Question 1
(a)
d ln(c)
1
1 d2 ln(c)
=− 2
= ,
2
dc
c
dc
c
⇒ −c
u00 (c)
= 1.
u0 (c)
1
1
+
= 0 ⇒ s∗ = 0.
∗
1−s
1 + s∗
√
1
1
1
1
6 1
∗
(c) FOC: −
+
+
=0 ⇒ s =
− .
∗
∗
∗
1−s
2 3/2 + s
1/2 + s
4
2
(b) FOC: −
Question 2
(a) µ (30, 000 − X) − 30, 000 + µ 100, 000 − 80, 000 = µ 30, 000 − 30, 000 + µ 80, 000 − 80, 000
1/2 1
1/2
⇒ − X
+
20, 000
=0
2
⇒ X = 5, 000.
(b) µ (30, 000 − X) − 30, 000 + µ 100, 000 − 100, 000
= µ 30, 000 − 30, 000 + µ 80, 000 − 100, 000
1/2
1/2
⇒ − X
= − 20, 000
⇒ X = 20, 000.
(c) They differ because of loss aversion – as implied by the derivative of µ(z)
for z < 0 being greater than the corresponding derivative for z > 1. A lossaverse individual who views the higher level of earnings as her reference
point is willing to pay more to secure it (i.e. to avert a perceived loss of
£20, 000) than an individual who views the lower level of earnings as her
reference point is willing to pay to secure it (i.e. to obtain a perceived gain
of £20, 000). This is a simple way of modelling the idea that education
choices are shaped by aspirations.