Carleton University ECON 1002A Assignment 1: Consumer Choice Analysis

This document provides a detailed solution to ECON 1002A Assignment 1, focusing on consumer choice theory and related economic concepts. The solution addresses two main problems: the first explores Bob's allocation of time between work and leisure, considering his budget constraint, utility maximization, and the impact of changes in wage and income. The second problem analyzes Jane's intertemporal consumption choices, examining her budget constraints, utility function, and optimal savings decisions across two periods, considering interest rates and income. Furthermore, the solution delves into principal-agent problems, using a Seinfeld clip to illustrate moral hazard and asymmetric information. Finally, it discusses adverse selection in the context of an "all you can eat" restaurant scenario, explaining how information asymmetry leads to adverse outcomes.

QUESTION 1
(a) Bob has 120 hours to allocate between working and leisure time. If Bob devotes L hours
of his time to leisure. He therefore take
(120-L) hours to work
Bob’s budget constraint. Every hour he works he earns a wage of W but he works for
(120-L)hours
And therefore the total amount he received is
$(120-L)W where W=5
$(120-L)5
He also get $10 from grandmother. So his total income
(120-L)5 +10
Again we realize that beer is $1 per unit. So his total expenditure on beer is
( (120-L)5+10)units and L is the leisure time
Which is Bob’s budget constraint.
(b) Bob is currently spending exactly half his time on leisure L=60
We know that utility is the total satisfaction received from consuming a good or service.
Hence he can raise his utility by increasing the number of hours he works. This is

because when he take many hours working his income also increases this is because its
income is directly proportional to the amount he spend on beer hence increase its utility.
On the other hand, if he decreases the number of hours his working this will ensure that
his income reduces and hence the amount that he will spend on beer consumption will be
low leading to decrease in utility.
(c) To solve for Bob’s optimal choice of hours worked, hours spent on leisure and beer
consumption. We have that Bob’s optimal choice of hours spent on leisure and beer
consumption satisfies
MRS= L/θC
=L/5C
where L is the leisure time and C is the consumption of beer and the value of θ is
determined by student number which is 5. Suppose we assume that he spend L hours on
leisure then he spend (120-L) hours working which implies that he spend (120-L)hours
consuming beer. Hence we have that
QP/QB =L/(120-L)
(d) Bob’s Grandmother now give him $100 instead of $10. Therefore his amount that he
spend on beer consumption would increase this is simply because his income has
increased. Furthermore, the number of hours he takes as leisure would also rise because
most of the time he will take consuming beer instead of working because of the increase
of income due to Grandmother’s addition of $100.

(e) Bob’s hourly wage rate increase by $1 will mean that the number of units of beer being
consumed would rise this is due to increase on the hourly wage. The number of hours he
take as leisure would reduce this is simply because he would like to work hence
spending many hours working due to increase on hourly wage. Moreover, his labour
supply would rise because he spend most of hours working due to hourly wage increase
and this make it possible for him to change his choices (Driscoll, 2003).
QUESTION 2
(a) Jane’s budget constraints in period one. The utility function U(c1,c2 )=ln(c1) + βln (c2)
Jane’s marginal utility from consumption in period one is given by
MUC1=∂U/∂C1=1/C1
And her marginal utility from consumption in period two is given by
MUC2=∂U/∂C2=β/C2
And so his marginal rate of substitution is
MRS=C2/C1β where β is determined by student
number and its value is 0.1
MRS=C2/0.1C1
Jane has an income of Y1=100,000 according to the student number. For every dollar that
Jane saves in period one she has (1+r) dollars available to spend in period two, where r is
the interest rate.
Y1=1C2
And her budget constraint in period two is
Y1 = 0.1(1+r)C1 where Y1=10000

