Behavioral Economics
Practice Degree Exam
Please answer ALL 4 questions.
1. Consider a set of lotteries which render wealth outcomes of £(−9),£0 and £16.
(a) Consider a decision maker who is an expected utility maximizer with utility
over certain money outcomes x given by v(x) =
√
x, and whose initial wealth
is £9. Using a Machina triangle, derive and draw the decision maker’s in-
difference curves and iso-expected value lines. Is this individual risk averse,
risk neutral, or risk loving? How can you tell?
(b) Suppose rather than caring about utility of final wealth, instead the decision
maker behaves according to prospect theory and cares only about how his
final wealth compares to his initial wealth, with v(x) =
√
(x − r) for x > r
and v(x) = −2
√
(r−x) for x < r. Suppose further his probability weighting
function is w(p) = 0.5 + 4(p− 0.5)3.
(i) Sketch how the indifference curves of this decision maker will look in the
Machina triangle. (You do not need to derive the curves, just a sketch
would suffice.) Explain how the Machina triangle can be used to identify
that an individual behaves according to the Prospect Theory.
(ii) Derive the equation of the indifference curve with EU = −1.
2. Suppose George cares about money c1 and trainers c2. George’s total utility is
U(c1, c2|r1, r2) = c1 + c2 + µ(c1 | r1) + µ(c2 | r2). For each dimension i = 1, 2,
µ(ci | ri) = 2(ci − ri) for ci > ri and µ(ci | ri) = −4(ri − ci) for ci ≤ ri. Suppose
George’s utility of trainers is c2 = 15 if he gets trainers, or c2 = 0 if he gets no
trainers. Assume that prices are deterministic.
(a) Show that there are two pure Personal Equilibria: one in which he will buy
trainers whenever the price p < 25 and the other in which he will not buy
trainers whenever the price p > 9. Derive his Preferred Personal Equilibrium.
(b) How does George’s behavior differ from that of a “neoclassical” consumer?
(c) Suppose that, in addition, within price range [9, 25], there is also a mixed
strategy Personal Equilibrium where, with probability q George expects to
buy at the current price p, and with probability 1− q George expects not to
buy. Show that this probability is q = 5
2
p−9
p+15
∈ [0, 1].
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3. Suppose an individual lives two periods t = 1, 2 discounts at a rate δ = 1 and has
instantaneous utility
U(ct,mt) = ln ct + λ(ln ct − lnmt)
where ct is consumption and mt is maximum possible consumption at time t.
Suppose further the individual has initial wealth w > 0 but no income in either
period. No interest is paid on any saving The parameter λ satisfies 1 > λ ≥ 0.
(a) Derive the optimal choice of consumption for this individual. How does it
depend on λ?
(b) Suppose that the individual can deposit a proportion k = w/4 of her initial
wealth into a locked savings account at time t = 0. It earns no interest and
cannot be withdrawn at t = 1 but it will be available at time t = 2. Will an
individual with λ > 0 want to invest in such an account?
(c) Interpret your results.
4. Suppose there are n individuals each of whom has utility
U(ci − c∗, xi) = ln(ci − c∗ + 1) + lnxi
where ci is conspicuous consumption of individual i, xi is her non-conspicuous
consumption or saving and c∗ is average conspicuous consumption, that is,
c∗ =
1
n
n∑
j=1
cj.
All individuals have income y and have a budget constraint y = ci(1 + t) + xi
where t is the tax rate on conspicuous consumption.
(a) Solve for the Nash equilibrium choice of conspicuous consumption and then
calculate equilibrium utility.
(b) If such a model were accurate, would it produce data consistent with the
supposed “Easterlin paradox”?
(c) Take tax t to be 0 for the moment. Suppose a social planner could dictate a
common consumption level of all individuals. If she wanted to maximise the
sum of all utilities (she is utilitarian), what c would she choose? How could
she implement this by choosing a tax rate t? Explain the intuition behind
your answer.
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