THE UNIVERSITY OF EDINBURGH

SCHOOL OF ECONOMICS

BEHAVIOURAL ECONOMICS

ECNM10066

Exam Date:

22 May

2023

Exam Diet:

May 2023

From and To:

13:00:00 - 15:00:00

Please read full instructions before commencing writing

Exam paper information

• Total number of pages: 4 (including this page).

• Please answerAll fourquestions.

• All questions have equal weight.

• You must provide explanations for all your answers and workings out.

Special instructions

• Attach your personalised barcode to EACH script book.

•

Complete questions 1 and 2 of Section A in one booklet, and questions 3 and 4

of Section B in the other booklet (i.e., you should use a total of two booklets),

with the personalized barcode attached, and your personal information filled

in completely and correctly

•You must start EACH QUESTION on a separate page. Questions must be

clearly numbered in the left margin.

•You must complete the exam within the time specified at the top of this page.

•Your exam number (e.g., B123456) must be clearly written at the top of each

page.

• Your answers must be clearly written.

• Answers may be subject to checks through TurnItIn.

• This examination will be marked anonymously.

• Students are allowed to keep the question sheet.

Special items

• Non-programmable calculators are permitted in this exam.

Examiners: Tim Worrall (Chair), Giacomo De Luca (External).

Page1of4(continued on next page)

Answer ALL 4 questions.

Section A

1.

Consider a set of lotteries with possible final wealth values of£0,£16, and£25.

Let lottery A pays £16 for sure; and lottery D pays £0 with 80% chance and £25

with 20% chance. Suppose there exist further two lotteries B and C such that

lottery C involves zero chance of getting £25, and the four lotteries A, B, C, and D

can be used to document the common consequence effect.

(a)

Consider a decision-maker who is a neoclassical utility maximizer with a

Bernoulli utility function given byv(x) =

√

x. Assuming that this decision

maker is indifferent between lotteries C and D, derive the two lotteries B and

C formally. (Hint: sketch the four lotteries A, B, C, and D in the Machina

triangle.)

(b)

Suppose,instead, this decision maker behaves according to the Prospect

Theory and cares about how his final wealth compares to his reference wealth

of £25, withv(x) =

√

x−rforx>randv(x) =−2

√

r−xforx

further his probability weighting function is

w(P) =0.5+3(P−0.5)

3

. Derive

the equation of his indifference curve which goes through the lottery D.

Sketch informally this indifference curve in the Machina triangle.

(c)

Consider the decision maker in part (b). Derive an additional lottery E

which involves zero chance of getting £25, such that this decision maker is

indifferent between lottery D and this lottery E. If given a choice between

lotteries C and E, which lottery would this decision maker choose? Use the

sketch you made for part (b) and explain your reasoning.

2. Suppose Valerie cares about moneyc

1

and a bicyclec

2

. Her total utility is

U(c

1

,c

2

|r

1

,r

2

) =c

1

+c

2

+μ(c

1

|r

1

)+μ(c

2

|r

2

).

For each dimensioni=1,2,μ(c

i

|r

i

) =3(c

i

−r

i

)forc

i

>r

i

andμ(c

i

|r

i

) =−7(r

i

−

c

i

)

forc

i

≤r

i

. Supposec

2

=0when Valerie gets no bicycle. Assume that the price

of the bicyclepis deterministic.

Page2of4(continued on next page)

(a)Suppose there exists a “pure” Personal Equilibrium where Valerie does not

buy the bicycle if and only ifp≥200. Solve for this Personal Equilibrium.

Derive her Preferred Personal Equilibrium.

(b)Compare and contrast Valerie’s behavior to that of a “neoclassical” consumer.

(c)Suppose that Valerie expects to throw a fair 24-sided dice. If the dice lands on

a number divisible by 3, she will be in the “buying” state of mind, otherwise

she will be in the “not buying” state of mind. What should the pricepbe at

which using such a randomization device would be Valerie’s mixed Personal

Equilibrium? Show your derivations. Interpret this “mixed” Personal Equi-

librium. Explain how the probability of buyingqin the “mixed” Personal

Equilibrium is affected by the pricep.

Section B

3.

Consider an individual who lives three periods t = 0, 1, 2, hasβ δpreferences with

δ=

3

4

and0<β≤1. Suppose further she has instantaneous utilityU(c

t

) =lnc

t

,

wherec

t

is consumption at timet. Her consumptionc

0

is fixed and gifted to her by

her guardians. The individual has no income in period 1, but has an income of 1 in

period 2. To fund her period 1 consumption, she can borrow a maximum ofkin

period 1 against her future period 2 income at a zero interest rate.

(a)Suppose first thatk=1. Derive the optimal choices of consumption in periods

1 and 2 for this individual as chosen at the beginning of period 1. How, if at

all, does it depend onβ?

(b) Suppose the individual is fully sophisticated withβ=

4

5

, and she is allowed

to choose how muchkto borrow at timet=0. Specifically, she can choose

one of two credit limits, either

4

7

or

5

8

. Which is better for her, given she is

choosing the credit limit att=0? How, if at all, does it depend onβ?

(c)Suppose the bank makes an error and, instead, gives her the other credit limit,

the one she did not ask for. Does this change her behaviour? Does this change

her welfare (from thet=0perspective of a rational long run agent, i.e., of a

patient time consistent agent), and if so, how? Explain your answer and show

your derivations.

Page3of4(continued on next page)

4. Suppose there arenindividuals, with each individualihaving a utility

U(s

i

,x

i

) =

√

s

i

+1

√

x

i

wherex

i

is non-conspicuous consumption, ands

i

is social status defined as

s

i

=c

i

−c

∗

, wherec

i

is conspicuous consumption andc

∗

is average conspicu-

ous consumption, i.e.,

c

∗

=

1

n

n

∑

j=1

c

j

.

All individuals have incomeyand have a budget constrainty=c

i

+x

i

(1−ψ)

whereψis the subsidy rate on non-conspicuous consumption.

(a)

Solve for the Nash equilibrium choice of conspicuous consumption and

calculate equilibrium utility. Discuss the welfare implications of such subsidy.

Is there any subsidy rateψwhich would achieve the efficient (or socially

optimal) level of conspicuous consumption (i.e., the level of conspicuous

consumption which individuals would have chosen if they could not affect

their social status)?

(b)If such a model were accurate, would it produce data consistent with the

supposed “Easterlin paradox”? Explain your reasoning.

(c)

Compare the results you derived in part (a) to the case when,instead, con-

spicuous consumption were taxed, so that all individual would face a budget

constrainty=c

i

(1+t)+x

i

. Compare and contrast the effects of a subsidy

rateψon non-conspicuous consumption as in part (a) and a tax rateton

conspicuous consumption here, and their potential to achieve the socially

efficient level of conspicuous consumption.

—— End of Examination Paper ——

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