10000=0.1(1+r)C1
(b) To combine these two budget constraints in order to have a single budget constraint that
relate C1 and C2 to Jane’s income and the interest rate
Y1=1C2+0.1(1+r)C1
10000=C2+0.1(1+r)C1
(c) If we assume that Jane is currently saving exactly 40% of her income in period one
40/100 *Y1=0.4Y1
=$4000
Every dollar that Jane save in period one she has (1+r) dollar available to spend in period two
0.4Y1(1+r)
4000(1+r)
She should increase her utility by increasing the amount she saves. This is because the more she
save in period one the more the interest rate leading to a larger amount in period two that can be
spent. On the other hand, decreasing the amount she saves lead to a decrease in her utility this is
because the interest rate would not yield to a larger amount in period two, hence less expenditure
leading to low utility (Kunst, 2006).
(d To solve for Jane’s optimal choice of saving, and how much to consume in periods one and
two. Jane’s budget constraint is given by
Y1=C2+(1+r)C1β
1000=C2+0.1(1+r)

Jane’s optimal choice of savings, and how much to consume in period one and two satisfies
MRS= 1/1+r
QUESTION 3
(a) In this principal-agent problem which is also referred to us the problem of moral hazard.
The principal according to this Seinfeld clip is the auto mechanic this is because
whenever the car get any damage the owner of the car who is the agent goes to the auto
mechanic. When we see that the auto mechanic can say any price of his or her choice. We
then see that the auto mechanic quotes a price of $2800 which the agent think as if it’s the
price of his car and therefore he tells the auto mechanic to stop repairing his vehicle as
he believes that he has his own auto mechanic who don’t screw him. As a result this
causes moral hazard problems (Asker, 2012).
(b) Asymmetric information occurs when one party has more or better information than the
other which creates an imbalance of power in transactions that can sometimes cause the
transactive to go awry. The source of the information asymmetry in this scene is seen
where the owner of the vehicle calls the auto mechanic so as to enquire the cost that the
auto mechanic may need. We realize that since the owner of the car has no or little
knowledge of cars, therefore this clip best describes this scenario. Moral hazard occurs
when a party insulated from risk behaves differently than it would behave if it were fully
exposed to the risk. We realize that the agent of the vehicle when he calls the way he
reacts shows that he does not take full consequences of his actions and therefore he has a
tendency to act less carefully, leaving another party to hold some responsibility for the
consequences of his actions. (Bhattacharya, 2001)

QUESTION 4
The concept of adverse selection predicts about the existence of “all you can eat” restaurant.
Adverse selection happens when there is insufficient symmetric information between a buyer and
a seller prior to a deal. Its majorly explains undesired outcome of a situation that is where one
party of a deal has a different information and more accurate than the second party. Mainly the
party at disadvantage is the one with inadequate information as compared to the party with
enough information. Now let assume there are two types of people in the population, those that
can eat and pay and the ones that can eat and don’t pay. It is obvious that you only eat if you can
pay cause this is someone’s business and therefore this person who can eat but can’t pay decides
to lie because he believes that is the only way which can allow him to ,hence this result in what
is called adverse selection(Myerson, 2012).

References
Asker, J. (2012). Action Principle-Agent. [online] Available at:
http://pages.stern.nyu.edu/~acollard/moral_hazard_2.pdf [Accessed 1 Feb. 2019].
Bhattacharya, J. (2001). [online] Available at:
http://web.stanford.edu/~jay/micro_class/lecture2.pdf [Accessed 1 Feb. 2019].
Driscoll, J. (2003). [online] Available at:
http://www.uh.edu/~bsorense/Macro_Lecture_Notes.pdf [Accessed 1 Feb. 2019].
Kunst, R. (2006). [online] Available at: https://homepage.univie.ac.at/robert.kunst/macro1.pdf
[Accessed 1 Feb. 2019].
Myerson, R. (2012). On Moral Hazard and Macroeconomics. [online] Available at:
http://home.uchicago.edu/~rmyerson/research/mhazmacro.pdf [Accessed 1 Feb. 2019].