)
1
EC202
2. An individual’s intertemporal reference-dependent preferences over levels of consumption,
c1 and c2 , in periods 1 and 2 are represented by
U (c1 , c2 , r1 , r2 ) = µ(c1 − r1 ) + δ µ(c2 − r2 ),
√
√
where µ(0) = 0, µ(z) = (1/2) z for z > 0, and µ(z) = − −z for z < 0; and where
r1 > 0, r2 > 0 represent reference consumption levels. Assume δ = 1.
The individual has £30, 000 when young (period 1), which she views as her first-period
reference point, but she can use a certain amount £X of her period-1 endowment to enrol
in school in period 1 and increase her earnings when old (period 2). The individual only
works in period 2. There are no savings (no lending nor borrowing).
(a) Suppose that the individual aspires to earn £80, 000 when old (period 2) – and
therefore views £80, 000 as her period-2 reference level – but that getting an education
in period 1 raises her period-2 earnings from £80, 000 to £100, 000. What is the
maximum amount £X that the individual will be willing to spend in period 1 to get
an education? (18 points)
(b) Suppose that the individual aspires to earn £100, 000 when old (period 2) – and
therefore views £100, 000 as her period-2 reference level – but that not getting an
education in period 1 lowers her period-2 earnings from £100, 000 to £80, 000. What
is the maximum amount £X that the individual will be willing to spend in period 1
to get an education? (18 points)
(c) If your answers to (a) and (b) are the same, explain why. If your answers to (a) and
(b) are different, explain why. (14 points)
(End)
2